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  • 1
    Electronic Resource
    Electronic Resource
    Large strain analysis of rubber-like materials based on a perturbed Lagrangian variational principle (1991)
    Springer
    Computational mechanics 8 (1991), S. 221-233 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A mixed finite element method is presented for the large strain analysis of rubber-like materials, which are considered to be nearly incompressible. Two types of constitutive relations are included: generalized Rivlin and Ogden's models. The finite element equations are derived on the basis of a perturbed Lagrangian variational principle from which both the displacement and pressure fields are independently approximated by appropriate shape functions. A physically meaningful pressure parameter is introduced in the expression of complementary energy. In the paper, a special effort is made to split the deformation energy into two distinct parts: isochoric and hydrostatic parts. By doing this, a quadratic convergence rate of nonlinear iterative solution is achieved, particularly for problems deformed in the large strain range. The finite element equations are specialized for a two-dimensional 9-node Lagrange element with three-term pressure parameters. Five examples are given to demonstrate the application of the proposed numerical algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00577376
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  • 2
    Electronic Resource
    Electronic Resource
    An Implicit integration scheme for generalized viscoplasticity with dynamic recovery (1998)
    Springer
    Computational mechanics 21 (1998), S. 429-440 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper is concerned with the development of a general implicit time-stepping integrator for the flow and evolution equations in a recent representative class of generalized viscoplastic models, involving both hardening and dynamic recovery mechanisms. To this end, the computational framework is developed on the basis of the unconditionally stable, backward Euler difference scheme. Its mathematical structure is of sufficient generality to allow a systematic treatment of several internal variables of the tensorial and scalar types. The matrix forms developed are directly applicable in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). The closed-form expressions for residual vectors and the algorithmic, (consistent) material tangent stiffness array are given explicitly, with the maximum matrix sizes “optimized” to depend only on the number of independent stress components, but not the number of internal state variables involved. Several numerical simulations are given to assess the performance of the developed schemes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050322
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  • 3
    Electronic Resource
    Electronic Resource
    Nonlinear material parameter estimation for characterizing hyper elastic large strain models (2000)
    Springer
    Computational mechanics 25 (2000), S. 66-77 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An automated, systematic, and computationally efficient methodology to estimate the material parameters for characterizing general nonlinear material models for large strain analysis (e.g., hyperelastic and hyper foam materials) is presented. Such constitutive material models often require a large number of material constants to describe a host of physical phenomena and complicated deformation mechanisms. Extracting such material constants for a model from the volumes of data generated in the test laboratory is usually a very difficult, and frustrating. The integrated code COMPARE (that is an acronym of Constitutive Material PARameter Estimator) is being developed to enable the determination of an “optimum” set material parameters by minimizing the errors between the experimental test data and the predicted response. The key ingredients of COMPARE are listed as follows: (i) primal analysis tools (response functionals) for differential form of constitutive models; (ii) sensitivity analysis; (iii) optimization technique of an error/cost function; and (iv) graphical user interface. The code COMPARE casts the estimation of the material parameters as a minimum-error, weighted-multiobjective, optimization problem. Detailed derivations and results generated by applying the proposed technique to a comprehensive set of test data are given. These results have clearly demonstrated the great practical utility of the automated scheme developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050016
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  • 4
    Electronic Resource
    Electronic Resource
    On the symbolic manipulation and code generation for elasto-plastic material matrices (1986)
    Springer
    Engineering with computers 1 (1986), S. 205-215 
    Details
    ISSN: 1435-5663
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A computerized procedure for symbolic manipulations and FORTRAN code generation of elasto-plastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, the Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01200137
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  • 5
    Electronic Resource
    Electronic Resource
    An efficient quadrilateral element for plate bending analysis (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1123-1155 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields. The crucial point of the selection of appropriate stress parameters is emphasized in the formulation. For this purpose, a set of guidelines is formulated based on the following considerations: (i) suppression of all kinematic deformation modes, (ii) the element has a favourable value for the constraint index in the thin plate limit, (iii) element properties are frame-invariant. For computer implementation the components of the element stiffness matrix are evaluated analytically using the symbolic manipulation package MACSYMA. The effectiveness and practical usefulness of the proposed element are demonstrated by the numerical results of a variety of problems involving thin and moderately thick plates under different loading and support conditions.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240607
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  • 6
    Electronic Resource
    Electronic Resource
