ADINA Theory

Page 7

For the theory used in ADINA, for structural analysis, CFD, and FSI, and also for the philosophy used in the program development, please refer to the publications given here:

  • Books by K.J. Bathe and co-authors


    Finite Element Procedures
     

    Finite Element Procedures in Engineering Analysis

    Numerical Methods in Finite Element Analysis
     


    The Mechanics of Solids and Structures — Hierarchical ...


    The Finite Element Analysis of Shells — Fundamentals


    Inelastic Analysis of Solids and Structures

     
     
    To Enrich Life
    (Sample pages here)
     

     

  • Proceedings edited by K.J. Bathe


    Computational Fluid and Solid Mechanics 2001-2011
    (6 volumes)

    Nonlinear Finite Element Analysis and ADINA: 1977-1999
    (12 volumes)


  • Theory and Modeling Guides distributed on the ADINA Installation CD.
    These manuals describe in short form the theory used in ADINA Structures, Thermal, CFD and EM, and give hints for modeling problems correctly. For ADINA users: manuals

  • Papers on the Development of Finite Element Methods, with some of these Papers Related to ADINA

    Some papers on the Theory used in ADINA (latest on Page 14):
    Page 14 Page 13 Page 12 Page 11 Page 10 Page 9 Page 8
    Page 7 Page 6 Page 5 Page 4 Page 3 Page 2 Page 1
     
  • For publications that reference the use of ADINA, please see here.

    An Arbitrary Lagrangian-Eulerian Velocity Potential Formulation for Fluid-Structure Interaction

    Nitikitpaiboon, C.; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 47, No, 4/5, 871-891, 1993.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Finite clement formulations for fluid-structure interaction, assuming an inviscid fluid, can be classified into two major categories: displacement-based formulations and potential-based formulations. Although displacement-based formulations have been used widely, the methods suffer from the presence of spurious circulation modes and locking behavior. Potential-based formulations are inherently irrotational and do not have the difficulties of the displacement-based formulations. Nevertheless most of the applications of these methods are still limited to cases with relatively small motions. We introduce in this paper an arbitrary Lagrangian-Eulerian formulation using the velocity potential and the density as fluid variables. The formulation can be applied to problems in which the fluid undergoes very large boundary motions and can be used equally well for both compressible and incompressible fluids. 

    Keywords: arbitrary Lagrangian-Eulerian formulation, locking behaviour, fluid structure interaction, finite element




    Adaptive Finite Element Analysis of Large Strain Elastic Response

    Kato, K.; Lee, Nam-Sua; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 47, No. 4/5, 829-855, 1993.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Some basic studies and developments for adaptive procedures in large strain finite element analysis are presented: an evaluation of higher-order elements, two pointwise indicators for errors in stresses, a mesh generator for remeshing on the deformed configuration of the body, and a general mapping scheme for transferring solution variables across models. The methods discussed constitute the ingredients of a proposed adaptive process that is demonstrated in solutions of two-dimensional stress analyses of rubber-like materials including contact conditions. 

    Keywords: adaptive finite element analysis, large strain, rubber-like material




    The Inf-Sup Test

    Chapelle, Dominique; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 47, No. 4/5, 537-545, 1993.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We briefly review the inf-sup condition for the finite element solution of problems in incompressible elasticity, and then propose a numerical test on whether the inf-sup condition is passed. The evaluation of elements with this test is simple, and various results are presented. This inf-sup test will prove useful for many discretizations of constrained variational problems.  

    Keywords: inf-sup test, constrained variational problem




    Higher-Order MITC General Shell Elements

    Bucalem, Miguel Luiz; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical Methods in Engineering, v 36, 3729-3754, 1993.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: Two mixed-interpolated general shell finite elements for non-linear analysis-a 9-node element and a 16-node element-are presented. The elements are based on the Mixed Interpolation of Tensorial Components (MITC) approach in which the covariant strain component fields for the in-plane and shear actions are interpolated and tied to the also interpolated displacement field. Both the 9-node element, referred to as the MITC9 element, and the 16-node element, referred to as the MITC16 element, are tested numerically and found to have high predictive capabilities.  

    Keywords: Mixed Interpolation of Tensorial Components, MITC, shell element




    Effects of Element Distortions on the Performance of Isoparametric Elements

    Lee, Nam-Sua; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical Methods in Engineering, v 36, 3553-3576, 1993.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: We discuss the effects of element distortions on the performance of displacement-based isoparametric quadrilateral finite elements. Suitable example problems for both the Lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions. The effects of angular and curved-edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields. We then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution. The conclusion is that the Lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use.

