ADINA Theory

Page 8

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.

    Keywords: convection-dominated flow, upwinding, inf-sup condition




    On a Parabolic Quadrilateral Finite Element for Compressible Flows

    Hendriana, Dena; Bathe, Klaus-Jürgen. Source: J. Computer Methods in Applied Mechanics and Engineering, v 186, 1-22, 2000.

    ISSN: 0045-7825

    Publisher: Elsevier Science B.V.

    Abstract: We present a 9-node finite element for compressible flow solutions. A high-order derivative upwind term and a shock capturing term are employed for stability and accuracy of the formulation. We give the solutions of various example problems to illustrate our experiences with the element.

    Keywords: finite element, compressible flow, upwind




    Finite Element Analysis of Fluid Flows Fully Coupled with Structural Interactions

    Bathe, Klaus-Jürgen; Zhang, Hou and Ji, Shanhong. Source: Computers & Structures, v 72, 1-16, 1999.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Some advances in capabilities for analysis of fluid flows fully coupled with structural interactions are presented. Incompressible Navier–Stokes and compressible Navier–Stokes or Euler fluids and the full interaction with structures undergoing large deformations, nonlinear material response and contact conditions can be considered. The analysis capabilities are available in the ADINA System, and are integrated within computer-aided design using the available ADINA modeler and CAD interfaces. Various analysis cases are presented to illustrate the solution capabilities.

    Keywords: finite element analysis, fluid flow, fluid structure interaction, ADINA, CAD




    Advances in Crush Analysis

    Bathe, Klaus-Jürgen; Walczak, Jan; Guillermin, Olivier; Bouzinov, Pavel A.; Chen Heng-Yee. Source” Computers & Structures, v 72, 31-47, 1999.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Advances in capabilities for the crush analysis of structures are presented. Such analyses are difficult to perform and require state-of-the-art analysis procedures: efficient and reliable shell elements, an effective and general contact algorithm, efficient procedures to calculate the element stresses in elasto-plasticity, the use of consistent tangent matrices, effective nonlinear incremental solution strategies and the efficient solution of the algebraic finite element equations. Moreover, the effectiveness of the complete analysis process can only be achieved by ensuring that each of the above solution procedures is in an effective manner integrated into a complete solution scheme. This paper focuses on the advances developed in ADINA and presents various analysis cases solved with the program.

    Keywords: crush analysis, shell element, elasto-plasticity, finite element, ADINA




    Crush simulation of cars with FEA

    Bathe, Klaus-Jürgen. Source: Mechanical Engineering, Nov 1998, v 120, no. 11; pp. 82-83.

    ISSN: 0025-6501

    Publisher: American Society of Mechanical Engineers

    Abstract: Finite-element analysis procedures are now used abundantly in the automotive industry. Linear static and dynamic analyses are conducted in a routine manner, and nonlinear analyses are increasingly pursued. Two analysis fields in which highly nonlinear conditions are simulated are the crash and crush analyses of complete motorcar models. The purpose of the crash analysis is to see how the car will behave in a frontal or sideways collision. In a crush analysis, a quite different physical phenomenon is considered. Here the purpose is to establish the ultimate strength of the car body in a static situation. While crash analyses of cars have been carried out with much success, a crush analysis is much more difficult to achieve. The reasons for this greater difficulty lie in the fact that slow-speed, almost static analysis requires increased robustness and efficiency in the solution algorithms.

    Keywords: finite element analysis, automobile safety, product testing, algorithms, finite element analysis, mechanical engineering




    Current Directions in Meshing

    Bathe, Klaus-Jürgen. Source: Mechanical Engineering, Jul 1998, v 120, no. 7; pp. 70-71.

