ALBERT

Description: In this paper, we present an algorithm for partitioning any given 2D domain into regions suitable for quadrilateral meshing. It is able to preserve the symmetry of the domain if any, and can deal with inner boundaries and multidomain geometries. Moreover, this method keeps the number of singularities at the junctions of the regions to a minimum. Although each part of the domain, being four-sided, can be easily meshed using a structured method, we provide a meshing process that guarantees near perfect quality for most quadrilaterals of the resulting mesh. The partitioning stage is achieved by solving a PDE-constrained equation based on the geometric properties of the domain boundaries. An analysis of the generated mesh quality is provided at the end, showcasing that the meshes obtained through our algorithm are especially suitable for finite element methods.

Description: This paper introduces a methodology for creating geometrically consistent subsurface simulation models, and subsequently tetrahedral finite element (FE) meshes, from geometric entities generated in gOcad software. Subsurface simulation models have an intrinsic heterogeneous characteristic due to the different geomechanics properties of each geological layer. This type of modeling should represent geometry of natural objects, such as geological horizons and faults, which have faceted representations. In addition, in subsurface simulation modeling, lower-dimension degenerated parts, such as dangling surfaces, should be represented. These requirements pose complex modeling problems, which, in general, are not treated by a generic geometric modeler. Therefore, this paper describes four important modeling capabilities that are implemented in a subsurface simulation modeler: surface re-triangulation, surface intersection, automatic volume recognition, and tetrahedral mesh generation. Surface re-triangulation is used for regenerating the underlying geometric support of surfaces imported from gOcad and of surface patches resulting from intersection. The same re-triangulation algorithm is used for generating FE surface meshes. The proposed modeling methodology combines, with some adaptation, meshing algorithms previously published by the authors. Two novel techniques are presented, the first for surface intersection and the second for automatic volume recognition. The main contribution of the present work is the integration of such techniques through a methodology for the solution of mesh generation problems in subsurface simulation modeling. An example illustrates the capabilities of the proposed methodology. Shape quality of generated triangular surface and tetrahedral meshes, as well as the efficiency of the 3D mesh generator, is demonstrated by means of this example.

Description: An automated approach to quadrilateral mesh generation with complex internal geometric feature constraints is presented in this paper. It can deal with all kinds of feature constraints such as internal holes, constraint lines, constraint points, density lines and density points, etc., and satisfy special requirements of mesh generation for numerical analysis. The quadrilateral mesh is generated based on the looping algorithm. As the core of the algorithm, the new splitting criteria are put forward to improve the quality and efficiency of mesh generation. The method of dealing with feature constraints is proposed by considering constraint lines and points, density lines and density points as internal holes with zero area. The method for generating boundary elements is also introduced to improve the element quality around the boundary and feature constraints. For the situation in which feature constraints subdivide the domain into sub-domains, an automatic determination method of sub-domain boundaries is presented. An improved looping algorithm is presented for 3D surface meshing with feature constraints. The determination of proper splitting plane and the handling of feature constraints are put forward. The program of quadrilateral mesh generation has been developed based on the method presented in this paper and successfully applied to mesh generation in several engineering fields.

Description: This paper aims to introduce a unified code for fluid flow modeling in complex channels reconstructed from imagery. Given a binary image of a cross-section or projection of planar connected channels with circular cross-sections, we wish to: (1) reconstruct a three-dimensional model of the boundary of the geometry, (2) establish boundary condition of the flow field, and (3) compute a fluid simulation based on a Cartesian grid. Our solution has the following advantages. First, we use the same mathematical tools throughout the process i.e. a level set function and a skeleton to describe the geometry. The skeleton of the geometry is essential in the imagery part to transform the 2D geometry into a 3D geometry but is also essential in the fluid flow part to construct a velocity field of reference for boundary conditions in the mechanical fluid flow model. Then, the integration of the geometry into the fluid mechanic code is simplified thanks to a Cartesian grid taking into account the geometry through the level set function. Finally, this work leads to a stand-alone code capable of simulating 3D flows in geometry reconstructed 2D images. We show its usefulness in applications to medical imagery (namely angiography) and bifluid flows in microchannels.

Description: This paper presents simulation methodology that combines a local nonmatching grid with a discrete fracture model. Designed for 2D and 3D multiphase flow simulations in standard simulators, the method handles matrix–matrix, fracture–fracture, and matrix–fracture connections in the context of an unstructured, local nonmatching grid. The grid is generated at the fracture intersections, enabling accurate modeling of small control volumes between connecting fractures. Grids are obtained simply by redistributing the volume of small control volumes surrounding the small control volumes, making the method computationally efficient. A unified method to calculate the interblock transmissibility is used for both matching and nonmatching mesh. An unstructured finite-volume graph-based reservoir simulator with a two-point flux approximation reads the new grid by making a simple modification to the graph of connections between the control volumes. The method requires no special treatment of fracture–fracture or matrix–fracture transmissibility calculations and has the flexibility to simulate any flow problem efficiently. Several 2D and 3D numerical examples demonstrate the method’s performance and accuracy. Both simple and complex fracture configurations are presented with various levels of geologic and fluid complexity. The numerical results are in good agreement with those of a reference solution obtained on a finely structured grid.

Description: Remeshing is an important problem in variety of applications, such as finite element methods and geometry processing. Surface remeshing poses some unique challenges, as it must deliver not only good mesh quality but also good geometric accuracy. For applications such as finite elements with high-order elements (quadratic or cubic elements), the geometry must be preserved to high-order (third-order or higher) accuracy, since low-order accuracy may undermine the convergence of numerical computations. The problem is particularly challenging if the CAD model is not available for the underlying geometry, and is even more so if the surface meshes contain some inverted elements. We describe remeshing strategies that can simultaneously produce high-quality triangular meshes, untangling mildly folded triangles and preserve the geometry to high-order of accuracy. Our approach extends our earlier works on high-order surface reconstruction and mesh optimization by enhancing its robustness with a geometric limiter for under-resolved geometries. We also integrate high-order surface reconstruction with surface mesh adaptation techniques, which alter the number of triangles and nodes. We demonstrate the utilization of our method to meshes for high-order finite elements, biomedical image-based surface meshes, and complex interface meshes in fluid simulations.

