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  • 1
    Electronic Resource
    Electronic Resource
    A curved quadrilateral element for static analysis of shells with geometric and material nonlinearities (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 617-635 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 48 degrees-of-freedom quadrilateral element, including the effect of both material and geometric nonlinearities, is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures. The element surface is described by a variable-order polynomial in curvilinear co-ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co-ordinates. Without being confined to the assumption of axisymmetry, this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones. In the formulation for geometric nonlinearity, the total Lagrangian approach is adopted. Only small strains and small rotations are allowed. In the formulation for plastic deformation, the concept of a layered element model is used. In the inelastic range, the material is assumed to obey the Von Mises yield criterion and the Prandtl-Reuss flow rule. A tangential stiffness formulation is combined with the modified Newton-Raphson iteration method for the solution of nonlinear problems. A systematic choice of examples ranging from fiat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210404
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  • 2
    Electronic Resource
    Electronic Resource
    Nonlinear dynamic analysis with a 48 d.o.f. curved thin shell element (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1115-1128 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The developments of an existing 48 degrees-of-freedom (d.o.f.), curved, quadrilateral, thin shell element, for materially and geometrically nonlinear static analysis of shell structures, are extended for the study of dynamic responses of nonlinear shells. The variable-order polynomial representations of the shell surface and the non-axisymmetric definition of the shell boundaries allow the study of the dynamic behaviour of a class of shell structures more general than those treated by using flat plate elements and elements with assumptions of axisymmetry. The equations of motion are based on a Lagrangian frame of reference. A combination of step-by-step and iterative procedures is used for the solution of nonlinear equations. The incremental equations of motion are linearized for computation purposes, and an algorithm for numerical integration based on Newmark's generalized operator for dynamic analysis, using optional iteration, is adopted. The flow theory of plasticity is used in the inelastic range, and perfectly plastic or isotropic strain hardening materials are considered. The spread of plastic zones in the thickness direction is treated by using a layered model. Numerical examples presented include the dynamic analyses of a square plate, a circular annulus, a cylindrical panel and a spherical cap. Comparisons with existing solutions demonstrate the validity and accuracy of the present developments.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210611
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  • 3
    Electronic Resource
    Electronic Resource
    Elastic-viscoplastic, large deformation formulations of a curved quadrilateral thin shell element (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1897-1909 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An elastic-viscoplastic constitutive law is implemented in the formulations of a curved quadrilateral element based on thin shell theory. The element surface is defined using variable-order polynomials allowing representation of a wide range of shell geometries. The large displacement effects are included by using an incremental stiffness procedure together with the Lagrangian mode of description of motion. The time rate effects may be treated by using explicit, semi-explicit or implicit time marching schemes. A scheme for automatic calculation of time step is used. By allowing steady-state conditions to be reached, plasticity solutions are obtained. Both perfect plasticity and strain hardening are considered. The Von Mises yield rule and the associated flow rule are used to determine plastic deformation. The spread of plasticity in the thickness direction is allowed by using a layered model. The procedures developed are applied to solve elastic-plastic, small and large displacement problems of thin plates and shells and the results obtained are compared with existing solutions to illustrate the validity and accuracy of the present developments.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620211013
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  • 4
    Electronic Resource
    Electronic Resource
    A simple element for static and dynamic response of beams with material and geometric nonlinearities (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 851-867 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified simple 6 degrees-of-freedom beam finite element and the associated computational procedures have been developed for the fast and efficient solution of a wide class of static and dynamic response problems of the beam type with material and/or geometrical nonlinearities.The material nonlinearity is treated by including its effect in the governing equations by forming the stiffness matrix of each element using a two-dimensional grid of Gauss points and using the material properties at each point corresponding to the uniaxial strain at that point. Examples are provided for metal and reinforced concrete beams.A powerful yet straightforward method for the solution of elastica problems of beams and frames, using the beam element developed by the senior author, has been extended for determining the dynamic response of beams undergoing large displacements, including large rotations.The solution procedure involves piecewise linearization of response equations and iterations at each incremental step to achieve equilibrium. The solution procedure is simple and easy to apply. A variety of problems is solved to determine the applicability of the proposed simple formulations. Excellent agreement with existing analytical solutions which employ higher order elements demonstrates the efficiency and versatility of the present simple beam element in nonlinear analysis.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200506
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  • 5
    Electronic Resource
    Electronic Resource
    An efficient through-thickness integration scheme in an unlimited layer doubly curved isoparametric composite shell element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2777-2793 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an efficient numerical integration scheme for evaluating the matrices (stiffness, mass, stress-stiffness and thermal load) for a doubly curved, multilayered, composite, quadrilateral shell finite element. The element formulation is based on three-dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells.The conventional formulation requires a 2 × 2 × 2 or 2 × 2 × 1 Gauss integration per layer for the calculation of element matrices. This method becomes uneconomical when a large number of layers is used owing to an excessive amount of computations. The present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables. With the through-thickness variables separated, they are combined with the thickness dependent material properties and integrated separately. The element matrices are computed using the integrated material matrices and only a 2 × 2 spatial Gauss integration scheme. The response results using the present formulation are identical to those obtained using the conventional formulation. For a small number of layers, the present method requires slightly more CPU time. However, for a larger number of layers, numerical data are presented to demonstrate that the present formulation is an order-of-magnitude economical compared to the conventional scheme.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281205