    ISSN: 0025-6501

    Publisher: American Society of Mechanical Engineers

    Abstract: The key to an efficient finite-element analysis is frequently an effective finite-element mesh. There is a need for further discussion of more advanced meshing issues and for comment on the current state of meshing procedures. Such techniques are widely available and are broadly based in many solution packages for finite-element analysis of solids, structures, and fluids, as well as packages for finite-difference and control volume analysis of fluids. There are 2 broad types of mesh-generation methods - schemes for structured and unstructured meshes. There are 2 major approaches to generating unstructured grids: the advancing-front method and the Delaunay triangulation. Powerful software for meshing is already available, the current limits are well understood, and new algorithms and programs can be expected that will continuously advance the state of meshing capabilities.

    Keywords: finite element analysis, automation, technological change, computer based modeling, mechanical engineering




    What can go wrong in FEA?

    Bathe, Klaus-Jürgen. Source: Mechanical Engineering, May 1998, v 120, No. 5; pp. 63-65.

    ISSN: 0025-6501

    Publisher: American Society of Mechanical Engineers

    Abstract: Finite-element methods are in abundant use in today's engineering practice through various general-purpose commercial computer programs and many special-purpose commercial computer programs written for specific applications. These techniques are, to an increasing extent, being used to help identify good new designs and improve designs with respect to performance and cost. Considering the important role that finite-element methods now play in various areas of engineering, practitioners need to ask themselves whether their procedures are the most appropriate techniques available and whether the methods will lead to accurate results. Finite-element methods can now be employed with great confidence, but only the methods considered reliable should be used. Earlier technology based on reduced integration should not be used, or should at any rate be employed with great care. By proceeding in this way, practitioners can have confidence that a finite-element analysis will be effective and will not go wrong.

    Keywords: finite element analysis, methods, accuracy, mathematical models, reliability, engineering, measurement




    Fluid-Structure Interactions

    Bathe, Klaus-Jürgen. Source: Mechanical Engineering, April 1998, v 120, No. 5; pp. 66-68.

    ISSN: 0025-6501

    Publisher: American Society of Mechanical Engineers

    Abstract: The fully coupled solution of fluid flows with structural interactions, a rapidly evolving discipline, represents the natural next step in simulating mechanical systems.

    Keywords: finite element analysis, methods, accuracy, mathematical models, reliability, engineering, fluid structure interaction




    How automatic is automatic meshing?

    Bathe, Klaus-Jürgen. Source: Mechanical Engineering, Mar 1998, v 120, no.. 3; pp. 40-41

    ISSN: 0025-6501

    Publisher: American Society of Mechanical Engineers

    Abstract: The most time-consuming step of finite-element analysis is creating a finite-element model. When considering the analysis process, it is useful to remember that a finite-element code solves a mathematical model, which is an idealization of a structure or system in the real world. In all cases, however, the finite-element model can only predict what is contained in the mathematical model, and the finite-element analysis should solve this mathematical model to a sufficient degree of accuracy. The use of an adequate finite-element mesh is crucial to this task, but the mathematical model must also have been chosen without creating artificial analysis difficulties. In practice, the most attractive way to analyze and thus mesh a part is to use the computer-aided-design geometry created with a solid modeler such as Unigraphics, I-DEAS, Solid-Works, and CATIA, but this geometry is frequently much too complex for analysis.

    Keywords: CAE, finite element analysis, CAD, computer based modeling, mathematical models




    Fundamental Considerations for the Finite Element Analysis of Shell Structures

    Chapelle, Dominique; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 66, 19-36, 711-712, 1998.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The objective in this paper is to present fundamental considerations regarding the finite element analysis of shell structures. First, we review some well-known results regarding the asymptotic behaviour of a shell mathematical model. When the thickness becomes small, the shell behaviour falls into one of two dramatically different categories; namely, the membrane-dominated and bending-dominated cases. The shell geometry and boundary conditions decide into which category the shell structure falls, and a seemingly small change in these conditions can result into a change of category and hence into a dramatically different shell behaviour. 

    Keywords: finite element analysis, shell structure




    On the Stability of Mixed Finite Elements in Large Strain Analysis of Incompressible Solids

    Pantuso, Daniel; Bathe, Klaus-Jürgen . Source: Finite Elements in Analysis and Design, v 28, 83-104, 1997.

