ADINA Theory

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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)

    Chinese translation of 2nd edition 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.

    A Solution Procedure for Thermo-Elastic-Plastic and Creep Problems

    Snyder, Mark D.; Bathe, Klaus-Jürgen. Source: J. Nuclear Engineering and Design, v 64, 49-80, 1981.

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

    Publisher: Elsevier Science B.V.

    Abstract: An effective solution procedure for finite element thermo-elastic-plastic and creep analysis with temperature-dependent material properties is presented. The material model employed is summarized, the basic iterative equations are developed and the solution procedure is theoretically analyzed and numerically tested for its stability and accuracy properties.

    Keywords: thermo-elastic-plastic analysis, creep analysis, finite element

    On Finite Element Large Displacement and Elastic-Plastic Dynamic Analysis of Shell Structures

    Ishizaki, Tairo; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 12, 309-318, 1980.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Finite element procedures for nonlinear dynamic analysis of shell structures are presented and assessed. Geometric and material nonlinear conditions are considered. Some results are presented that demonstrate current applicabilities of finite element procedures to the nonlinear dynamic analysis of two-dimensional shell problems. The nonlinear response of a shallow cap, an impulsively loaded cylindrical shell and a complete spherical shell is predicted. In the analyses the effects of various finite element modeling characteristics are investigated. Finally, solutions of the static and dynamic large displacement elastic-plastic analysis of a complete spherical shell subjected to external pressure are reported. The effect of initial imperfections on the static and dynamic buckling behavior of this shell is presented and discussed.

    Keywords: shell structure, finite element, dynamic buckling, spherical shell

    On Some Current Procedures and Difficulties in Finite Element Analysis of Elastic-Plastic Response

    Bathe, Klaus-Jürgen; Snyder, Mark D.; Cimento, Arthur P.; Rolph, W. Donald III. Source: J. Computers & Structures, v 12, 607-624, 1980.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Some finite element procedures for the analysis of elastic-plastic response are presented and critically discussed: a consistent large displacement and large strain formulation is summarized, a versatile elastic-plastic model applicable to the analysis of metals and geological materials is presented, the choice of an appropriate finite element discretization is discussed, and some effective methods for the solution of the nonlinear finite element equations are briefly summarized. Finally, to illustrate the strength and shortcomings of the procedures used, the results of some sample analyses are presented and evaluated.

    Keywords: finite element, elastic-plastic response

    Study of Three-Node Triangular Plate Bending Elements

    Batoz, Jean-Louis; Bathe, Klaus-Jürgen; Ho, Lee-Wing. Source: International Journal for Numerical Methods in Engineering, v 15, 1771-1812, 1980.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: An assessment of flat triangular plate bending elements with displacement degrees-of-freedom at the three corner nodes only is presented, with the purpose of identifying the most effective for thin plate analysis. Based on a review of currently available elements, specific attention is given to the theoretical and numerical evaluation of three triangular 9 degrees-of-freedom elements; namely, a discrete Kirchhoff theory (DKT) element, a hybrid stress model (HSM) element and a selective reduced integration (SRI) element. New and efficient formulations of these elements are discussed in detail and the results of several example analyses are given. It is concluded that the most efficient and reliable three-node plate bending elements are the DKT and HSM elements.

    Keywords: discrete Kirchhoff theory element, hybrid stress model element, selective reduced integration element, plate bending element

    An Accelerated Subspace Iteration Method

    Bathe, Klaus-Jürgen; Ramaswamy, Seshadri. Source: J. Comp. Meth. In Appl. Mech. and Eng., v 23, 313-331, 1980.

    ISSN: 0045-7825

    Publisher: Elsevier Science B.V.

    Abstract: The subspace iteration method for solving symmetric eigenproblems in computational mechanics is considered. Effective procedures for accelerating the convergence of the basic subspace iteration method are presented. The accelerated subspace iteration method has been implemented and the results of some demonstrative sample solutions are presented and discussed.