Description: This paper presents an anisotropic adaptive strategy for CFD that combines a nearly body-fitted mesh strategy with an iterative anisotropic adaptation to the flow solution. The nearly body-fitted mesh method consists in modelling embedded interfaces by a level-set representation in combination with local anisotropic mesh refinement and mesh adaptation (Quan et al. in Comput Methods Appl Mech Eng 268:65–81, 2014 ). The generated nearly body-fitted meshes are used to perform CFD simulations. Besides, anisotropic mesh adaptation based on the Hessian of the flow solution is used to improve the accuracy of the solution. We show that the method is beneficial in challenging CFD simulations involving complex geometries and time dependent flow, as it suppresses the need for the tedious process of body-fitted mesh generation, without altering the finite element formulation nor the prescription of boundary conditions. The methodology yields accurate flow solutions for a reasonable computational cost, despite very limited user interaction.

Description: In this paper, two PDE-based mapping operators for the generation of unstructured meshes are compared. While the Winslow operator allows the construction of valid meshes for most configurations, the functional-based operators based on area, length, orthogonality and their combinations provide a finer control on the resulting meshes. Two distinct discretization methods of the operators are also compared. An original approach using a finite difference scheme on unstructured meshes is implemented and compared to a finite volume formulation. While more complex to implement and control, mainly because of the cross-derivative terms which must be carefully discretized, the finite volume method yields a more robust and stable formulation that allows dealing with sharp curvature variations of the boundaries. Finally, a criterion for the mesh smoothness which has a global definition is presented in order to compare the smoothness of the resulting mesh obtained by different operators.

Description: Development and application of metal matrix composite materials and increased application of calculations, simulations and modeling in the area of semi-solid solidification ask for the knowledge of compocasting for these materials. In this study, a self-organizing hierarchical particle swarm optimizer is implemented for computational modeling and optimization of the compocast high strength and highly uniform Al matrix composites. The matrix of the composite was a 6061 Al alloy and the reinforcement was alumina particle (Al 2 O 3 p). Experimental results were obtained for hardness, tensile and fatigue properties of the Al alloys with different vol.% of micro-particles. The tensile strength of the composites increased considerably by increasing the reduction ratio in the cold rolling process. It is observed that the presence of reinforcement in the Al alloy degrades the low-cycle fatigue property when the Al matrix composites are subject to strain-controlled cyclic loading. The method combines position update rules, the standard velocity and the strengths of particle swarm optimization with the ideas of selection, crossover and mutation from GA.

Description: In this paper, we present formulae for evaluating differential quantities at vertices of triangular meshes that may approximate potential piecewise smooth surfaces with discontinuous normals or discontinuous curvatures at the joint lines. We also define the C 1 and C 2 discontinuity measures for surface meshes using changing rates of one-sided curvatures or changing rates of curvatures across mesh edges. The curvatures are computed discretely as of local interpolating surfaces that lie within a tolerance to the mesh. Together with proper estimation of local shape parameters, the obtained discontinuity measures own properties like sensitivity to salient joint lines and being scale invariant. A simple algorithm is finally developed for detection of C 1 or C 2 discontinuity joint lines on triangular meshes with even highly non-uniform triangulations. Several examples are provided to demonstrate the effectiveness of the proposed method.

Description: We propose simple and efficient optimization-based untangling strategies for 2D polygonal and 3D polyhedral meshes. The first approach uses a size-based mesh metric, which eliminates inverted elements by averaging element size over the entire mesh. The second method uses a hybrid quality metric, which untangles inverted elements by simultaneously averaging element size and improving element shape. The last method using a variant of the hybrid quality metric gives a high penalty for inverted elements and employs an adaptive sigmoid function for handling various mesh sizes. Numerical experiments are presented to show the effectiveness of the proposed untangling strategies for various 2D polygonal and 3D polyhedral meshes.

Description: In this paper, we present a Delaunay refinement algorithm for 4-dimensional ( \(\hbox {3D}+t\) ) segmented images. The output mesh is proved to consist of sliver-free simplices. Assuming that the hyper-surface is a closed smooth manifold, we also guarantee faithful geometric and topological approximation. We implement and demonstrate the effectiveness of our method on publicly available segmented cardiac images. Finally, we devise a tightly coupled parallelization technique to boost the performance of our 4-dimensional mesher, thereby taking advantage of the multi-core and many-core platforms already available in the market.

Description: Shape idealization transformations are very common operations when adapting a CAD component to FEA requirements. Here, an idealization approach is proposed that is based on generative shape processes used to decompose an initial B-Rep solid, i.e., extrusion processes with material addition are used to segment a solid. The corresponding extrusion primitives form the basis of candidate sub-domains for idealization and their connections conveyed through the generative processes they belong to, bringing robustness to set up the appropriate connections between idealized sub-domains. This is made possible because the connections between extrusion primitives have an explicit geometric representation and can be used to bound the connections between idealized sub-domains. Taking advantage of an existing construction tree as available in a CAD software does not help much because it may be complicated to use it for idealization processes because this tree structure is not unique. Using generative processes attached to an object that is no longer reduced to a single construction tree but to a graph containing all non-trivial construction trees, is more useful for the engineer to evaluate variants of idealization. From this automated decomposition, each primitive is subjected to a morphological analysis to define whether it can idealized or not. Subsequently, geometric interfaces between primitives form also a graph that can be used to process the connections between the idealized sub-domains generated from the primitives. These interfaces are taken into account to determine more precisely the idealizable sub-domains and their contours when primitives are incrementally merged to come back to produce the global morphological analysis of the initial object. A user-defined threshold is used to tune the morphological analysis with respect to further user parameters. Finally, the idealizable sub-domains and their connections are processed to locate the mid-surfaces and connect them using generic criteria that the user can tune locally using complementary criteria.

Description: Automotive companies continuously strive to design better products faster and more cheaply using simulation models to evaluate every possible aspect of the product. Multidisciplinary design optimization (MDO) can be used to find the best possible design taking into account several disciplines simultaneously, but it is not yet fully integrated within automotive product development. The challenge is to find methods that fit company organizations and that can be effectively integrated into the product development process. Based on the characteristics of typical automotive structural MDO problems, a metamodel-based MDO process intended for large-scale applications with computationally expensive simulation models is presented and demonstrated in an example. The process is flexible and can easily fit into existing organizations and product development processes where different groups work in parallel. The method is proven to be efficient for the discussed example and improved designs can also be obtained for more complex industrial cases with comparable characteristics.