    ISSN: 0168-874X

    Publisher: Elsevier Science B.V.

    Abstract: Some mixed finite elements for large deformation analysis of incompressible solids are studied. The elements are based on the displacement/pressure and enhanced strain mixed formulations. Specifically, it is shown that a quadrilateral 4-node element that satisfies the inf-sup condition in linear analysis - and hence is an effective element in such conditions - fails in large strain analysis. The reasons for this element behavior are explored. Some comparisons of element predictive capabilities are given.

    Keywords: mixed finite elements, loss of ellipticity, large strains




    On the Constraint Function Method for Contact Problems

    Bathe, Klaus-Jürgen; Bouzinov, Pavel A. Source: Computers & Structures, v 64, no. 5/6, 1069-1085, 1997.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The objective in this paper is to present some theoretical insight and valuable numerical experiences for the analysis of contact problems. We review the theoretical basis of the constraint function method for general contact problems and discuss some important characteristics of the method. In the presentation, we consider static and dynamic conditions. We then give numerical experiences with the method through the solution of some demonstrative test problems and through the results obtained in some industrial analysis cases.

    Keywords: constraint function method, contact problem, finite element analysis

    Some Advances in the Analysis of Fluid Flows

    Bathe, Klaus-Jürgen; Zhang, Hou; Zhang, Xiaoli. Source: Computers & Structures, v 64, no. 5/6, 909-930, 1997.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We review some new solution capabilities developed and available in the ADINA-F CFD (computational fluid dynamics) program and present example solutions. Unique features and advances are that incompressible and compressible flows with structural interactions can be analyzed and that a general radiation heat transfer analysis capability based on specular and diffusive reflectivities and transmittance is available. This paper is largely a continuation of the presentation given in Ref. [1].

    Keywords: incompressible flow, compressible flow, CFD, ADINA, fluid structure interaction; FSI




    Advances in Nonlinear Finite Element Analysis of Automobiles

    Bathe, Klaus-Jürgen; Guillermin, Olivier; Walczak, Jan; Chen, Heng-Yee. Source: Computers & Structures, v 64, no., 5/6, 881-891, 1997.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The objective in this paper is to present some recent advances for the finite element analysis of automobile structures. These advances pertain to the development of effective basic finite element procedures and the efficient solution of large systems of equations. With these new procedures, it is possible to model much more accurately (and reliably) the actual nonlinear physical behavior of complex structures. The illustrative solutions given in the paper include the solution of a roof-crush problem that was solved appropriately, according to the actual physical situation, using implicit time integration (resulting practically in a static analysis).

    Keywords: finite element analysis, automobile, roof crush




    On Evaluating the Inf-Sup Condition for Plate Bending Elements

    Iosilevich, Alexander; Bathe, Klaus-Jürgen; Brezzi, Franco. Source: Int. Journal for Numerical Methods in Engineering, v 40, 3639-3663, 1997.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: This paper addresses the evaluation of the inf-sup condition for Reissner-Mindlin plate bending elements. This fundamental condition for stability and optimality of a mixed finite element scheme is, in general, very difficult to evaluate analytically, considering for example distorted meshes. Therefore, we develop a numerical test methodology. To demonstrate the test methodology and to obtain specific results, we apply it to standard displacement-based elements and elements of the MITC family. Whereas the displacement-based elements fail to satisfy the inf-sup condition, we fmd that the MITC elements pass our numerical test for uniform meshes and a sequence of distorted meshes.

    Keywords: Reissner-Mindlin plate elements, inf-sup condition




    Displacement/Pressure Based Mixed Finite Element Formulations for Acoustic Fluid-Structure Interaction Problems

    Wang, Xiaodong; Bathe, Klaus-Jürgen. Source: Int. Journal for Numerical Methods in Engineering, v 40, 2001-2017, 1997.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: We present reliable finite element discretizations based on displacement/pressure interpolations for the analysis of acoustic fluid-structure interaction problems. The finite element interpolations are selected using the inf-sup condition, and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation. We show that with our analysis procedure no spurious non-zero frequencies are encountered, as heretofore calculated with other displacement-based discretizations.

