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 a Composite Implicit Time Integration Procedure for Nonlinear Dynamics

    Bathe, Klaus-Jürgen; Baig, M. M. I. Source: Computers & Structures, v 83, 2513 – 2534, 2005.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Transient analysis of nonlinear problems in structural and solid mechanics is mainly carried out using direct time integration of the equations of motion. For reliable solutions, a stable and efficient integration algorithm is desirable. Methods that are unconditionally stable in linear analyses appear to be a natural choice for use in nonlinear analyses, but unfortunately may not remain stable for a given time step size in large deformation and long time range response solutions. A composite time integration scheme is proposed and tested in some example solutions against the trapezoidal rule and the Wilson theta-method, and found to be effective where the trapezoidal rule fails to produce a stable solution. These example results are indicative of the merits of the composite scheme.

    Keywords: finite element method, composite integration, trapezoidal rule




    A Flow-Condition-Based Interpolation Finite Element Procedure for Triangular Grids

    Kohno, Haruhiko; Bathe, Klaus-Jürgen. Source: Int. J. Num. Meth. in Fluids, v 51, 673-699, 2006.

    ISSN: 0271-2091 (print); 1097-0363 (online)

    Publisher: John Wiley & Sons, Ltd.

    Abstract: A flow-condition-based interpolation finite element scheme is presented for use of triangular grids in the solution of the incompressible Navier-Stokes equations. The method provides spatially isotropic discretizations for low and high Reynolds number flows. Various example solutions are given to illustrate the capabilities of the procedure.

    Keywords: incompressible flows, stability, accuracy, flow-condition-based interpolation

    Goal-oriented Error Estimation in the Analysis of Fluid Flows with Structural Interactions

    Grätsch, Thomas; Bathe, Klaus-Jürgen. Source: Comp. Meth. in Applied Mech. and Eng., v 195, 5673-5684, 2006.

    ISSN: 0045-7825

    Publisher: Elsevier Ltd

    Abstract: We present some developments for the extension of goal-oriented error estimation procedures to the analysis of Navier–Stokes incompressible fluid flows with structural interactions. Particular focus is given on error assessment of specific quantities of interest defined on the structural part. The goal is to establish relatively coarse meshes to model the fluid flow but achieve acceptable accuracy in the quantities of interest. A nonlinear goal-oriented error estimation procedure is presented which is applicable to general nonlinear analyses. Some illustrative solutions using ADINA are given.

    Keywords: goal-oriented error estimation, Navier–Stokes fluid flow, nonlinear structures, interactions; FSI




    Insight into Finite Element Shell Discretizations by Use of the Basic Shell Mathematical Model

    Lee, Phill-Seung; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 83, 69-90, 2005.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The objective of this paper is to gain insight into finite element discretizations of shells using the basic shell mathematical model and, in particular, regarding the sources of "locking". We briefly review the "basic shell mathematical model" and present a formulation of shell finite elements based on this model. These shell finite elements are equivalent to the widely-used continuum mechanics based shell finite elements. We consider a free hyperboloid shell problem, which is known to be difficult to solve accurately. Using a fine mesh of MITC9 elements based on the basic shell mathematical model, a detailed analysis is performed giving the distributions of all strain terms. A similar analysis using the MITC6 shell element shows why this element locks when the shell thickness is very small.

    Keywords: shell structures, basic shell mathematical model, MITC shell elements




    Influence Functions and Goal-Oriented Error Estimation for Finite Element Analysis of Shell Structures

    Grätsch, Thomas; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical Methods in Eng., v 63, 709-736, 2005.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd

    Abstract: In this paper, we first present a consistent procedure to establish influence functions for the finite element analysis of shell structures, where the influence function can be for any linear quantity of engineering interest. We then design some goal-oriented error measures that take into account the cancellation effect of errors over the domain to overcome the issue of over-estimation. These error measures include the error due to the approximation in the geometry of the shell structure. In the calculation of the influence functions we also consider the asymptotic behaviour of shells as the thickness approaches zero. Although our procedures are general and can be applied to any shell formulation, we focus on MITC finite element shell discretizations. In our numerical results, influence functions are shown for some shell test problems, and the proposed goal-oriented error estimation procedure shows good effectivity indices.