Description: A new indirect quadrangular mesh generation algorithm which relies on sequential decision-making techniques to search for optimal triangle recombinations is presented. In contrast to the state-of-art Blossom-quad algorithm, this new algorithm is a good candidate for addressing the 3D problem of recombining tetrahedra into hexahedra.

Description: Haptic feedback usually involves two types of stimulation forces: forces that address the touch sense and forces that address the kinesthetic perception. Touch forces have a low intensity and a complex structure since they reflect contact phenomena where friction plays an important role. Therefore, they are quite difficult to simulate. Virtual prototyping with haptic feedback should ideally involve both types of forces, but the integration of the touch feeling makes the simulator very complex. In this paper, we present a novel concept for virtual prototyping in which the touch interaction is separated from the kinesthetic force feedback. This is possible using a prototype that has a real part undertaking the touch interaction and a virtual part that simulate feedback for the kinesthetic forces. In this way, a full haptic interaction with the virtual prototype is established by means of a device that provides a realistic simulation of the product. In order to illustrate the concept, several experiments have been carried out for the case of specific subsystems of a car, which are particularly involved in the driver–car interaction: steering system, clutch pedal and the gearshift. A user test is described in the last part as well as the conclusions of the research.

Description: A new closed advancing-layer method for generating high-aspect-ratio elements in the boundary-layer (BL) region is presented. This approach utilizes a recent connectivity optimization-based moving mesh strategy for deforming the volume mesh as the BL is inflated. It handles very efficiently BL front collision and produces a natural smooth anisotropic blending between colliding layers. Moreover, it provides a robust strategy to couple unstructured anisotropic mesh adaptation and high-aspect-ratio elements pseudo-structured BL meshes. The proposed method is directly compared to a well-established open advancing-layer method. Results for typical aerospace configurations are presented that provide a clear comparison between both methods as well as the effectiveness of the connectivity optimization-based moving mesh strategy. They show that the closed method yields similar results in terms of mesh quality and efficiency, and that the considered moving mesh strategy is an efficient and effective method for deforming the unstructured volume mesh.

Description: An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high efficiency of the Levenberg–Marquardt algorithm for medium-sized problems and has the additional advantage of being relatively simple to implement. It is also applicable to both autonomous and non-autonomous systems. As an example of its use, it is employed to find periodic orbits in the Rössler system, a coupled Rössler system, as well as an eight-dimensional model of a flexible rotor-bearing; problems which have been treated previously via two related methods. The results agree with the previous methods and are seen to be more accurate in some cases. A simple implementation of the method, written in the Python programming language, is provided as an Appendix.

Description: The structural health evaluation is performed by comparing the responses between the undamaged and damaged states. Because it is impractical to collect the response data at the intact state, it is important to establish the baseline data to be compared at measurement. The measured frequency response functions (FRFs) in the neighborhood of the first resonance frequency are transformed to the proper orthogonal mode (POM) corresponding to the first proper orthogonal value (POV). The POM data set at the first measurement on the damage-expected structure is taken as the baseline datum, and it is compared with another set extracted from the structure to attach a small mass on an element. The POM difference between two states is utilized as an index to detect damage. The FRF variation before and after a small mass attachment for the purpose of detecting the damage is investigated. The validity of the proposed method based on POM variation is illustrated in the damage detection of a two-dimensional frame structure model. It is shown that the damage region in the frame structure can be inferred by gradually narrowing from the global structure to the damage-expected element.

Description: The aim of this paper is to achieve the 3D reconstruction of blood vessels from a limited number of 2D transversal cuts obtained from scanners. This is motivated by the fact that data can be missing. The difficulty of this work is in connecting the blood vessels between some widely spaced cuts to produce the graph corresponding to the network of vessels. We identify the vessels on each transversal cut as a mass to be transported along a graph which allows to determine the bifurcation points of vessels. Specifically, we are interested in branching transportation Brasco et al. (SIAM J Math Anal 43(2):1023–1040, 2011 ) to model an optimized graph associated with the network of vessels. At this stage, we are able to reconstruct a 3D level set function by using the 2D level set functions given by the transversal cuts and the graph information. When the whole scanner data are available, a global reconstruction is proposed in a simple manner, without using the mass transfer problem.

Description: A novel second-order time integration algorithm for solving dynamic problems is presented. To demonstrate the abilities of this formulation, several linear and geometrical nonlinear structures are solved. The outcomes of authors’ technique are compared with the ones obtained by other researchers. The findings not only confirm the improved accuracy of the new scheme but also indicate that the suggested method remains stable when the trapezoidal rule fails to produce a stable solution. Effectively maximizing high-frequency numerical dissipation, without inducing excessive algorithmic damping in the important low-frequency region, is one of the proposed tactic merits. Spurious oscillations are removed, and small numerical dispersion error is achieved, when using this approach.

Description: This paper proposes a new iso-parametric tool path generation scheme for trimmed parametric surface based on two discrete parameterization techniques, namely, the Partial Differential Equation method and the newly developed “Boundary Interpolation method”. The efficiency of the scheme is measured in terms of path length and computational time for machining some typical surfaces. The side-steps and forward-steps have been formulated to suit the discrete nature of the surface representation. Conventionally the forward-step is calculated by approximating the cutting curve with osculating circle. Due to this approximation there is a possibility that the tolerance can go beyond given limit. In this paper an improved tolerance constraint method has been presented to keep the tolerance in forward-step under given value by considering the true profile of the cutting curve. Case studies show that the method presented here significantly improves the path profile by maintaining the tolerance limit.

Description: Load balancing is an important aspect of Grid resource scheduling. This paper attempts to address the issue of load balancing in a Grid, while maintaining the resource utilization and response time for dynamic and decentralized Grid environment. Here, to its optimum value, a hierarchical load balancing technique has been analysed based on variable threshold value. The load is divided into different categories, such as lightly loaded, under-lightly loaded, overloaded, and normally loaded. A threshold value, which can be found out using load deviation, is responsible for transferring the task and flow of workload information. In order to improve response time and to increase throughput of the Grid, a random policy has been introduced to reduce the resource allocation capacity. The proposed model has been rigorously examined over the GridSim simulator using various parameters, such as response time, resource allocation efficiency, etc. Experimental results prove the superiority of the proposed technique over existing techniques, such as without load balancing, load balancing in enhanced GridSim.

