ADINA Theory

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.




    On the Automatic Solution of Nonlinear Finite Element Equations

    Bathe, Klaus-Jürgen; Dvorkin, Eduardo N. Source: J. Computers & Structures, v 17, 871-879, 1983

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: An algorithm for the automatic incremental solution of nonlinear finite element equations in static analysis is presented. The procedure is designed to calculate the pre- and post-buckling/collapse response of general structures. Also, eigensolutions for calculating the linearized buckling response are discussed. The algorithms have been implemented and various experiences with the techniques are given.

    Keywords: nonlinear finite element equation, eigensolution, buckling, collapse




    A Simple and Effective Pipe Elbow Element—Some Nonlinear Capabilities

    Bathe, Klaus-Jürgen; Almeida, Carlos A.; Ho, Lee W. Source: J. Computers & Structures, v 17, 659-667, 1983.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: In some earlier communications we presented the formulation of a simple pipe elbow element for linear analysis. In this paper we extend this formulation to include some nonlinear effects. Elastic-plastic conditions can be modeled, and some kinematic nonlinearities (due to large displacement beam behavior) can also be represented. The results of some sample solutions are given to illustrate the use of the element.

    Keywords: pipe elbow element, finite element




    An Efficient Algorithm for Nonlinear Heat Transfer with Phase Changes

    Rolph, W. Donald III; Bathe, Klaus-Jürgen. Source: International Journal for Numerical Methods in Engineering, v 18, 119-134, 1982.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: A new, simple and effective finite element procedure is presented for the practical solution of heat transfer conditions with phase changes. In this method, a fixed finite element mesh is employed, and a relatively coarse finite element mesh and large time step can be used in the incremental solution. The results of various numerical studies using the algorithm are presented that demonstrate the effectiveness of the procedure.

    Keywords: nonlinear heat transfer, phase change, finite element




    A Simple and Effective Pipe Elbow Element—Pressure Stiffening Effects

    Bathe, Klaus-Jürgen; Almeida, Carlos A. Source: J. Appl. Mech., v 49, 914-916, 1982.

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

    Publisher: American Society of Mechanical Engineers

    Abstract: The objective in this paper is to show how a pipe element formulation can be extended in a very simple way to include internal pressure stiffening effects. As has been established experimentally and theoretically, the effect of the internal pressure on the stiffness of an elbow section can be significant when relatively thin pipes are considered.

    Keywords: pipe element, curved element, ovalization, pressure-stiffening




    On the Displacement Formulation of Torsion of Shafts with Rectangular Cross-section

    Bathe, Klaus-Jürgen; Chaudhary, Anil. Source: International Journal for Numerical Methods in Engineering, v 18, 1565-1568, 1982.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: The use of warping displacement functions for the torsional stiffness representation of beams with rectangular cross-sections is studied. These functions can directly be employed in the displacement-based formulation of Hermitian and isoparametric three-dimensional beam elements for linear, elastic-plastic or large displacement/large rotation analysis. the results of some studies are given to demonstrate the applicability and use of the proposed functions.

    Keywords: Hermitian beam element, isoparametric beam element, finite element




    A Simple and Effective Pipe Elbow Element—Interaction Effects

    Bathe, Klaus-Jürgen; Almeida, Carlos A., “A Simple and Effective Pipe Elbow Element—Interaction Effects”, J. Appl. Mech., v 49, 165-171, 1982.

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

    Publisher: American Society of Mechanical Engineers

    Abstract: Our elbow element presented in an earlier communication is enhanced to account for interaction effects between elbows and rigid flanges, elbows of different curvatures, and elbows joining straight pipe sections. The interaction effects are modeled by including the appropriate additional strain terms in the stiffness matrix formulation and by using a penalty procedure to enforce the continuity of the derivatives in the pipe skin radial displacements. The enhancement in the formulation has been implemented and the results of various sample analyses are presented.

    Keywords: pipe element, curved element, interaction effects, interior penalty

    On Nonlinear Dynamic Analysis Using Substructuring and Mode Superposition

    Bathe, Klaus-Jürgen; Gracewski, Sheryl. Source: J. Computers & Structures, v 13, 699-707, 1981.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The solution of nonlinear dynamic equilibrium equations using mode superposition and substructuring is studied. The objective is to design schemes that in some analyses can significantly decrease the computational effort involved when compared to a complete direct integration solution. Specific schemes for mode superposition analysis and substructuring are proposed. These techniques have been implemented in ADINA. The results of a few sample analyses are presented and recommendations are given on the use of these procedures in practical analysis.

    Keywords: nonlinear dynamic analysis, substructuring, mode superposition




    On Thermo-Elastic-Plastic Analysis of Heat Treatment Processes Including Creep and Phase Changes

    Rammerstorfer, F. G.; Fischer, D. F.; Mitter, W.; Bathe, K. J.; Snyder, M. D. Source: J. Computers & Structures, v 13, 771-779, 1981.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: A method is described for calculating the stresses in a body during heat-treatment and for calculating the remaining residual stress distribution. Special attention is given to the thermo-elastic-plastic material behaviour which is highly temperature-dependent. A pseudo-plasticity effect due to microstresses appearing during phase transformations is taken into account. The stress analysis of a cylinder is performed using ADINA. Calculated results are compared with results obtained experimentally.

    Keywords: heat treatment, residual stress distribution, thermo-elastic-plastic material, ADINA




    A Simple and Effective Element for Analysis of General Shell Structures

    Bathe, Klaus-Jürgen; Ho, Lee-Wing. Source: J. Computers & Structures, v 13, 673-681, 1981.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: A simple flat three-node triangular shell element for linear and nonlinear analysis is presented. The element stiffness matrix with 6 degrees-of-freedom per node is obtained by superimposing its bending and membrane stiffness matrices. An updated Lagrangian formulation is used for large displacement analysis. The application of the element to the analysis of various linear and nonlinear problems is demonstrated.

    Keywords: shell structure, finite element, updated Lagrangian formulation, nonlinear analysis




    The Application of Quasi-Newton Methods in Fluid Mechanics

    Engelman, M. S.; Strang, G.; Bathe, K. J. Source: International Journal for Numerical Methods in Engineering, v 17, 707-718, 1981.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: The use of quasi-Newton methods is studied for the solution of the nonlinear finite element equations that arise in the analysis of incompressible fluid flow. An effective procedure for the use of Broyden's method in finite element analysis is presented. The quasi-Newton method is compared with the commonly employed successive substitution and Newton-Raphson procedures, and it is concluded that the use of Broyden's method can constitute an effective solution strategy.

    Keywords: quasi-Newton methods, Broyden's method, finite element analysis, nonlinear finite element equation, incompressible fluid flow




    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 4

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