Theory Used in ADINA

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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



    To Enrich Life
    (Sample pages here)

  • To Download — Second Edition of the Book "Finite Element Procedures" (6th 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
  • CompFSM
    Computational Fluid and Solid Mechanics 2001-2011
    (6 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

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  • For publications that reference the use of ADINA, please see here.

    An Infinite Element for Analysis of Transient Fluid-Structure Interactions

    Olson, Lorraine G; Bathe, Klaus-Jürgen. Source: J. Engineering Computations, v 2, 319-329, 1985.

    ISSN: 0264-4401

    Publisher: MCB UP Ltd

    Abstract: An infinite element based on the doubly asymptotic approximation (DAA) for use in finite element analysis of fluid—structure interactions is presented. Fluid finite elements model the region near the solid. Infinite elements account for the effects of the outer fluid on the inner region. The DAA-based infinite elements involve an approximate calculation of the added mass using static mapped infinite elements, plus a consistent damping term. Simple test analyses for a range of fluid properties demonstrate the performance of the solution technique. The analyses of a Helmholtz resonator (open pipe) and a circular plate in water indicate the practical use of the solution approach.

    Keywords: fluid structure interaction, infinite element

    Analysis of Fluid-Structure Interactions—A Direct Symmetric Coupled Formulation Based on a Fluid Velocity Potential

    Olson, Lorraine G; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 21, 21-32, 1985.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We present a symmetric finite element method for solving fluid-structure interaction problems. The formulation uses velocity potentials and a hydrostatic pressure as unknowns in each fluid region, and displacements as unknowns in the solid. The hydrostatic pressure is an unknown variable at only one node per fluid region. A C matrix (multiplied by time derivatives of the nodal variables, but not a damping matrix) enforces the coupling between the variables. The resulting matrix equations are banded and symmetric, making them easy to incorporate in standard displacement-based finite element codes. Several test cases indicate that this approach works well for static, transient, and frequency analyses.

    Keywords: fluid structure interaction, coupling

    Studies of Finite Element Procedures—On Mesh Selection

    Sussman, Theodore; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 21, 257-264, 1985.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: This is a tutorial paper on the use of finite element procedures in engineering practice. First, we discuss some basic concepts used to identify whether a finite element mesh has provided an accurate solution for a linear elastic static analysis, and hence when mesh refinement is necessary. We then demonstrate these concepts by presenting in detail a finite element analysis of an axisymmetric pressure vessel subjected to an internal pressure load. The goal of the analysis is the accurate determination of stresses on a prespecified line. We show that a mesh of 240 six-node and eight-node isoparametric finite elements, when the stresses are sampled at the nodes, can accurately determine the desired stresses.

    Keywords: finite element, mesh selection

    A Four-Node Plate Bending Element Based on Mindlin/Reissner Plate Theory and a Mixed Interpolation

    Bathe, Klaus-Jürgen; Dvorkin, Eduardo N. Source: International Journal for Numerical Methods in Engineering, v 21, 367-383, 1985.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: This communication discusses a 4-node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4-node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.

    Keywords: Mindlin/Reissner plate theory, shell element

    A Solution Method for Planar and Axisymmetric Contact Problems

    Bathe, Klaus-Jürgen; Chaudhary, Anil. Source: International Journal for Numerical Methods in Engineering, v 21, 65-88, 1985.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: A solution procedure for the analysis of planar and axisymmetric contact problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure are the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm.

    Keywords: contact problem, traction, large deformation

    A Continuum Mechanics Based Four-Node Shell Element for General Nonlinear Analysis

    Dvorkin, Eduardo N; Bathe, Klaus-Jürgen. Source: Engineering Computations, v 1, 77-88, 1984.

    ISSN: 0264-4401

    Publisher: MCB UP Ltd

    Abstract: A new four-node (non-flat) general quadrilateral shell element for geometric and material non-linear analysis is presented. The element is formulated using three-dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

    Keywords: continuum mechanics, shell element

    A Study of Displacement-Based Fluid Finite Elements for Calculating Frequencies of Fluid and Fluid-Structure Systems

    Olson, Lorraine G; Bathe, Klaus-Jürgen. Source: J. Nuclear Engineering and Design, v 76, 137-151, 1983.

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

    Publisher: Elsevier Science B.V.

    Abstract: The widely-used displacement-based finite element formulation for inviscid, compressible, small displacement fluid motions is examined, with the specific objective of calculating fluid-structure frequencies. It is shown that the formulation can be employed with confidence to predict the static response of fluids. Also the resonant frequencies of fluids in rigid cavities and the frequencies of fluids in flexible boundaries are solved successfully if a penalty on rotations is included in the formulation. However, the reason for writing this paper is that problems involving structures moving through fluids that behave almost incompressibly - such as an ellipse vibrating on a spring in water - could not be solved satisfactorily, for which a general explanation is given.

    Keywords: displacement-based finite element, fluid structure frequency

    On Elastic-Plastic Analysis of I-Beams in Bending and Torsion

    Bathe, Klaus-Jürgen; Wiener, Philippe M. Source: J. Computers & Structures, v 17, 711-718, 1983.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The use of various models is studied to represent an I-beam for its elastic-plastic bending and torsional response including warping. The rectangular cross-section 2-node Hermitian beam element, the 4-node isoparametric beam element, and the 9-node isoparametric shell element of ADINA with constraint equations are used to establish the models. The linear elastic and elastic-plastic solutions of a cantilevered I-beam are given, and it is concluded that the I-beam model constructed with the isoparametric beam element can be used for general analysis.

    Keywords: I-beam, Hermitian beam element, isoparametric shell element

    On the Analysis of Creep Stability and Rupture

    Walczak, Jan; Sieniawski, Jan; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 17, 783-792, 1983.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The analysis of problems involving creep material failure and creep buckling is considered. Creep buckling analyses are presented for some columns. A finite element creep rupture analysis of a rotating disc is performed and the results are compared with other solutions. Calculations are also reported for titanium notched tensile specimens and the numerical results are compared with experimental creep investigations, in which micrographs have been taken to study the rupture mechanisms.

    All numerical solutions have been carried out using ADINA in which a creep-damage material law and the updated-Lagrangian-Jaumann formulation for the thermo-elastic-plastic and creep material model were implemented.

    Keywords: creep, rupture, buckling, finite element, ADINA, updated-Lagrangian-Jaumann formulation

    Our Discrete Kirchhoff and Isoparametric Shell Elements for Nonlinear Analysis—An Assessment

    Bathe, Klaus-Jürgen; Dvorkin, Eduardo N.; Ho, Lee W, Source: J. Computers & Structures, v 16, 89-98, 1983.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The theory and use of two effective shell elements are briefly surveyed, assessed and compared. The elements considered are our high-order (degenerate) isoparametric shell element and our simple flat triangular element, which both can be employed for analysis of large displacement/large rotation and plastic response of general shell structures. Specific emphasis is placed on the theoretical differences between the elements and some resulting practical consequences.

    Keywords: discrete Kirchhoff shell element, isoparametric shell element, shell structure

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