Description: An inverse analysis methodology for determining the parameters of the kinematic law of sheet metals is proposed. The sensitivity of the load versus displacement curves, obtained by reverse shear tests of rectangular and notched specimens, to the kinematic law parameters are studied following a forward analysis, based on finite element simulations. Afterwards, an inverse analysis methodology using a gradient-based Levenberg–Marquardt method is established, by evaluating the relative difference between numerical and experimental results of the shear test, i.e. the load evolution in function of the displacements of the grips. The use of a notched specimen is proposed in order to allow an easy and suitable numerical representation of the boundary conditions of the shear experimental test. This methodology has proven to be appropriate for determining the parameters of the kinematic hardening law.

Description: In this paper, we have investigated the role of dependencies in the design process of mechatronic products. Since explicit modeling of dependencies is largely considered unnecessary today, current languages do not support dependency modeling due to lack of sufficiently expressive language constructs. However, this paper argues that modeling dependencies is important in managing the overall design process. The paper highlights dependencies between two important viewpoints: system design and mechanical design. We have looked closely at how mechanical design (supported by CAD tools) establishes a backbone for the overall design concept. Mechanical design cannot be isolated from other design activities, and the mismanagement of dependencies there leads to problems in other domains too. To illustrate the process, the paper presents an example of modeling dependencies between system hierarchy in OMG SysML™ and the CAD assembly in Solid Edge for a mechatronic design example. The paper presents two different approaches to capturing dependencies—using a general purpose modeling language such as SysML and using a domain specific modeling language (DSML). We argue for using a DSML instead of a general purpose language and provide a DSML called the dependency modeling language (DML). An example DML model for a two degree of freedom robot use case is discussed. The paper also illustrates the complete process of capturing dependencies in a general purpose modeling language like SysML, which served as a good exercise on how to fetch data from a CAD tool and how to represent dependencies inside a significantly different modeling language. Lessons learned from doing this were applied to the construction of DML. Our aim for the future is to reduce the human effort required to build dependency models. Machine learning techniques and automated model transformations are valuable techniques to support this cause.

Description: In this research, influences of two factors in adaptive metamodeling, noise level of samples and initial size of samples, are investigated through comparative study. Two cases of adaptive metamodeling considering the best output point for optimization and the best fit in a specific output parameter space are considered. Three different metamodels, kriging, radial basis function, and multivariate polynomial, are employed in this study. Various test functions are used to create the sample data and evaluate the quality and efficiency of the adaptive metamodeling methods considering influences of noise and initial size of samples. The results of this research provide guidelines for selecting appropriate adaptive metamodeling methods to solve various engineering problems. Effectiveness of the developed guidelines has been demonstrated through case study applications.

Description: In geometric modeling, surface parameterization plays an important role for converting triangle meshes to spline surfaces. Parameterization will introduce distortions. Conventional parameterization methods emphasize on angle-preservation, which may induce huge area distortions and cause large spline fitting errors and trigger numerical instabilities.To overcome this difficulty, this work proposes a novel area-preserving parameterization method, which is based on an optimal mass transport theory and convex geometry. Optimal mass transport mapping is measure-preserving and minimizes the transportation cost. According to Brenier’s theorem, for quadratic distance transportation costs, the optimal mass transport map is the gradient of a convex function. The graph of the convex function is a convex polyhedron with prescribed normal and areas. The existence and the uniqueness of such a polyhedron have been proved by the Minkowski-Alexandrov theorem in convex geometry. This work gives an explicit method to construct such a polyhedron based on the variational principle, and formulates the solution to the optimal transport map as the unique optimum of a convex energy. In practice, the energy optimization can be carried out using Newton’s method, and each iteration constructs a power Voronoi diagram dynamically. We tested the proposal algorithms on 3D surfaces scanned from real life. Experimental results demonstrate the efficiency and efficacy of the proposed variational approach for the optimal transport map.

Description: This paper presents specific procedures for locally refining nodal connectivity of two-dimensional unstructured triangular meshes to improve the quality of the mesh as well as to increase solution accuracy and computational speed. Details of the procedure are outlined along with a discussion of similar work, and an example problem from hydrodynamics is shown.

Description: In recent days, due to the rapid technological advancements, the grid computing has become an important area of research in distributed systems. The load balancing is a very important and complex problem in grid computing. In this paper, we propose a dynamic-distributed load-balancing technique called the improved load balancing on enhanced GridSim with deadline control (IEGDC) for computational grids. Here, we provide a new mechanism of scheduling to enhance the utilization of the resources and to prevent the resource overloading. A selection method for scheduling by considering the state of resource bandwidth and capacity of various resources is presented. We simulate the proposed load-balancing strategy on the GridSim platform. The proposed mechanism on comparison is found to outperform the existing schemes in terms of response time, resubmitted time, finished and unfinished Gridlets. The simulation results are presented.

Description: This article addresses the problem of NURBS surface deformation design using surface feature transplantation. To represent the semantic surface feature, a new surface feature representation called normal feature membrane is proposed. In the proposed method, the base surfaces of the source surface with the feature that the designer is highly interested in and the target surface to be deformed are first constructed. This is followed by extracting the normal feature membrane of the source surface. The deformation design is then realized by transplanting the extracted normal feature membrane of the source surface to the base surface of the target surface through four main operations, which are normal feature membrane preprocessing, normal feature membrane transplanting, surface fairing, and boundary feature decaying, respectively. The proposed method provides an easy copy–paste operation of the semantic surface feature for surface deformation of complex product. The examples of the surface feature transplantation for the surface design of automobile bodies are given to verify the validity and feasibility of the proposed method.

Description: Backbreak is one of the undesirable effects of blasting operations causing instability in mine walls, falling down the machinery, improper fragmentation and reduction in efficiency of drilling. Backbreak can be affected by various parameters such as the rock mass properties, blasting geometry and explosive properties. In this study, the application of the artificial neural network (ANN), an adaptive neuro-fuzzy inference system (ANFIS) for prediction of backbreak, was described and compared with the traditional statistical model of multiple regression. The performance of these models was assessed through the root mean square error, correlation coefficient ( R 2 ) and mean absolute percentage error. As a result, it was found that the constructed ANFIS exhibited a higher performance than the ANN and multiple regression for backbreak prediction.

