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ADINA
Structures, Heat Transfer and CFD
ADINA Theory

Page 10

Theory Used in ADINA

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:

  • Theory and Modeling Guides distributed on the ADINA Installation CD.
    These manuals describe in short form the theory used in ADINA Structures, Thermal, and CFD, and give hints for modeling problems correctly.

  • K.J. Bathe, Finite Element Procedures, Prentice Hall, 1996
    This book gives in various chapters the theory used in the ADINA programs, with many worked out example solutions. The book also describes the philosophy used in the program development — that a strong mathematical foundation and reliability of the methods is very important.

  • K.J. Bathe, To Enrich Life, 2007
    This book tells about the life of the founder of ADINA R & D, Prof. K.J. Bathe, M.I.T., and the history and philosophy of the ADINA program development. Some pages are given here.

  • Papers on the Theory used in ADINA

    Some papers on the Theory used in ADINA:
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    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




    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




    Some papers on the Theory used in ADINA:
    Page 1 Page 2 Page 3 Page 4 Page 5 Page 6
    Page 7 Page 8 Page 9 Page 10 Page 11 Page 12
     

    Page 10




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