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  • 1
    Electronic Resource
    Electronic Resource
    OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES - I. SHAPE OPTIMIZATION METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 33-50 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forming process ; optimal design ; forging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Pseudoconsistent load vector and mass matrix for the discrete Kirchhoff triangle and the discrete shear triangle elements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 317-330 
    Details
    ISSN: 1069-8299
    Keywords: DKT and DST elements ; pseudo consistent load vector ; pseudo consistent mass matrix ; plate bending elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many finite elements based on Reissner-Mindlin plate bending theory with discrete constraints have been developed in the past few years. This approach avoids the C1 continuity required by the classical Kirchhoff plate theory. However, in those elements the shape functions for deflections (or their derivatives) are not integrated. Particularly in DKT (discrete Kirchhoff triangle) and in DST (discrete shear triangle) elements, the lateral deflections are defined only on the boundaries. In the paper we briefly discuss the definition of the transverse displacement for these elements, and present a simple approach to define a pseudoconsistent load vector and mass matrix.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110405
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  • 3
    Electronic Resource
    Electronic Resource
    A SPACE-TIME FINITE ELEMENT METHOD FOR THE EXTERIOR STRUCTURAL ACOUSTICS PROBLEM: TIME-DEPENDENT RADIATION BOUNDARY CONDITIONS IN TWO SPACE DIMENSIONS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1635-1657 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; radiation boundary conditions ; absorbing boundary conditions ; discontinuous Galerkin method ; structural acoustics ; wave equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A time-discontinuous Galerkin space-time finite element method is formulated for the exterior structural acoustics problem in two space dimensions. The problem is posed over a bounded computational domain with local time-dependent radiation (absorbing) boundary conditions applied to the fluid truncation boundary. Absorbing boundary conditions are incorporated as ‘natural’ boundary conditions in the space-time variational equation, i.e. they are enforced weakly in both space and time. Following Bayliss and Turkel, time-dependent radiation boundary conditions for the two-dimensional wave equation are developed from an asymptotic approximation to the exact solution in the frequency domain expressed in negative powers of a non-dimensional wavenumber. In this paper, we undertake a brief development of the time-dependent radiation boundary conditions, establishing their relationship to the exact impedance (Dirichlet-to-Neumann map) for the acoustic fluid, and characterize their accuracy when implemented in our space-time finite element formulation for transient structural acoustics. Stability estimates are reported together with an analysis of the positive form of the matrix problem emanating from the space-time variational equations for the coupled fluid-structure system. Several numerical simulations of transient radiation and scattering in two space dimensions are presented to demonstrate the effectiveness of the space-time method.
    Additional Material: 13 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES - II. APPLICATION OF SHAPE OPTIMIZATION IN FORGING (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 51-65 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forging ; preform design ; optimal design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is the second part of a two-part article about shape optimization of metal forming processes. This part is focused on numerical applications of the optimization method which has been described in the first paper. The main feature of this work is the analytical calculations of the derivatives of the objective function for a non-linear, non-steady-state problem with large deformations. The calculations are based on the differentiation of the discrete objective function and on the differentiation of the discrete equations of the forging problem. Our aim here is to show the feasibility and the efficiency of such a method with numerical examples. We recall the formulation and the resolution of the direct problem of hot axisymmetrical forging. Then, a first type of shape optimization problem is considered: the optimization of the shape of the initial part for a one-step forging operation. Two academic problems allow for checking the accuracy of the analytical derivatives, and for studying the convergence rate of the optimization procedure. Both constrained and unconstrained problems are considered. Afterwards, a second type of inverse problem of design is considered: the shape optimization of the preforming tool, for a two-step forging process. A satisfactory shape is obtained after few iterations of the optimization procedure.
    Additional Material: 21 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    A VELOCITY BASED APPROACH INCLUDING ACCELERATION TO THE FINITE ELEMENT COMPUTATION OF VISCOPLASTIC PROBLEMS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3439-3451 
    Details
    ISSN: 0029-5981
    Keywords: finite element computation ; viscoplastic Norton-Hoff law ; metal forming ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a velocity based approach including acceleration to the finite element computation of metal forming problems, based on the viscoplastic Norton-Hoff law. In order to reduce computational cost, we suggest substituting the classical solution procedure based on standard Newton-Raphson method for solving the set of non-linear equations, with a new one which needs only one computation inside a time step and which is based on the linearization of the non-linear equations over time. The new procedure was introduced as an option in the existing computer code FORGE2©. Some examples are used for comparison between the classical procedure and the new one. They show that the new procedure is stable and accurate, and in comparison to the classical one it reduces the total number of resolutions of linear systems. Therefore, significant computer time reduction can be expected for 3-D problems.
