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.

      Challenges and Advances in the Analysis of Structures

      Bathe, Klaus-Jürgen. Source: Proceedings Fourth International Conference on Structural Engineering, Mechanics and Computation — SEMC 2010, Cape Town, South Africa (A. Zingoni, ed), 2010.

      Abstract: The objective in this presentation is to briefly present major challenges in the analysis of structures and some recent developments in finite element procedures that we have pursued. The general challenges are to solve problems more reliably, accurately and efficiently, and to solve problems that so far cannot be analyzed. We present our recent developments for – the finite element analysis of shells, the solution of wave propagation problems, the time integration in long-time large deformation analyses, the analysis of large deformations of beam structures, and the simulation of fluid flow-structure interactions including various physical phenomena.

      Publisher: Taylor & Francis/Balkema

      On the Ellipticity Condition for Model-Parameter Dependent Mixed Formulations

      Chapelle, Dominique, and Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 88, 581–587, 2010.

      Abstract: When establishing and analyzing model-parameter dependent mixed formulations, it is common to consider required ellipticity and inf–sup conditions for the continuous and discrete problems. However, in the modeling of some important categories of problems, like in the analysis of plates and shells, the ellipticity condition usually considered does not naturally hold, and the inf–sup condition can only be stated in an abstract form and can hardly be evaluated analytically. In this paper we present a new and practical ellipticity condition which together with the inf–sup condition guarantees that (i) when the model parameter goes to zero, the limit problem solution is uniformly approached, and (ii) an optimal finite element discretization has been established (for the interpolations used). In practice, a numerical test might be performed to see whether the proposed ellipticity condition is satisfied.

      ISSN: 0045-7949 CODEN: CMSTCJ

      Publisher: Elsevier Ltd

      Keywords: Mixed method, coercivity, inf–sup, small parameter dependence, finite element

      The Quadratic MITC Plate and MITC Shell Elements in Plate Bending

      Lee, Phill-Seung and Bathe, Klaus-Jürgen. Source: Advances in Engineering Software, v. 41, 712-728, 2010.

      Abstract: The analysis of plates can be achieved using the quadratic MITC plate or MITC shell elements. The plate elements have a strong mathematical basis and have been shown to be optimal in their convergence behavior, theoretically and numerically. The shell elements have not (yet) been analyzed mathematically in depth for their rates of convergence, with the plate/shell thickness varying, but have been shown numerically to perform well. Since the shell elements are general and can be used for linear and nonlinear analyses of plates and shells, it is important to identify the differences in the performance of these elements when compared to the plate elements. We briefly review the quadratic quadrilateral and triangular MITC plate and shell elements and study their performances in linear plate analyses.

      ISSN: 09659978 CODEN: AESODT

      Publisher: Elsevier Ltd

      Keywords: Plate, shell, MITC, mixed formulation, finite element, locking, optimal convergence

      A Finite Element Procedure for Multiscale Wave Equations with Application to Plasma Waves

      Kohno, Haruhiko; Bathe, Klaus-Jürgen; Wright, John C. Source: Computers & Structures, v. 88, 87-94, 2010.

      Abstract: A finite element wave-packet procedure is presented to solve problems of wave propagation in multi-scale behavior. The proposed scheme combines the advantages of the finite element and spectral methods. The basic formulation is presented, and the capabilities of the procedure are demonstrated through the solution of some illustrative problems, including a problem that characterizes the mode-conversion behavior in plasmas.

      ISSN: 0045-7949 CODEN: CMSTCJ

      Publisher: Elsevier Ltd

      Keywords: Multi-scale, spectral method, finite elements, plasma, radio frequencies

      Performance of a New Partitioned Procedure versus a Monolithic Procedure in Fluid-Structure Interaction

      Degroote, Joris; Bathe, Klaus-Jürgen; Vierendeels, Jan. Source: Computers & Structures, v. 87, 793-801, 2009.

      Abstract: Fluid–structure interaction (FSI) can be simulated in a monolithic way by solving the flow and structural equations simultaneously and in a partitioned way with separate solvers for the flow equations and the structural equations. A partitioned quasi-Newton technique which solves the coupled problem through nonlinear equations corresponding to the interface position is presented and its performance is compared with a monolithic Newton algorithm. Various structural configurations with an incompressible fluid are solved, and the ratio of the time for the partitioned simulation, when convergence is reached, to the time for the monolithic simulation is found to be between 1/2 and 4. However, in this comparison of the partitioned and monolithic simulations, the flow and structural equations have been solved with a direct sparse solver in full Newton–Raphson iterations, only relatively small problems have been solved and this ratio would likely change if large industrial problems were considered or if other solution strategies were used.

      ISSN: 0045-7949 CODEN: CMSTCJ

      Publisher: Elsevier Ltd

      Keywords: Fluid–structure interaction, partitioned, quasi-Newton, monolithic, Newton–Raphson

      Advances in Finite Element Procedures for Nonlinear Dynamic Response

      Bathe, Klaus-Jürgen. Source: Proceedings European Conference on Computational Mechanics — SEECM 2009, Rhodes, Greece, June 2009.