    Keywords: isoparametric element, finite element, Lagrangian element




    On the Treatment of Inequality Constraints Arising from Contact Conditions in Finite Element Analysis

    Eterovic, Adrian Luis; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 40, No. 2, 203-209, 1991.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Existing methods for the analysis of contact problems deal with the inequality constraints arising from contact conditions by means of an implicit iteration on all constraints. This paper presents a formulation for contact problems with friction for large deformations where all inequality constraints are enforced explicitly. A robust solution technique for the resulting system of nonlinear equations can then be used. This approach admits the use of line search procedures to enlarge the region of convergence.   

    Keywords: finite element, contact condition, line search procedure




    A Note on the Use of the Additive Decomposition of the Strain Tensor in Finite Deformation Inelasticity

    Eterovic, Adrian Luis; Bathe, Klaus-Jürgen. Source: J. Comp. Methods in Applied Mech. and Eng., v 93, 31-38, 1991.

    ISSN: 0045-7825

    Publisher: Elsevier Science B.V.

    Abstract: This note explores some consequences of the assumption of the additive decomposition of the strain tensor in the formulation of constitutive equations for finite deformation inelastic analysis. It is shown that the incremental elastic response can depend on the prior inelastic deformations, and explicit formulas are given that quantify this effect.   

    Keywords: strain tensor, finite deformation elasticity, constitutive equation




    Displacement and Stress Convergence of the MITC Plate Bending Elements

    Bathe, Klaus-Jürgen; Bucalem, Miguel Luiz; Brezzi, Franco. Source: J. Eng. Computations, v 7, no. 4, 291-302, 1990.

    ISSN: 0264-4401

    Publisher: MCB UP Ltd

    Abstract: We briefly summarize the theoretical formulations of our MITC plate bending elements and then present numerical convergence results. The elements are based on Reissner-Mindlin plate theory and a mixed-interpolation of the transverse displacement, section rotations and transverse shear strain components. We consider our 4, 9 and 16-node quadrilateral elements and our 7 and 12-node triangular elements. The theoretical and numerical results indicate the high reliability and effectiveness of our elements.

    Keywords: MITC plate bending element, Reissner-Mindlin




    A Hyperelastic-Based Large Strain Elasto-Plastic Constitutive Formulation with Combined Isotropic-Kinematic Hardening Using the Logarithmic Stress and Strain Measures

    Eterovic, Adrian Luis.; Bathe, Klaus-Jürgen. Source: Int. J. Numerical Methods in Engineering, v 30, 1099-1114, 1990.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: This paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity. The combined isotropic-kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions: (i) the formulation is hyperelastic based, (ii) the stress-strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the Hencky strain tensor and its elastic work conjugate stress tensor, and (iii) the multiplicative decomposition of the deformation gradient is adopted. Since no stress rates are present, the formulation is, of course, numerically objective in the time integration. It is shown that the model gives adequate physical behaviour, and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor.

    Keywords: hyperelastic, isotropic-kinematic hardening




    A Discourse on the Stability Conditions for Mixed Finite Element Formulations

    Brezzi, Franco; Bathe, Klaus-Jürgen. Source: J. Computer Methods in Applied Mechanics and Engineering, v 82, 27-57, 1990.

    ISSN: 0045-7825

    Publisher: Elsevier Science B.V.

    Abstract: We discuss the general mathematical conditions for solvability, stability and optimal error bounds of mixed finite element discretizations. Our objective is to present these conditions with relatively simple arguments. We present the conditions for solvability and stability by considering the general coefficient matrix of mixed finite element discretizations, and then deduce the conditions for optimal error bounds for the distance between the finite element solutions and the exact solution of the mathematical problem. To exemplify our presentation we consider the solutions of various example problems. Finally, we also present a numerical test that is useful to identify numerically whether, for the solution of the general Stokes flow problem, a given finite element discretization satisfies the stability and optimal error bound conditions.


    Some papers on the Theory used in ADINA (latest on Page 14):
    Page 14 Page 13 Page 12 Page 11 Page 10 Page 9 Page 8
    Page 7 Page 6 Page 5 Page 4 Page 3 Page 2 Page 1
     

    Page 7

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