ADINA Theory

Page 6

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)


  • To Download — Second Edition of the Book "Finite Element Procedures" (4th printing)

    You are welcome to download the second edition of the book, 4th printing, however, please note that the book is copyrighted and should only be used in the same manner as a purchased hard-copy of the book.

    Improved versions will be made available here, from time to time, as the 5th printing, and so on.

    "Finite Element Procedures", 2nd Edition (.pdf)

    Solutions to exercises in the book "Finite Element Procedures", 2nd Edition, 2014 are given in this manual (.pdf)

    The Chinese translation of the 2nd edition is also available: Vol. 1 Vol. 2

  • 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.

    Keywords: mixed finite element formulation, Stokes flow problem, error bound

    Nonlinear Analysis of Concrete Structures

    Bathe, Klaus-Jürgen; Walczak, Jan; Welch, Alan; Mistry, Nagin. Source: J. Computers & Structures, v 32, No. 3/4, 563-590, 1989.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Solution capabilities for two- and three-dimensional nonlinear finite element analysis of concrete structures are presented. The concrete material is modeled including the triaxial nonlinear stress-strain behavior, tensile cracking, tension-stiffening, compression crushing and strain-softening. The results of various sample analyses are given to demonstrate the constitutive model and the solution strategies. These analyses include the response predictions of a test beam and of small scale models of two reactor vessels.

    Keywords: nonlinear analysis, concrete structure, constitutive model

    Some Advances in the Analysis of Semi-deformable Media

    Sussman, Theodore; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 30, No. 1/2, 105-112, 1988.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Semi-deformable media are materials in which certain modes of deformation are prohibited (for example, incompressible materials). The displacement/pressure (u/p) finite element formulation can be used to effectively analyze semi-deformable media. We summarize the basic characteristics of the formulation and present some representative numerical examples in linear and nonlinear analysis.

    Keywords: semi-deformable media, finite element

    A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis

    Sussman, Theodore; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 26, 357-409, 1987.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We introduce a displacement-pressure (u/p) finite element formulation for the geometrically and materially nonlinear analysis of compressible and almost incompressible solids. The (u/p) formulation features the a priori replacement of the pressure computed from the displacement field by a separately interpolated pressure; this replacement is performed without reference to any specific material description. Considerations for incremental nonlinear analysis (including contact boundary conditions) are discussed and various (u/p) elements are studied. Numerical examples show the performance of the (u/p) formulation for two- and three-dimensional problems involving isotropic, orthotropic, rubber-like and elasto-plastic materials.

    Keywords: finite element, nonlinear analysis, isotropic material; orthotropic material, rubber-like material, elasto-plastic material

    Studies of Finite Element Procedures—Stress Solution of a Closed Elastic Strain Path with Stretching and Shearing Using the Updated Lagrangian Jaumann Formulation

    Kojić, Miloš; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 26, 175-179, 1987.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The updated Lagrangian Jaumann formulation is used for the analysis of an elastic closed strain path involving stretching and shearing. The analytical stress solution for each phase of the strain path is given and the final stresses at zero strain are calculated.

    We do not present any new concept or procedures but study an interesting example solution that gives insight into the use of the updated Lagrangian Jaumann formulation.

    Keywords: finite element, strain path, updated Lagrangian Jaumann formulation

    Thermo-Elastic-Plastic and Creep Analysis of Shell Structures

    Kojić, Miloš; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 26, 135-143, 1987.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The effectivc-stress-function algorithm previously proposed for general 2-D and 3-D thermo-elastic-plastic and creep analysis is specialized to the stress and strain conditions of shell and beam structures. Von Mises plasticity with isotropic and kinematic hardening assumptions and the potential theory of creep are considered. The governing equations to compute the plastic and creep effects are given, and the numerical results obtained in the analysis of some demonstrative beam and shell problems are presented.