Description: We present a parametric model for generating unit cells with randomly distributed inclusions. The proposed algorithm possesses (1) robustness by yielding unit cells with fiber volume fraction of up to 45 % for aspect ratios as high as 20, (2) computationally efficiency accomplished through a hierarchy of algorithms with increasing computational complexity, and (3) versatility by generating unit cells with different inclusion shapes. A statistical study aimed at determining the effective size of the unit cell is conducted. The method has been applied to various random inclusion microstructure composites, including: (1) two-dimensional chopped tow composites employed in automotive applications, (2) polyurea or polyethene coating consisting of hard and soft domains (segments) employed for energy absorption in military and industrial applications, and (3) fiber framework called fiberform embedded in or free from an amorphous matrix used as heat shield on space crafts to prevent structural damage during reentry into the atmosphere.

Description: Integrating analysis and design models is a complex task due to differences between the models and the architectures of the toolsets used to create them. This complexity is increased with the use of many different tools for specific tasks during an analysis process. In this work various design and analysis models are linked throughout the design lifecycle, allowing them to be moved between packages in a way not currently available. Three technologies named Cellular Modeling, Virtual Topology and Equivalencing are combined to demonstrate how different finite element meshes generated on abstract analysis geometries can be linked to their original geometry. Cellular models allow interfaces between adjacent cells to be extracted and exploited to transfer analysis attributes such as mesh associativity or boundary conditions between equivalent model representations. Virtual Topology descriptions used for geometry clean-up operations are explicitly stored so they can be reused by downstream applications. Establishing the equivalence relationships between models enables analysts to utilize multiple packages for specialist tasks without worrying about compatibility issues or substantial rework.

Description: Grid-based methods for generating all-hex meshes show tremendous promise in automating and speeding up turnaround for computational simulations for solid mechanics. Recognizing some of the inherent weaknesses of grid-based methods, there has been hesitancy in accepting this technology as a viable option for critical FEA. The authors extend previous work on a grid-based method known as sculpt, and evaluate its effectiveness in practice. This study attempts to compare meshes generated with traditional manual pave-and-sweep technologies with those generated with sculpt’s automatic overlay grid method. We use a simple torsion pin analysis to understand both linear-elastic and non-linear elastic–plastic responses with grid-based meshes. We also introduce improvements to the sculpt grid-based procedure, including adaptive optimization-based smoothing, hex-dominant and pillowing to capture curve features as proposed techniques for improving mesh quality. This study demonstrates that in the cases tested, equivalent or superior results were achieved with grid-based meshes when compared to pave-and-sweep meshes.

Description: The modern engineering design process often relies on numerical analysis codes to evaluate candidate designs, a setup which formulates an optimization problem which involves a computationally expensive black-box function. Such problems are often solved using a algorithm in which a metamodel approximates the true objective function and provides predicted objective values at a lower computational cost. The metamodel is trained using an initial sample of vectors, and this implies that the procedure by which the initial sample is generated can impact the overall effectiveness of the optimization search. Approaches for generating the initial sample include the statistically based design of experiments, and the more recent search-driven sampling which generates the sample vectors with a direct-search optimizer. This study compares these two approaches in terms of their overall impact on the optimization search and formulates guidelines in which scenario is each approach preferable. An extensive analysis shows that: (a) the main factor affecting search-driven sampling is the size of the initial sample, and such methods performed better in large initial samples, (b) design of experiments methods tended to perform better in lower sample sizes, (c) generating a sample which is space-filling improved the overall search effectiveness

Description: The sweeping algorithm is one of the most robust techniques to generate hexahedral meshes. During one-to-one sweeping, the most difficult thing is to map an all-quad source surface mesh onto its target surface. In this paper, a harmonic function is used to map meshes from a source surface to its target surface. The result shows that it can generate an all-quad mesh on the target surface with good mesh quality for the convex, concave or multiply-connected surface and thus avoid expensive smoothing algorithm (untangling). Meanwhile, the cage-based deformation method is used to locate interior nodes between the source and target surface during sweeping. Finally, examples are provided and the execution time for our proposed algorithm is discussed.

Description: This paper describes an overset approach that comprised virtual boundary-layer -like near-body grid coupled with an off-body adaptive mesh refinement far-field mesh for viscous fluids simulations. Unlike most a priori grid generation systems for the Reynolds-Averaged Navier–Stokes equations, the strand meshing paradigm is automatic, fast and requires little memory to provide boundary-layer coverage. In addition, the stacks of elements implied by the strands can be used to the simulation’s advantage, where they naturally provide a line direction for semi-implicit solving.

Description: This work recovers an established technique for improving quadrilateral shell element performance in both out-of-plane and in-plane bending cases using a mixed formulation. A four-field variational principle is established and we relate, at the discrete level, the Lagrange multipliers and secondary right Cauchy–Green field with the displacement and rotation fields. This is the main contribution of this work. High coarse-mesh accuracy is observed for distorted meshes and the robustness is shown to be adequate for crack propagation simulations. A consistent director normalization is performed, as an alternative to our recent spherical interpolation. Covariant metric components are deduced and exact linearization of the shell element is performed. Full assessment of the element is accomplished, showing similar performance to more costly approaches such as enhanced assumed strain. Patch test is satisfied ab-initio and benchmarks present very accurate results. Numerical experimentation for geometrically and material nonlinear problems is presented, as well as one fracture example using our recently proposed cracked edge technique.

Description: This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular finite elements. This method can be used to guarantee that a curvilinear triangle is geometrically valid, i.e., its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an efficient way to measure the quality of triangles. The key feature of the method is to expand the Jacobian determinant using a polynomial basis, built using Bézier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates.

Description: In this work, we introduce a new method for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to Eulerian-based codes that generate volume fraction data on a Cartesian grid. A step-by-step procedure for generating an all-hexahedral mesh is presented. We focus specifically on the challenges of developing a parallel implementation using the message passing interface to ensure a continuous, conformal and good quality hex mesh.

Description: This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements to best approximate the input, without estimating any differential quantities. Therefore, it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated.

Description: Solving partial differential equations using finite element (FE) methods for unstructured meshes that contain billions of elements is computationally a very challenging task. While parallel implementations can deliver a solution in a reasonable amount of time, they suffer from low cache utilization due to unstructured data access patterns. In this work, we reorder the way the mesh vertices and elements are stored in memory using Hilbert space-filling curves to improve cache utilization in FE methods for unstructured meshes. This reordering technique enumerates the mesh elements such that parallel threads access shared vertices at different time intervals, reducing the time wasted waiting to acquire locks guarding atomic regions. Further, when the linear system resulting from the FE analysis is solved using the preconditioned conjugate gradient method, the performance of the block-Jacobi preconditioner also improves, as more nonzeros are present near the stiffness matrix diagonal. Our results show that our reordering reduces the L1 and L2 cache miss-rates in the stiffness matrix assembly step by about 50 and 10 %, respectively, on a single-core processor. We also reduce the number of iterations required to solve the linear system by about 5 %. Overall, our reordering reduces the time to assemble the stiffness matrix and to solve the linear system on a 4-socket, 48-core multi-processor by about 20 %.