      Abstract: The objective in this presentation is to briefly survey some recent developments in finite element procedures that we have pursued to solve dynamic problems more accurately and more efficiently, and to solve new classes of problems. We present some developments regarding the finite element analysis of shells, the solution of wave propagation problems with mode conversions, the time integration in long-time large deformation analyses, the solution of normal modes of proteins with the subspace iteration method in nonlinear conformations, and fluid flow-structure interactions.

      Keywords: Dynamic, nonlinear, shell, wave, proteins, fluid

      Insight into a Model for Large Strain Anisotropic Plasticity

      Kim, Do-Nyun; Montáns, Francisco Javier; Bathe, Klaus-Jürgen. Source: Computational Mechanics, v. 44, 651-668, 2009.

      Abstract: Efficient and accurate simulation of the deformations in anisotropic metallic sheets requires a constitutive model and an accompanying algorithm at large strains which take into account the anisotropy of both the elastic and plastic material behaviors, as well as their evolution with plastic strains. Recently we proposed such a constitutive model based on continuum energy considerations, the Lee decomposition and an anisotropic stored energy function of the logarithmic strains in which the rotation of the orthotropic axes is also considered. We obtained a framework similar to the one used in isotropic elasto-plasticity. In the present work we give some physical insight into the parameters of the model and their effects on the predictions, both in proportional and in non-proportional loading problems. We also present a procedure to obtain the spin parameter of the model from Lankford R-values.

      ISSN: 01787675 CODEN: CMMEEE

      Publisher: Springer Verlag

      Keywords: Plasticity, anisotropic plasticity, orthotropy, plastic spin, large strain plasticity

      A Triangular Six-Node Shell Element

      Kim, Do-Nyun; Montáns, Francisco Javier; Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 87, 1451-1460, 2009.

      Abstract: We present a triangular six-node shell element that represents an important improvement over a recently published element. The shell element is formulated, like the original element, using the MITC procedure. The element has the attributes to be spatially isotropic, to pass the membrane and bending patch tests, to contain no spurious zero energy mode, and is formulated without an artificial constant. In particular, the improved element does not show the instability sometimes observed with the earlier published element. We give the convergence behavior of the element in discriminating membrane- and bending-dominated benchmark problems. These tests show the effectiveness of the element.

      ISSN: 0045-7949 CODEN: CMSTCJ

      Publisher: Elsevier Ltd

      Keywords: Shells, finite element, triangular element, spatial isotropy, MITC method, six-node element

      A Holistic Method to Design an Optimized Energy Scenario and Quantitatively Evaluate Promising Technologies for Implementation

      Deilmann, Christian; Bathe, Klaus-Jürgen. Source: International Journal of Green Energy, v. 6, 1-21, 2009.

      Abstract: In this article we focus on today's worldwide energy system, a fundamentally illogical and unsustainable system. Today, 85% of the world wide energy system depends on carbon-based fossil fuels. We develop a holistic method to analyze mankind's use of energy in a broad way and to design optimized, normative energy scenarios that conform to important scientific principles. The procedure is based on an abstraction process and helps to overcome thinking barriers and prejudice. The proposed method is applied to a general analysis of energy and to a simplified normative energy scenario for the United States in 2060. Important technologies for the implementation are evaluated in a bottom-up analysis. Since research endeavors and policies affect free-market decisions within the energy system, the developed method aims at guiding researchers and politicians to embark on strategies toward sustainable and scientifically optimized energy concepts for the future.

      ISSN: 15435075

      Publisher: Taylor and Francis Inc.

      Keywords: Energy system analysis, normative scenario technique, bottom-up analysis

      The Subspace Iteration Method in Protein Normal Mode Analysis

      Sharifi Sedeh, Reza; Bathe, Mark; Bathe, Klaus-Jürgen. Source: J. Computational Chemistry, DOI 10.1002/jcc, 2009.

      Abstract: Normal mode analysis plays an important role in relating the conformational dynamics of proteins to their biological function. The subspace iteration method is a numerical procedure for normal mode analysis that has enjoyed widespread success in the structural mechanics community due to its numerical stability and computational efficiency in calculating the lowest normal modes of large systems. Here, we apply the subspace iteration method, to proteins to demonstrate its advantageous properties in this area of computational protein science. An effective algorithm for choosing the number of iteration vectors in the method is established, offering a considerable improvement over the original implementation. In the present application, computational time scales linearly with the number of normal modes computed. Additionally, the method lends itself naturally to normal mode analyses of multiple neighboring macromolecular conformations, as demonstrated in a conformational change pathway analysis of adenylate kinase. These properties, together with its computational robustness and intrinsic scalability to multiple processors, render the subspace iteration method an effective and reliable computational approach to protein normal mode analysis.

      ISSN: 01928651 CODEN: JCCHDD

      Publisher: John Wiley and Sons Inc.

      Keywords: Frequency, mode shape, macromolecule, conformational change pathway

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