    Keywords: subspace iteration method, finite element, eigenproblem

    On Effective Implicit Time Integration in Analysis of Fluid - Structure Problems

    Bathe, Klaus-Jürgen; Sonnad, Vijay. Source: International Journal for Numerical Methods in Engineering, v 15, 943-948, 1980.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: An effective solution of fluid-structure systems (and 'stiff and flexible domains' in general) can frequently be calculated using an implicit time integration for the complete structural model with a lumped mass idealization and the recently proposed BFGS method. In the analysis procedure used, the response is calculated with implicit time integration for the fluid and the structure without setting up a stiffness matrix of the fluid, and by satisfying the dynamic equilibrium equations using the BFGS iterations.

    Keywords: fluid structure interaction, FSI, BFGS method, time integration

    Some Practical Procedures for the Solution of Nonlinear Finite Element Equations

    Bathe, Klaus-Jürgen; Cimento, Arthur P. Source: J. Computer Meth. In Applied Mech. and Eng., v 22, 59-85, 1980.

    ISSN: 0045-7825

    Publisher: Elsevier Science B.V.

    Abrstract: Procedures for the solution of incremental finite element equations in practical nonlinear analysis are described and evaluated. The methods discussed are employed in static analysis and in dynamic analysis using implicit time integration. The solution procedures are implemented, and practical guidelines for their use are given.

    Keywords: nonlinear finite element, implicit time integration, dynamic analysis

    A Simple and Effective Pipe Elbow Element—Linear Analysis

    Bathe, Klaus-Jürgen; Almeida, Carlos A. Source: J. Applied Mech., v 47, 93-100, September 1980.

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

    Publisher: American Society of Mechanical Engineers

    Abstract: The formulation of a new, simple, and effective displacement-based pipe bend element is presented. The displacement assumptions are axial, torsional, and bending displacements that vary cubically along the axis of the elbow with plane sections remaining plane, and a generalization of the von Karman pipe radial displacement patterns to include the ovalization effects. The amount of ovalization varies cubically along the elbow with full compatibility between elbows. The pipe bend element has been implemented, and the results of various sample analyses are presented, which illustrate the effectiveness of the element.

    Keywords: pipe element, curved element, ovalization effects

    A Geometric and Material Nonlinear Plate and Shell Element

    Bathe, Klaus-Jürgen; Bolourchi, Saïd. Source: J. Computers & Structures, v 11, 23-48, 1980.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: A displacement-based versatile and effective finite element is presented for linear and geometric and material nonlinear analysis of plates and shells. The element is formulated by interpolating the element geometry using the mid-surface nodal point coordinates and mid-surface nodal point normals. A total and an updated Lagrangian formulation are presented, that allow very large displacements and rotations. In linear analysis of plates, the element reduces to well-established plate bending elements based on classical plate theory, whereas in linear analysis of shells and geometrically nonlinear analysis of plates and shells by use of the element, in essence, a very general shell theory is employed. The element has been implemented as a variable-number-nodes element and can also be employed as a fully compatible transition element to model shell intersections and shell-solid regions. In the paper various sample solutions are presented that illustrate the effectiveness of the element in practical analysis.

    Keywords: nonlinear shell element, classical plate theory, finite element

    On Three-Dimensional Nonlinear Analysis of Concrete Structures

    Bathe, Klaus-Jürgen; Ramaswamy, Seshadri. Source: J. Nuclear Engineering and Design, v 52, 385-409, 1979.

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

    Publisher: Elsevier Science B.V.

    Abstract: Solution capabilities for three-dimensional geometric and material nonlinear finite element analysis of concrete structures are presented. The concrete material is modeled including triaxial nonlinear stress-strain behavior, tensile cracking, compression crushing and strain-softening. The objective in this work was the development of a practical nonlinear concrete analysis capability. The material model can also be employed to represent some rock materials. The results of various sample analyses are given, in which the stability and accuracy of the finite element representations have been studied.

    Keywords: nonlinear analysis, concrete structure

    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

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