Description: The development of parallel algorithms for mesh generation, untangling, and quality improvement is of high importance due to the need for large meshes with millions to billions of elements and the availability of supercomputers with hundreds to thousands of cores. There have been prior efforts in the development of parallel algorithms for mesh generation and local mesh quality improvement in which only one vertex is moved at a time. But for global mesh untangling and for global mesh quality improvement, where all vertices are simultaneously moved, parallel algorithms have not yet been developed. In our earlier work, we developed a serial global mesh optimization algorithm and used it to perform mesh untangling and mesh quality improvement. Our algorithm moved the vertices simultaneously to optimize a log-barrier objective function that was designed to untangle meshes as well as to improve the quality of the worst quality mesh elements. In this paper, we extend our work and develop a parallel log-barrier mesh untangling and mesh quality improvement algorithm for distributed-memory machines. We have used the algorithm with an edge coloring-based algorithm for synchronizing unstructured communication among the processes executing the log-barrier mesh optimization algorithm. The main contribution of this paper is a generic scheme for global mesh optimization, whereby the gradient of the objective function with respect to the position of some of the vertices is communicated among all processes in every iteration. The algorithm was implemented using the OpenMPI 2.0 parallel programming constructs and shows greater strong scaling efficiency compared to an existing parallel mesh quality improvement technique.

Description: We present different linear parametrization techniques for the purpose of surface remeshing: the energy minimizing harmonic map, the convex map, and the least square conformal map. The implementation of those mappings as well as the associated boundary conditions is presented in a unified manner and the issues of triangle flipping and folding that may arise with discrete linear mappings are discussed. We explore the optimality of these parametrizations for surface remeshing by applying several classical 2D meshing algorithms in the parametric space and by comparing the quality of the generated elements. We present various examples that permit to draw guidelines that a user can follow in choosing the best parametrization scheme for a specific topology, geometry, and characteristics of the target output mesh.

Description: We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. We take a genus-zero solid as a basis of our study, but at the end of the work we explain the way to generalize the results to any genus solids. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain to preserve the features of the surface triangulation. We present some results of the application of isogeometric analysis with T-splines to the resolution of Poisson equation in solids parameterized with this technique.

Description: This paper presents a method for detecting holes during the surface wrapping process which cause surface leaks into the volume parts that shall not be meshed. The method solves a heat-diffusion equation on the background octree mesh, which is generated based on user-defined parameters, and its resolution corresponds to the resolution of the wrapper surface mesh. The heat problem is posed with the constant heat source in the volume, and the holes are detected as regions of high temperature gradients. The method detects both holes with open-boundary edges and semantic holes due to some missing parts. The sensitivity of the method is controlled via user-adjustable parameter which represents the ratio between the volume that shall not be meshed and the area of the hole. In addition, it is demonstrated that the method can be used to correct the orientation of normals in the surface mesh by utilising the property that high temperature is always found inside the volume. The potential of the method is presented on complex engineering examples.

Description: In this paper, a novel approach to automatically sub-divide a complex geometry and apply an efficient mesh is presented. Following the identification and removal of thin-sheet regions from an arbitrary solid using the thick/thin decomposition approach developed by Robinson et al. [ 1 ], the technique here employs shape metrics generated using local sizing measures to identify long-slender regions within the thick body. A series of algorithms automatically partition the thick region into a non-manifold assembly of long-slender and complex sub-regions. A structured anisotropic mesh is applied to the thin-sheet and long-slender bodies, and the remaining complex bodies are filled with unstructured isotropic tetrahedra. The resulting semi-structured mesh possesses significantly fewer degrees of freedom than the equivalent unstructured mesh, demonstrating the effectiveness of the approach. The accuracy of the efficient meshes generated for a complex geometry is verified via a study that compares the results of a modal analysis with the results of an equivalent analysis on a dense tetrahedral mesh.

Description: The presence of a few inverted or poor-quality mesh elements can negatively affect the stability, convergence and efficiency of a finite element solver and the accuracy of the associated partial differential equation solution. We propose a mesh quality improvement and untangling method that untangles a mesh with inverted elements and improves its quality. Worst element mesh quality improvement and untangling can be formulated as a nonsmooth unconstrained optimization problem, which can be reformulated as a smooth constrained optimization problem. Our technique solves the latter problem using a log-barrier interior point method and uses the gradient of the objective function to efficiently converge to a stationary point. The method uses a logarithmic barrier function and performs global mesh quality improvement. We have also developed a smooth quality metric that takes both signed area and the shape of an element into account. This quality metric assigns a negative value to an inverted element. It is used with our algorithm to untangle a mesh by improving the quality of an inverted element to a positive value. Our method usually yields better quality meshes than existing methods for improvement of the worst quality elements, such as the active set, pattern search, and multidirectional search mesh quality improvement methods. Our method is faster and more robust than existing methods for mesh untangling, such as the iterative stiffening method.

Description: A procedure to quantify the distortion (quality) of a high-order mesh composed of curved tetrahedral elements is presented. The proposed technique has two main applications. First, it can be used to check the validity and quality of a high-order tetrahedral mesh. Second, it allows the generation of curved meshes composed of valid and high-quality high-order tetrahedral elements. To this end, we describe a method to smooth and untangle high-order tetrahedral meshes simultaneously by minimizing the proposed mesh distortion. Moreover, we present a \(p\) -continuation procedure to improve the initial configuration of a high-order mesh for the optimization process. Finally, we present several results to illustrate the two main applications of the proposed technique.