    Keywords: shell structure, creep analysis, thermo-elastic-plastic analysis

    The 'Effective-Stress-Function' Algorithm for Thermo-Elasto-Plasticity and Creep

    Kojić, Miloš; Bathe, Klaus-Jürgen. Source: Int. Journal for Numerical Methods in Engineering, v 24, 1509-1532, 1987.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: An algorithm for stable and accurate computations of stresses in finite element thermo-elastic-plastic and creep analysis of metals is presented. The effective-stress-function algorithm solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective-stress-function: a functional relationship which involves as unknown only the effective stress. The derivation of the effective-stress-function for thermo-elasto-plasticity conditions, including creep, for 2-D and 3-D analysis is presented, and the algorithmic steps of the stress solution are discussed. For use in the stiffness matrix a tangent material stress-strain relationship is evaluated consistent with the effective-stress-function algorithm. The solution of some demonstrative problems shows the effectiveness of the solution procedure

    Keywords: effective-stress-function algorithm, finite element, thermo-elastic-plastic analysis, creep analysis

    Causes and Consequences of Nonuniqueness in an Elastic-Perfectly-Plastic Truss

    Hodge, P. G. Jr.; Bathe, Klaus-Jürgen; Dvorkin, Eduardo N. Source: Journal of Applied Mechanics, v 53, 235-241, 1986.

    ISSN: 0021-8936 (print); 1528-9036 (online)

    Publisher: American Society of Mechanical Engineers

    Abstract: A complete solution to collapse is given for a three-bar symmetric truss made of an elastic/perfectly-plastic material, using linear statics and kinematics, and the solution is found to be partially nonunique in the range of contained plastic deformation. The introduction of a first-order deviation from symmetry and/or the inclusion of first order nonlinear terms in the equilibrium equations is found to restore uniqueness. The significance of these effects is analyzed and discussed from mathematical, physical, modeling, computational and engineering points of view.

    Keywords: elasto-plasticity, collapse analysis, uniqueness of solution, truss structure

    Finite Elements in CAD and ADINA

    Bathe, Klaus-Jürgen. Source: Nuclear Engineering and Design, 57-67, 1986.

    ISSN: 0029-5493 (print); 1872-759X (online)

    Publisher: Elsevier Science B.V.

    Abstract: The use of finite element methods in computer-aided-design — CAD — is discussed. Some current capabilities are presented and important future developments are outlined. The discussion focusses on the use of the ADINA program in CAD applications.

    Keywords: finite element, CAD, ADINA

    Studies of Finite Element Procedures - Stress Band Plots and the Evaluation of Finite Element Meshes

    Sussman, Theodore; Bathe, Klaus-Jürgen. Source: J. Engineering Computations, v 3, No. 3, 178-191, 1986.

    ISSN: 0264-4401

    Publisher: MCB UP Ltd

    Abstract: We describe a visual method—stress band plots—for displaying the stress solution within a two-dimensional finite element mesh. The stress band plots differ from conventional stress contour plots because stress band plots display unaveraged stresses (the stresses are computed directly from the solution variables) and stress discontinuities in the finite element solution are directly displayed. Stress band plots are useful in judging the accuracy of a finite element solution, in the comparison of different finite element solutions and during mesh refinement. These uses are demonstrated in an axisymmetric pressure vessel analysis.

    Keywords: finite element, stress band plot

    A Formulation of General Shell Elements—The Use of Mixed Interpolation of Tensorial Components

    Bathe, Klaus-Jürgen; Dvorkin, Eduardo N. Source: Int. Journal for Numerical Methods in Engineering, v 22, 697-722, 1986.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: We briefly discuss the requirements on general shell elements for linear and nonlinear analysis in practical engineering environments, and present our approach to meet these needs. We summarize and give further insight into our formulation of a 4-node shell element using a mixed interpolation of tensorial components, and present a new 8-node element using this approach. Specific attention is given to the general applicability of the elements and their efficient use in practice.

    Keywords: shell element, mixed interpolation of tensorial components

    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 6

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