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)

    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.

    On the Calibration of the Electrical Potential Technique for Monitoring Crack Growth Using Finite Element Methods

    Ritchie, R. O.; Bathe, Klaus-Jürgen. Source: J. of Fracture, v 15, 47-55, 1979.

    ISSN: 0376-9429 (print); 1573-2673 (online)

    Publisher: Springer

    Abstract: Finite element analysis procedures are utilized to provide theoretical calibration curves for the electrical potential crack-monitoring system as applied to single-edge-notch (SEN) and compact tension (CT) fracture specimens. The results are compared to existing calibrations for such test piece geometries derived using experimental, electrical analog and analytical (conformal mapping) procedures.

    Keywords: finite element, crack growth

    Finite Element Formulation and Solution of Nonlinear Heat Transfer

    Bathe, Klaus-Jürgen; Khoshgoftaar, Mohammad R. Source: J. Nuclear Engineering and Design, v 51, 389-401, 1979.

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

    Publisher: Elsevier Science B.V.

    Abstract: A general and effective finite element formulation for analysis of nonlinear steady-state and transient heat transfer is presented. Heat conduction conditions, and convection and radiation boundary conditions are considered. The solutions of the incremental heat transfer equations is achieved using Newton-Raphson iteration, and in transient analysis using a one-step α-family time integration scheme. The stability and accuracy of the time integration is discussed. The solution techniques have been implemented, and the results of various sample solutions are discussed and evaluated.

    Keywords: finite element, nonlinear heat transfer, Newton-Raphson iteration

    Large Displacement Analysis of Three-Dimensional Beam Structures

    Bathe, Klaus-Jürgen; Bolourchi, Saïd. Source: International Journal for Numerical Methods in Engineering, v 14, 961-986, 1979.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: An updated Lagrangian and a total Lagrangian formulation of a three-dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.

    Keywords: beam structure, updated Lagrangian formulation, total Lagrangian formulation, finite element

    Finite Element Free Surface Seepage Analysis Without Mesh Iteration

    Bathe, Klaus-Jürgen; Khoshgoftaar, Mohammad R. Source: J. of Num. and Anal. Methods in Geomechanics, v 3, 13-22, 1979.

    ISSN: 0363-9061 (print); 1096-9853 (online)

    Publisher: John Wiley & Sons, Ltd.

    Abstract: An effective solution procedure for the finite element analysis of free surface seepage problems is presented. The solution algorithm employs a non-linear permeability description of the material and avoids iteration with the finite element mesh. The results and experiences obtained in the analyses of some problems are presented to demonstrate the usefulness of the technique.

    Keywords: seepage analysis, finite element

    On Transient Analysis of Fluid-Structure Systems

    Bathe, Klaus-Jürgen; Hahn, W. F. Source: J. Computers & Structures, v 10, 383-391, 1978.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Finite element procedures for the dynamic analysis of fluid-structure systems are presented and evaluated. The fluid is assumed to be inviscid and compressible and is described using an updated Lagrangian formulation. Variable-number-nodes isoparametric two- and three-dimensional elements with lumped or consistent mass idealization are employed in the finite element discretization, and the incremental dynamic equilibrium equations are solved using explicit or implicit time integration. The solution procedures are applied to the analysis of a number of fluid-structure problems including the nonlinear transient analysis of a pipe test.

    Keywords: finite element, fluid structure interaction, updated Lagrangian formulation

    Some Computational Capabilities for Nonlinear Finite Element Analysis

    Bathe, Klaus-Jürgen; Bolourchi, Saïd; Ramaswamy, Seshadri; Snyder, Mark D. Source: J. Nuclear Engineering and Design, v 46, 429-455, 1978.

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

    Publisher: Elsevier Science B.V.

    Abstract: The computational capabilities available in the current version of the computer program ADINA for stress analysis of structures and continua are described. The program can be employed effectively for various linear and nonlinear static and dynamic finite element analyses. The solutions of some problems using ADINA are presented to indicate the solution capabilities of the program.

    Keywords: nonlinear finite element analysis, stress analysis, ADINA

    On Finite Element Analysis of Pipe Whip Problems

    Ma, S. M.; Bathe, Klaus-Jürgen. Source: J. Nuclear Engineering and Design, v 37, 413-430, 1976.

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

    Publisher: Elsevier Science B.V.

    Abstract: The nonlinear dynamic finite element solution of pipe whip problems is presented. The finite element modelling used, the step-by-step incremental solution of the nonlinear equations of motion and design considerations are discussed. The influence of various physical parameters on the response of the pipe and the restraint, and the effects of using different finite element models are considered. Specific emphasis is directed to the verification of the accuracy of the solutions obtained using energy balance checks.

    Keywords: pipe whip, finite element

    Elastic-Plastic Large Deformation Static and Dynamic Analysis

    Bathe, Klaus-Jürgen; Ozdemir, Haluk. Source: J. Computers & Structures, v 6, no. 2, 81, 1976.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The problem of formulating and numerically implementing finite element elastic-plastic large deformation analysis is considered. In general, formulations can use different kinematic descriptions and assumptions in the material law, and analysis results can vary by a large amount. In this paper, starting from continuum mechanics principles, two consistent formulations for elastic-plastic large deformation analysis are presented in which either the initial configuration or the current configuration is used for the description of static and kinematic variables. The differences between the formulations are clearly identified and it is established that, depending on the elastic-plastic material description, identical numerical results can be obtained. If, in practice, certain constitutive transformations are not included, the differences in the analysis results are relatively small in large displacement but small strain problems. The formulations have been implemented and representative sample analyses of large deformation response of beams and shells are presented.

    Keywords: finite element, elastic-plastic large deformation analysis, beams, shells

    Finite Element Formulations for Large Deformation Dynamic Analysis

    Bathe, Klaus-Jürgen; Ramm, Ekkehard.; Wilson, Edward L.. Source: International Journal for Numerical Methods in Engineering, v 9, 353-386, 1975.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: Starting from continuum mechanics principles, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non-linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber-like) and hypoelastic elastic-plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.

    Keywords: continuum mechanics, finite element, large displacements, large strains, material non-linearities

    Finite Element Analysis of Linear and Nonlinear Heat Transfer

    Wilson, Edward L.; Bathe, Klaus-Jürgen; Peterson, Fred E. Source: J. Nuclear Engineering and Design, v 29, 110-124, 1974.

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

    Publisher: Elsevier Science B.V.

    Abstract: The finite element method is rapidly becoming a popular procedure for the evaluation of thermal stresses in complex structures. In linear analysis the method has been used extensively and has been coupled with stress analysis computer programs in order to automate thermal stress analysis. However, for the method to be effective, efficient numerical techniques need to be used. The purpose of this paper is to survey the recent developments in linear heat transfer analysis and, specifically, to present the techniques that permit the practical analysis of large and complex three-dimensional heat conduction problems. Typical practical problems are described and solution times are presented. In the analysis of systems with nonlinear thermal properties the method has had limited application. In this paper the general formulation of the incremental equations used in nonlinear heat transfer analysis are presented. An efficient numerical solution of the equations is given. Several types of nonlinearities are discussed and the solutions of some typical problems are presented.

    Keywords: finite element analysis, nonlinear heat transfer

    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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