    Additional Material: 10 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Prediction of pile capacity from stress-wave measurements: A neural network approach (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 19 (1995), S. 107-126 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A neural network approach for the prediction of pile bearing capacity by the stress-wave matching technique is presented. The main advantage of this approach over the traditional manual or automated matching approach is that it avoids the time-consuming process of iterative adjustment. This makes it feasible to determine the static pile capacity in real time in the field. Another benefit of this approach is that as more case histories become available, the neural network can be improved by learning from these new examples.A three-layer back-propagation network is set up to illustrate the capability of the proposed approach for 70 dynamically tested concrete bored piles. A wave equation model developed at the National University of Singapore and coded in the NUSWAP computer program is used to formulate the problem. Up to 14 of the 70 piles (20 percent) are used in training the network. The NUSWAP program is used to generate simulation training examples based on the manually fitted training examples for further training of the network. Different network configurations are examined. The trained network produces results exhibiting good stress-wave matching qualities compared to those obtained by manual fitting. The pile bearing capacities predicted by the two approaches agree very closely. The load-settlement curve and axial load distribution in the pile computed using the network-predicted soil parameters are in good agreement with the field measurements obtained from a maintained load test.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610190204
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  • 7
    Electronic Resource
    Electronic Resource
    A B-spline finite element method for the regularized long wave equation (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 59-68 
    Details
    ISSN: 1069-8299
    Keywords: RLW equation ; finite elements ; splines ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method with quadratic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank-Nicolson approximation. Standard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110109
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  • 8
    Electronic Resource
    Electronic Resource
    A superposition method for the solution of crack problems (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 243-254 
    Details
    ISSN: 1069-8299
    Keywords: fracture ; boundary elements ; superposition ; stress intensity factor ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We discuss a two-step superposition method for calculating linear elastic stress intensity factors. The procedure requires the solution to the full cracked problem and the solution to a problem on the same mesh assuming the singularity due to a crack tip in an infinite region. We show that this is equivalent to the well known subtraction of singularity method if the two solutions are characterized by crack tip stress. The advantages of our procedure are that no modifications need to be made to a standard computer program and that once one singular solution is available on a given cracked mesh, solutions with different boundary conditions on the same mesh may be obtained in one step without including any singular crack effects. The mesh required to represent the singular crack tip field may also be studied independently of the complete problem. The additional computational cost of a two-step procedure is minimal since the solution matrix from step one may be reused with a new right-hand side. Numerical experiments using the boundary element method demonstrate the high accuracy and simplicity of the superposition approach.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110307
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  • 9
    Electronic Resource
    Electronic Resource
    Direct application of constraints to symmetric algebraic systems (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 563-573 
    Details
    ISSN: 1069-8299
    Keywords: constraints ; boundary conditions ; rigid inclusions ; inextensibility ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Constraints arise naturally in the context of rigid inclusions, incompressibility, inextensible fibres and deformed finite elements. Typical methods for handling constraints in the governing matrix equation include Lagrange multipliers, penalty weights and elimination of variables. Each procedure has a particular undesirable feature. Proposed here is an approach in which each constraint is handled directly and sequentially through a modification of the rows and columns of the governing matrix and force vector. Positive definiteness, symmetry and the dimensions of the matrix remain unchanged. Elementary examples involving both the static and dynamic response of a bar are given to illustrate the procedure.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110703
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  • 10
    Electronic Resource
    Electronic Resource
    Hierarchic and mixed-interpolated finite elements for Reissner-Mindlin problems (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 549-562 
    Details
    ISSN: 1069-8299
    Keywords: plate problem ; Reissner-Mindlin ; finite elements ; hierarchic elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The focus of the present work is directed towards the construction of a family of special finite elements for the numerical solution of the Reissner-Mindlin plate problem. The model describes the deformation of a plate when transverse shear deformation is taken into account. The model is widely used for thin to moderately thick plates. Despite its simple formulation, the numerical approximation is not straightforward. When standard low-order finite elements are used for the approximation the solution degenerates very rapidly for small thickness (locking phenomenon). To overcome such behaviour, non-standard formulations of the problem are usually combined with low-order finite elements to weaken or possibly eliminate the locking of the numerical solution.In recent years high-order finite elements have been introduced and successfully applied in several fields. Previously we have constructed a family of hierarchic high-order finite elements to solve the Reissner-Mindlin problem in its plain formulation. The locking was strongly reduced but was still active for very thin plates. Meanwhile some mixed-interpolated finite elements have been developed and shown to be locking free. In this paper we combine the two approaches, namely, the hierarchic high-order elements and the mixed-interpolated elements. The result is a family of special finite elements that exhibits both properties of convergence and robustness.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110702
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