Description: The generation of meshes that correctly reproduce a prescribed size function is crucial for quadrilateral meshing due to two reasons. First, quadrilateral meshes are difficult to adapt to a given size field by refining or coarsening the elements without compromising the element quality. Second, after the meshing algorithm is finished, it may be necessary to apply a smoothing algorithm to improve the global quality. This smoothing step may modify the element size and the final mesh will not reproduce the prescribed element size. To solve these issues, we propose to combine the size-preserving method with a smoothing technique that takes into account both the element shape and size. The size-preserving technique allows directly generating a quadrilateral mesh that reproduces the size function, while the proposed smoother allows obtaining a high-quality mesh while maintaining the element size. In adaptive processes, the proposed approach may reduce the number of iterations to achieve convergence, since at each iteration the background mesh is properly reproduced. In addition, we detail new theoretical results that provide more insight to size-preserving size functions. Specifically, we prove that the maximum gradient of a one-dimensional size-preserving size function is bounded. Finally, several applications that show the benefits of applying the proposed techniques are presented.

Description: In this paper compute unified device architecture programming and open multiprocessing are used for the graphics processing unit and central processing unit parallel computation of material damage. The material damage is evaluated by a multilevel finite element analysis within material domains reconstructed from a high-resolution micro-focus X-ray computed tomography system. An effective computational method is investigated for solving the linear equations of finite element analysis. Numerical results show an encouraging trend in reducing the computation cost for the digital diagnosis of material damage.

Description: This paper presents a novel algorithm that enables the semi-automatic reconstruction of human-made structures (e.g., buildings) into piecewise planar 3D models from a single image. This allows the models to be readily used in virtual or augmented reality visual simulations or for data acquisition in 3D geographic information systems. Contrary to traditional labor-intensive but accurate single view reconstruction (SVR) solutions based purely on geometric constraints, and contrary to recent fully automatic albeit low-accuracy SVR algorithms based on statistical inference, the presented method achieves a compromise between speed and accuracy, leading to less user input and acceptable visual effects. The user input required in the presented approach is primarily a line drawing that represents an outline of the building to be reconstructed. Using this input, the developed method takes advantage of a newly proposed vanishing point (VP) detection algorithm that can simultaneously estimate multiple VPs in an image. With those VPs, the normal direction of planes—which are projected onto the image plane as polygons in the line drawing—can be automatically calculated. Following this step, a linear system similar to the traditional SVR solutions can be used to achieve 3D reconstruction. Experiments that demonstrate the efficacy and visual outcome of the developed method are also described, highlighting the method’s potential use for rapid geometric model building of surrounding structures in visual simulation of engineering processes.

Description: Efficient development and engineering of high performing interactive devices, such as haptic robots for surgical training benefits from model-based and simulation-driven design. The complexity of the design space and the multi-domain and multi-physics character of the behavior of such a product ask for a systematic methodology for creating and validating compact and computationally efficient simulation models to be used in the design process. Modeling the quasi-static stiffness is an important first step before optimizing the mechanical structure, engineering the control system, and performing hardware in the loop tests. The stiffness depends not only on the stiffness of the links, but also on the contact stiffness in each joint. A fine-granular Finite element method (FEM) model, which is the most straightforward approach, cannot, due to the model size and simulation complexity, efficiently be used to address such tasks. In this work, a new methodology for creating an analytical and compact model of the quasi-static stiffness of a haptic device is proposed, which considers the stiffness of actuation systems, flexible links and passive joints. For the modeling of passive joints, a hertzian contact model is introduced for both spherical and universal joints, and a simply supported beam model for universal joints. The validation process is presented as a systematic guideline to evaluate the stiffness parameters both using parametric FEM modeling and physical experiments. Preloading has been used to consider the clearances and possible assembling errors during manufacturing. A modified JP Merlet kinematic structure is used to exemplify the modeling and validation methodology.

Description: Computational fluid dynamics is not often used early in the conceptual design stage of product development due to the lengthy computation times involved with solving complex computational fluid dynamics models. At this early stage, design options are being explored and significant changes are common, and therefore updated solutions must be found quickly to make these models effective. Because of this, computational fluid dynamics models are often reduced to analysis tools used later in the process and are used for refinement rather than for creative engineering design. This paper presents a novel method to create computational fluid dynamics models that can be used earlier in the engineering design process. The key aspects of analysis models used in the initial, creative phase of design are the ability to make changes and re-analyze the altered model quickly. Typically, computational fluid dynamics analysts choose to re-analyze the entire altered model to maintain the same level of accuracy. This can take a significant amount of time because the entire domain must be recalculated. Much of this time is devoted to fine-tuning the model, i.e., improving the accuracy of details of the domain that are sometimes non-essential to the bulk characteristics of the flowfield. However, in the early stage of the design process, decisions are often made based on the large-scale behavior of the fluid flow; fine details are often inconsequential. We have taken advantage of this premise to decrease the turnaround time required to re-analyze a computational fluid dynamics model using the Adaptive Modeling by Evolving Blocks Algorithm. The Adaptive Modeling by Evolving Blocks Algorithm is a genetic programming-based optimization program that segregates a flowfield and places minimal cost solvers in regions with simple flow dynamics while placing full-scale computational fluid dynamics solvers in the more complex regions to preserve accuracy. The program evolves the combined segregation scheme and solver placement until a reliably accurate, faster multi-solver model is found. Substantial reductions in solution times have been found in some cases. The results show an improvement in the speed of the multi-solver when compared with a single-model solution with no significant loss of accuracy.

Description: In the traditional programming paradigm, data structures and algorithms are developed for specific data types and requirements. This leads to code redundancy and inflexibility, thus not allowing effective code reuse for similar applications. One effective approach to increase code reuse is generic programming, which focuses on the development of efficient, reusable software libraries through suitable abstractions for the common requirements. In this paper, we present how we applied generic programming to an ongoing effort for mesh-based adaptive simulations on massively parallel computers. Three generic components, iterator, set and tag, were developed using design pattern, C++ template programming and the standard template library. The scaling studies on petascale supercomputers demonstrate the efficiency of the reusable, generic components which do not sacrifice the performance of the previous tools developed in the traditional object-oriented programming paradigm.

Description: We introduce a reliable intersection algorithm for manifold surface meshes. The proposed algorithm builds conforming surface meshes from a set of intersecting triangulated surfaces. This algorithm effectively handles all degenerate triangle–triangle intersection cases. The key idea of the algorithm is based on an extensive set of triangle–edge intersection cases, combined with an intersection curve tracking method. The intersection operations do not rely on global spatial search operations and no remeshing steps are needed. The intersection curves are introduced into each surface mesh using a unique curve imprinting algorithm. The imprinting algorithm naturally handles degenerate intersection cases of many surfaces at an edge or at a point. The algorithm produces a consistent mesh data structure for subsequent mesh optimization operations. The mesh intersection algorithm is used within a general framework for modelling and meshing of geological formations, which are essential for reliable mathematical modelling of oil reservoirs.