    A hybrid/mixed model for non-linear shell analysis and its applications to large-rotation problemsThis work is supported by National Science Foundation, under Research Grant Number EET-8714628 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 407-446 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Adopting an updated Lagrange approach, the general framework for the fully non-linear analysis of curved shells is developed using a simple quadrilateral C0 model (HMSH5). The governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified Hellinger/Reissner type with independent assumptions for displacement and strain fields. Emphasis is placed on devising effective solution procedures to deal with large rotations in space, finite stretches and generalized rate-type material models. In particular, a geometrically exact scheme for configuration update is developed by making use of the so-called exponential mapping algorithm, and the resulting element was shown to exhibit a quadratic rate of (asymptotic) convergence in solving practical shell problems with Newton-Raphson type iterative schemes. For the purpose of updating the spatial stress field of the element, an ‘objective’ generalized midpoint integration rule is utilized, which relies crucially on the concept of polar decomposition for the deformation gradient, and is in keeping with the underlying mixed method. Finally, the effectiveness and practical usefulness of the HMSH5 element are demonstrated through a number of test cases involving beams, plates and shells undergoing very large displacements and rotations.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290213
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  • 7
    Electronic Resource
    Electronic Resource
    Shear-flexible models for spatial buckling of thin-walled curved beamsThis work is supported NSF under research grant no. EET-8714628 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 729-757 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing non-linear finite element equations for the spatial stability analysis of curved beams, using a simple two-noded model, are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross-sectional warping and bending/twisting rotations. The formulation is valid for both open-and closed-type thin-walled sections, and this is accomplished by the use of a kinematic description based on a generalized beam theory in which shear deformation due to both flexural-and warping-torsional actions is accounted for. The effect of finite rotations in space is included, resulting in a second-order accurate geometric stiffness matrix and ensuring that all significant instability modes can be predicted. Finally, the results obtained in a number of numerical simulations for lateral-torsional bifurcation buckling of circular arches are presented to illustrate the model effectiveness and practical usefulness, and to provide explanations for the source of discrepancies noted in the results obtained in previous investigations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310407
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  • 8
    Electronic Resource
    Electronic Resource
    Generalized mixed finite element model for pre- and post-quasistatic buckling response of thin-walled framed structures (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 297-322 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Adopting an updated Lagrangian approach, the general framework for the fully non-linear analysis of thin-walled framed structures is developed using a simple, two-node, C0-model (HMB2). The governing equations are derived based on a consistent linearization of an incremental mixed variational principle of modified Hellinger/Reissner type with independent assumptions for displacement and strain fields. All coupled significant modes of deformations, i.e. stretching, bending, shear, torsion and warping, are accounted for in the generalized-beam theory employed. Emphasis is placed on devising effective solution procedures to deal with finite rotations in space, particularly with regard to their effect on the derivations of load-correction matrices corresponding to configuration-dependent externally applied forces/moments. The effectiveness and practical usefulness of present model are demonstrated through a number of test problems involving beam assemblages undergoing large displacements and rotations in space.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370208
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  • 9
    Electronic Resource
    Electronic Resource
    Effective modelling of spatial buckling of beam assemblages, accounting for warping constraints and rotation-dependency of moments (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 469-502 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, two-noded, finite element model for the three-dimensional buckling analysis of beam assemblages is developed. The underlying generalized-beam theory employed accounts for all coupled significant modes of deformations, including stretching, bending, shear and torsion, as well as warping. Its mixed formulation is of the two-field type, utilizing linear and constant interpolants for displacements and strain fields. Due considerations are given to the effect off inite rotations in space on the non-linear kinematic descriptions as well as the configuration-dependent behaviour of externally applied moment vectors of the conservative and non-conservative types. The performance of the model, and particularly the accuracy of its geometric and load-correction stiffnesses, is assessed in a fairly complete set of numerical simulations.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330303
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  • 10
    Electronic Resource
    Electronic Resource
    On the development of explicit robust schemes for implementation of a class of hyperelastic models in large-strain analysis of rubbers (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1237-1249 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The issue of developing effective and robust schemes to implement a class of the Ogden-type hypereiastic constitutive models, for large-strain analysis of rubber-like materials, is addressed. To this end, explicit forms for the corresponding material tangent-stiffness tensors are developed, and these are valid for the entire deformation range; i.e. with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of the complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials, which are becoming increasingly popular in recent years. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330609
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