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  • 6
    Electronic Resource
    Electronic Resource
    An infinite boundary element formulation for three-dimensional potential problems (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2079-2100 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An infinite boundary element (IBE) is presented for the analysis of three-dimensional potential problems in an unbounded medium. The IBE formulations are done to allow their coupling with the finite element (FE) matrices for finite domains and to obtain the overall matrices without destroying the banded structure of the FE matrices. The infinite body is divided into a number of zones whose contributions are expressed in terms of the nodal quantities at FE nodes by employing suitable decay functions and performing mainly analytical integrations of the boundary element kernels. The continuity and compatibility conditions for the potential and the flux at the FE-IBE interface are developed. The relationships for the contributions of the IBE flux vectors to the FE load vectors are given. The final equations for the IBE are obtained in the usual FE stiffness-load vector form and are easily assembled with the FE matrices for the finite object. A series of numerical examples in heat transfer and electromagnetics were solved and compared with alternative solutions to demonstrate the validity of the present formulations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620351010
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  • 7
    Electronic Resource
    Electronic Resource
    A boundary element formulation for the inverse elastostatics problem (iesp) of flaw detection (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2189-2202 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary integral formulation is presented for the detection of flaws in planar structural members from the displacement measurements given at some boundary locations and the applied loading. Such inverse problems usually start with an initial guess for the flaw location and size and proceed towards the final configuration in a sequence of iterative steps. A finite element formulation will require a remeshing of the object corresponding to the revised flaw configuration in each iteration making the procedure computationally expensive and cumbersome. No such remeshing is required for the boundary element approach. The inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured displacements and the computed displacements for the assumed flaw configuration. The geometric condition that the flaw lies within the domain of the object is imposed using the internal penalty function approach in which the objective function is augmented by the constraint using a penalty parameter. A first-order regularization procedure is also implemented to modify the objective function in order to minimize the numerical fluctuations that may be caused in the numerical procedure due to errors in the experimental measurements for displacements. The flaw configuration is defined in terms of geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach. A series of numerical examples involving the detection of circular and elliptical flaws of various sizes and orientations are solved using the present approach. Good predictions of the flaw shape and location are obtained.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361304
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  • 8
    Electronic Resource
    Electronic Resource
    SINGULAR p-VERSION FINITE ELEMENTS FOR STRESS INTENSITY FACTOR COMPUTATIONS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1091-1114 
    Details
    ISSN: 0029-5981
    Keywords: finite element methods ; fracture mechanics ; singular elements ; f-version ; stress intensity factors ; mixed mode ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element analysis of linear elastic fracture mechanics problems is complicated by the presence of the singular and finite non-singular stress distributions in the crack tip region. The availability of a constant stress term in addition to the singular term in the standard h-version singular finite elements is insufficient to model the finite nonsingular stress zone. A p-version singular finite element capable of modelling the higher-order non-singular stress terms in addition to the singular term and the constant term is presented. The formulation for the displacement substitution technique for computing the stress intensity factors using singular p-version triangular finite elements is developed. Unlike the standard h-version formulation, the stress intensity factors computed using the p-version displacement substitution technique do not depend on the specific arrangement and length of the quarter point elements, and require simple mesh designs as well as fewer number of degrees of freedom. Numerical studies comparing the convergence of the stress intensity factors computed by the p-version method against other available alternatives such as the h-version method and the contour integral method are presented to demonstrate the effectiveness of the present developments. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Analysis of symmetric domains in advanced applications with the boundary element method (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2373-2388 
    Details
    ISSN: 0029-5981
    Keywords: symmetric domains ; boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The strategy in the boundary element method for the analysis of symmetric domains that does not require the modelling of contours corresponding to the axes of symmetry is investigated for a number of advanced applications. These applications include: treatment of domain loadings, two-dimensional time domain transient elastodynamics, and the analysis of probabilistic problems in elastostatics with a random geometric configuration. Both symmetric as well as arbitrary loadings acting on the symmetric objects are considered. A number of case studies are presented to provide comparisons of computer memory and CPU time requirements for the analyses of the entire object versus the analyses of only the symmetric portion of the object. The numerical data presented clearly demonstrates the advantages of developing efficient symmetric formulations for advanced applications.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381405
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  • 10
    Electronic Resource
    Electronic Resource
    On improved hybrid finite elements with rotational degrees of freedom (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 785-800 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A set of three new hybrid elements with rotational degrees-of-freedom (d.o.f.'s) is introduced. The solid, 8-node, hexahedron element is developed for solving three-dimensional elasticity problems. This element has three translational and three rotational d.o.f.'s at each node and is based on a 42-parameter. three-dimensional stress field in the natural convected co-ordinate system. For two-dimensional, plane elasticity problems, an improved triangular hybrid element and a quadrilateral hybrid element are presented. These elements use two translational and one rotational d.o.f. at each node. Three different sets of five-parameter stress fields defined in a natural convected co-ordinate system for the entire element are used for the mixed triangular element. The mixed quadrilateral element is based on a nine-parameter complete linear stress field in natural space. The midside translational d.o.f.'s are expressed in terms of the corner nodal translations and rotations using appropriate transformations. The stiffness matrix is derived based on the Hellinger-Reissner variational principle. The elements pass the patch test and demonstrate an improved performance over the existing elements for prescribed test examples.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280405
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