Description: This paper focuses on the development of a new backcalculation method for concrete road structures based on a hybrid evolutionary global optimization algorithm, namely shuffled complex evolution (SCE). Evolutionary optimization algorithms are ideally suited for intrinsically multi-modal, non-convex, and discontinuous real-world problems such as pavement backcalculation because of their ability to explore very large and complex search spaces and locate the globally optimal solution using a parallel search mechanism as opposed to a point-by-point search mechanism employed by traditional optimization algorithms. SCE, a type of evolutionary optimization algorithms based on the tradeoff of exploration and exploitation, has proved to be an efficient method for many global optimization problems and in some cases it does not suffer the difficulties encountered by other evolutionary computation techniques. The SCE optimization approach is hybridized with a neural networks surrogate finite-element based forward pavement response model to enable rapid computation of global or near-global pavement layer moduli solutions. The proposed rigid pavement backcalculation model is evaluated using field non-destructive test data acquired from a full-scale airport pavement test facility.

Description: This paper presented a grid-based hexahedral element mesh generation algorithm for solid models with concave curved boundary lines. A deep study was focused on the boundary matching and quality improvement techniques. Firstly, a method for computing the curvature values of the triangle facets and sub-surfaces was proposed. In order to improve the surface mesh quality, a layer of new elements was inserted on the surface of the jagged core mesh. Then, a relative position relationship method was used to match C - edges of the solid model. Eight different types of free quadrilateral facet configurations were established. In order to handle the concave curve-matching problem, this paper proposed a method to modify the matching properties of the degenerate quadrilateral facets fitted on the same concave curved boundary line by unifying their orientations to point to the same sub-surface. In addition, six mixed templates were newly proposed to improve the geometrical topology of the degenerate elements associated with concave curves and sharp features. The positions of the nodes were smoothed by the modified Laplacian method and objective function. Finally, the effectiveness and reliability of the algorithms proposed in this paper were demonstrated by a practical example.

Description: Indirect methods recombine the elements of triangular meshes to produce quadrilaterals. The resulting quadrilaterals are usually randomly oriented, which is not desirable. However, by aligning the vertices of the initial triangular mesh, precisely oriented quads can be produced. Levy’s algorithm is a non-linear optimization procedure that can align points according to a locally defined orientation matrix. It minimizes an energy functional based on the L p distance. The triangulation of a set of vertices smoothed with Levy’s algorithm is mainly composed of right-angled triangles, which is ideal for quad recombination. An implementation of Levy’s algorithm based on numerical integration is presented. The implementation has the advantage of not modifying the edge meshes. It also features automatic calculation of the orientation angle. When used in combination with an indirect recombination algorithm, it can create quads of varying size and orientation. It has been tested on two-dimensional surfaces as well as globally parametrized three-dimensional surfaces. The results demonstrate an increase in the number of nodes having four neighbors and an improvement of the quads quality. The development took place in the framework of the Gmsh free software.

Description: This paper presents a fully automated high-order hexahedral mesh generation algorithm for shell-like structures based on enhanced sweeping methods. Traditional sweeping techniques create all-hexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming high-order all-hexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skew-angled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a so-called interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.

Description: Medial axis transform of a pocket with free-form closed boundaries is a completed, compact representation of the pocket geometric shape and topology. It is very useful to multiple cutters selection and their tool paths generation for CNC machining of complex pockets. In the past decades, much research has been successfully conducted on the topic of finding the medial axis of a shape domain bounded with a polygon or simple geometries, e.g., lines and circles. Currently, more pockets with free-form boundaries are adopted in mechanical parts; however, the prior medial axis generation methods cannot handle this type of pockets well, resulting in long computation time and low medial axis accuracy. To address this problem, an efficient, accurate approach to calculating the medial axis transforms of these pockets is proposed in this work. An original optimization model of bisectors is established, and a new optimization method—the hybrid global optimization method—is developed to efficiently and accurately solve the optimization model of bisectors. The new optimization model and solver have been applied to many examples, and the testing results have demonstrated the advantages of this innovative approach over the prior medial axis methods. It can be an effective solution to the medial axis transforms of complex pockets.

Description: The gear is a main part of gear pump, the fault of it will affect the working performance of the gear pump. The multiple cracks is a main fault for gear pump gear, therefore, the application of wavelet finite element method on identification of multiple cracks is studied in depth. First, the working principle of gear pump is introduced, the causes of multiple cracks are analyzed, and the relating researches are discussed. Second, the vibration wavelet finite element formulations of intact and cracked gear pump gear are constructed, respectively. Third, the basic theory of blind source separation and particle swarm algorithm are studied, and the frequency measurement procedure of gear pump gear is designed. Finally, the simulation on multiple cracks of gear pump gear is carried out, and results show that the wavelet finite element can identify the location and size of the multiple cracks of gear pump gear correctly.

Description: Many natural systems have inspired the design of engineering artifacts. Example systems include a broad array of products inspired by pseudo-fractal structures found in nature, including bronchial tubes, watersheds, lightning, and leaf veins. Notably, these systems all resolve a volume-to-point flow problem, i.e., diffusive transportation of heat, energy or fluid into a single flow channel from an initial dispersal throughout a substrate volume (coalescence). Flow diffuses slowly throughout the bulk of the substrate medium towards channels. Once in the channels, flow proceeds rapidly towards the sink. These channels are branched and converge at a single point. Several engineering design problems require a volume-to-point flow solution, e.g., the internal conductive cooling of a microchip. This work introduces a novel geometry-based transport analysis, referred to as path length analysis, for evaluating the performance of systems designed for volume-to-point flow. The analysis is inspired by two principles. First, diffusive flow tends to follow the “path of least resistance.” Second, the effort required to diffuse material or energy along a path is proportional to the length of the path. Novel channel configurations may be developed using these two principles. These configurations have a pseudo-fractal type structure and are significantly more efficient than the state-of-the-art for cooling problems such as the conductive cooling of a microchip. An extensive finite element analysis confirms the performance for the example of microchip cooling. The primary results include (1) path length optimization leads to high performing structures with a ‘natural’ appearance, and (2) path length analysis facilitates a new understanding and design tool for analyzing volume-to-point flow problems.