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)

  • 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.

    A Mesh Adaptivity Procedure for CFD and Fluid-Structure Interactions

    Hou, Zhang and Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 87, 604-617, 2009.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We present a procedure to adapt and repair meshes in the general solution of Navier–Stokes incompressible and compressible fluid flows, including structural interactions. For fluid-structure interactions, FSI, the fluid is described by an arbitrary-Lagrangian–Eulerian formulation fully coupled to general solids and structures described by Lagrangian formulations. The solids and structures can undergo highly nonlinear response due to large deformations, nonlinear material behavior, contact and temperature. We focus on the need to adapt the fluid mesh in pure CFD solutions when high gradients are present or boundary layer effects are important, and FSI solutions when large structural deformations take place. The procedure is a practical scheme to solve complex problems. We illustrate the proposed scheme in various example solutions.

    Keywords: CFD, fluid-structure interaction, FSI large structural deformations, mesh adaptivity

    A Model of Incompressible Isotropic Hyperelastic Material Behavior using Spline Interpolations of Tension-Compression Test Data

    Sussman, Theodore; Bathe, Klaus-Jürgen. Source: Communications in Numerical Methods in Engineering, v. 25, 53-63, 2009.

    ISSN: 1069-8299 (print); 1099-0887 (online)

    Publisher: John Wiley & Sons, Ltd.

    Abstract: We present a model of incompressible isotropic hyperelastic material behavior based on a strain energy description separable in terms of logarithmic strains and piecewise spline interpolations of uniaxial tension-compression test data. Valuable attributes are that no fitting of model constants is carried out and the model replicates even physically complicated test data very accurately for small and large strains and for tension and compression. The model is well suited for use in finite element analysis.

    Keywords: material modeling, finite element analysis, incompressible materials, hyperelasticity, rubber-like materials

    The Finite Element Method

    Bathe, Klaus-Jürgen. Source: Chapter in Wiley Encyclopedia of Computer Science and Engineering, B.W. Wah (ed.), Dec 2008.

    ISBN: 978-0-471-38393-2

    Publisher: John Wiley and Sons, Ltd

    Abstract: The objective of this article is to give an overview of finite element methods that are currently used extensively in academia and industry. The method is described in rather general terms, the basic formulation is presented, and some issues regarding effective finite element procedures are summarized. Various applications are briefly given to illustrate the current use of the method. Finally, the article concludes with key challenges for the further development of the method.

    Keywords: finite element method, structures, CFD, FSI, shells, meshing, mesh-gluing, locking, CAD, error estimation

    On Finite Element Methods for Nonlinear Dynamic Response

    Bathe, Klaus-Jürgen. Source: Proceedings EURODYN 2008, Southampton, July 2008, M.J. Brennan (ed.)

    Abstract: In this paper we briefly focus on the nonlinear analysis of solids and structures when these undergo large deformations, possibly over long time durations, and perhaps subjected to fluid-structure interactions. The analysis should be conducted with finite element methods, including the time integration, that are reliable and effective. The requirement of reliability is particularly important in nonlinear finite element analysis because physical test data are frequently not available.

    ISBN: 978-0-854-32882-6

    Publisher: Institute of Sound and Vibration Research, University of Southampton, UK

    Keywords: finite element method, solids, structures, dynamics, time integration, FSI

    A 4-node 3D-Shell Element to Model Shell Surface Tractions and Incompressible Behavior

    Kim, Do-Nyun; Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 86, 2027-2041, 2008.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We present in this paper a shell element that models the three-dimensional (3D) effects of surface tractions, like needed when a shell is confined between other solid media. The element is the widely used MITC4 shell element enriched by the use of a fully 3D stress-strain description, appropriate through-the-thickness displacements to model surface tractions, and pressure degrees of freedom for incompressible analyses. The element formulation avoids instabilities and ill-conditioning. Various example solutions are presented to illustrate the capabilities of the element.

    Keywords: shells, MITC4 element, 3D-shell model, surface tractions, incompressible analysis, ill-conditioning

    Benchmark Problems for Incompressible Fluid Flows with Structural Interactions

    Bathe, Klaus-Jürgen; Ledezma, G. A. Source: Computers & Structures, v 85, 628-644, 2007

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Various methods of analysis for the solution of fluid flows with structural interactions have been proposed in the literature, and new techniques are being developed. In these endeavors, to advance the field, thorough evaluations of the procedures are necessary. To help in establishing such evaluations, we present in this paper the solutions of some benchmark problems. The results can be used to evaluate existing and new formulations of incompressible fluid flows with structural interactions.

    Keywords: incompressible fluid flows, Navier-Stokes equations, fluid-structure interactions, benchmark problems, ADINA

    Conserving Energy and Momentum in Nonlinear Dynamics: A Simple Implicit Time Integration Scheme

    Bathe, Klaus-Jürgen. Source: Computers & Structures, v 85, 437-445, 2007

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We focus on a simple implicit time integration scheme for the transient response solution of structures when large deformations and long time durations are considered. Our aim is to have a practical method of implicit time integration for analyses in which the widely used Newmark time integration procedure is not conserving energy and momentum, and is unstable. The method of time integration discussed in this paper is performing well and is a good candidate for practical analyses.

    Keywords: nonlinear dynamics, implicit time integration, conservation of momentum and energy, trapezoidal rule, composite scheme

    Insight into 3-node Triangular Shell Finite Elements: the Effects of Element Isotropy and Mesh Patterns

    Lee, Phill-Seung; Noh, Hyuk-Chun; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 85, 404-418, 2007.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: In this paper, we study the convergence characteristics of some 3-node triangular shell finite elements. We review the formulations of three different isotropic 3-node elements and one non-isotropic 3-node element. We analyze a clamped plate problem and a hyperboloid shell problem using various mesh topologies and present the convergence curves using the s-norm. Considering simple bending tests, we also study the transverse shear strain fields of the shell finite elements. The results and insight given are valuable for the proper use and the further development of triangular shell finite elements.

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

    The CIP Method Embedded in Finite Element Discretizations of Incompressible Flows

    Banijamali, Bahareh; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical Methods in Eng., v 71, 66-80, 2007.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: Quite effective low-order finite element and finite volume methods for incompressible fluid flows have been established and are widely used. However, higher-order finite element methods that are stable, have high accuracy and are computationally efficient are still sought. Such discretization schemes could be particularly useful to establish error estimates in numerical solutions of fluid flows. The objective of this paper is to report on a study in which the cubic interpolated polynomial (CIP) method is embedded into 4-node and 9-node finite element discrefizations of 2D flows in order to stabilize the convective terms. To illustrate the capabilities of the formulations, the results obtained in the solution of the driven flow square cavity problem are given.

    Keywords: incompressible flows, finite element discretization, CIP technique, FCBI approach

    A Nine-node Quadrilateral FCBI Element for Incompressible Navier-Stokes Flows

    Kohno, Haruhiko; Bathe, Klaus-Jürgen. Source: Comm. in Num. Methods in Eng., v 22, 917-931, 2006.

    ISSN: 1069-8299 (print); 1099-0887 (online)

    Publisher: John Wiley & Sons, Ltd.

    Abstract: We propose a nine-node flow-condition-based interpolation (FCBI) finite element for the analysis of 2D incompressible flows. Emphasis in the FCBI approach is on obtaining an element that is stable and can be used in rather coarse meshes even when considering high Reynolds number flows. The formulation of the element is presented and the results obtained in the solution of some test cases are given.

    Keywords: incompressible flows, flow-condition-based interpolation, FCBI approach

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