    Keywords: shell structures, influence functions, goal-oriented error estimation, MITC shell elements




    A posteriori Error Estimation Techniques in Practical Finite Element Analysis

    Grätsch, Thomas; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 83, 235-265, 2005

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: In this paper we review the basic concepts to obtain a posteriori error estimates for the finite element solution of an elliptic linear model problem. We give the basic ideas to establish global error estimates for the energy norm as well as goal-oriented error estimates. While we show how these error estimation techniques are employed for our simple model problem, the emphasis of the paper is on assessing whether these procedures are ready for use in practical linear finite element analysis. We conclude that the actually practical error estimation techniques do not provide mathematically proven bounds on the error and need to be used with care. The more accurate estimation procedures also do not provide proven bounds that, in general, can be computed efficiently. We also briefly comment upon the state of error estimations in nonlinear and transient analyses and when mixed methods are used.

    Keywords: finite element analysis, a posteriori error estimation, goal-oriented error estimation, dual problem, practical procedures




    Insight into the Flow-Condition-Based Interpolation Finite Element Approach: Solution of Steady-State Advection-Diffusion Problems

    Kohno, Haruhiko; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical Methods in Eng., v 63, 197-217, 2005.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd

    Abstract: The flow-condition-based interpolation (FCBl) finite element approach is Studied in the solution of advection-diffusion problems. Two FCBI procedures are developed and tested with the original FCBI method: in the first scheme, a general solution of the advection-diffusion equation is embedded into the interpolation, and in the second scheme, the link-cutting bubbles approach is used in the interpolation. In both procedures, as in the original FCBI method, no artificial parameters are included to reach stability for high Peclet number flows. The procedures have been implemented for two-dimensional analysis and the results of some test problems are presented. These results indicate good stability and accuracy characteristics and the potential of the FCBI Solution approach.

    Keywords: advection-diffusion, stabilization, flow-condition-based interpolations




    On The Reliable Solution of Contact Problems in Engineering Design

    Elabbasi, Nagi; Hong, Jung-Wuk; Bathe, Klaus-Jürgen. Source: Int. J. of Mechanics and Materials in Design, v 1, 3-16, 2004.

    ISSN: 1569-1713 (Print) 1573-8841 (Online)

    Publisher: Springer Netherlands

    Abstract: In this paper we examine briefly the reliability of solution needed for the accurate and effective analysis of engineering design problems involving contact conditions. A general finite element formulation for treating the frictional contact problem using constraint functions is first summarized. Then we address general reliability issues and those related to the selection of appropriate elements that provide optimal performance. These elements of course do not lock and would provide the best solution an analyst can expect when simulating a design problem. Reliability issues specific to the contact formulation are also presented. A promising procedure to increase the reliability of an analysis is the method of finite spheres. The method does not require a mesh and in particular can be used with a finite element discretization as described in the paper. Finally, the results of several illustrative analysis problems are given.

    Keywords: contact, reliability, finite element solution, finite spheres, design




    Coupling and Enrichment Schemes for Finite Element and Finite Sphere Discretizations

    Hong, Jung-Wuk; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 83, 1386-1395, 2005.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We present a technique to couple finite element and finite sphere discretizations. The finite elements and finite spheres are coupled with full displacement compatibility. We also present a technique in which a finite element discretization is enriched with finite spheres. We consider two-dimensional conditions and present solutions to illustrate the analysis procedures.

    Keywords: finite element, finite sphere, discretization, coupling




    Development of MITC Isotropic Triangular Shell Finite Elements

    Lee,Phill-Seung; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 82, 945-962, 2004.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We present a simple methodology to design isotropic triangular shell finite elements based on the Mixed Interpolation of Tensorial Components (MITC) approach. Several mixed-interpolated isotropic triangular shell finite elements are proposed. We perform well-established numerical tests and show the performance of the new elements.

    Keywords: shell structures, finite elements, triangular elements, MITC shell elements




    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 11

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