    Keywords: acoustic fluid, fluid structure interaction, mixed finite element formulation, inf-sup condition




    On Mixed Elements for Acoustic Fluid-Structure Interactions

    Wang, Xiaodong; Bathe, Klaus-Jürgen. Source: Mathematical Models & Methods in Applied Sciences, v 7, no. 3, 329-343, 1997.

    ISSN: 0218-2025

    Publisher: World Scientific Publishing Company

    Abstract: In this paper we investigate the performance of some mixed finite elements used in the displacement/pressure (u/p) and displacement-pressure-vorticity moment (u-p-Lambda) formulations for acoustic fluid-structure interactions. In particular, we show that certain elements pass a numerical inf-sup test and are valuable for general applications. Also considered are macroelements that are based on simple four-node elements. 

    Keywords: fluid structure interaction, mixed finite element, inf-sup test




    Finite Element Analysis of Shell Structures

    Bucalem, Miguel Luiz; Bathe, Klaus-Jürgen. Source: Archives of Computational Methods in Engineering, v 4, 3-61, 1997.

    ISSN: 1134-3060 (print); 1886-1784 (online)

    Publisher: Springer

    Abstract: A survey of effective finite element formulations for the analysis of shell structures is presented. First, the: basic requirements for shell elements are discussed, in which it is emphasized that generality and reliability are most important items. A general displacement-based formulation is then briefly reviewed. This formulation is not effective., but it is used as a starting point for developing a general and effective approach using the mixed interpolation of the tensorial components. The formulation of various MITC elements (that is, elements based on Mixed Interpolation of Tensorial Components) are presented. Theoretical results (applicable to plate analysis) and various numerical results of analyses of plates and shells are summarized. These illustrate some current capabilities and the potential for further finite element developments.  

    Keywords: Mixed Interpolation of Tensorial Components




    A Four-Node Quadrilateral Mixed-Interpolated Element for Solids and Fluids

    Pantuso, Daniel; Bathe, Klaus-Jürgen. Source: Mathematical Models and Methods in Applied Sciences, v 5, No. 8, 1113-1128, 1995.

    ISSN: 0218-2025

    Publisher: World Scientific Publishing Company

    Abstract: A four-node quadrilateral element is presented which shows promise for general compressible and incompressible two-dimensional analysis of solids and fluids. The element is based on a mixed interpolation of displacements (velocities), pressure and strains (velocity strains). We show that the element satisfies a numerical inf-sup test, and give results of some analysis problems that demonstrate the capabilities of the element. 

    Keywords:mixed-interpolated element, inf-sup test




    Some Computational Issues in Large Strain Elasto-Plastic Analysis

    G. Gabriel; Bathe, Klaus-Jürgen . Source: Computers & Structures, v 56, No. 2/3, pp. 249-267, 1995.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The stress integration procedure proposed by Eterovic and Bathe [Int. J. numer. Meth. Engng 30, 1099–1114 (1990).] is studied in detail. The elasto-plasticity formulation is based on the use of the total logarithmic strains and Cauchy stresses, and the Euler backward method of time integration. The accuracy of the procedure is assessed in the solution of various analysis problems and is compared with the accuracy of other schemes. Two important conclusions are reached. First, for a selected level of accuracy, the use of the total strain formulation, in general, allows larger time steps than the use of a stress-rate based formulation (such as a formulation based on the Jaumann stress rate). Second, the original procedure of Eterovic and Bathe can be improved in accuracy by using the trapezoidal rule with a measure to limit the magnitude of the elasto-plastic strain increment per step. This improvement allows for the change of principal stress directions during the incremental step. This capability seems to be unique to this formulation and time integration.

    Keywords: stress integration, large strain analysis, elasto-plastic




    A Mixed Displacement-Based Finite Element Formulation for Acoustic Fluid-Structure Interaction

    Bathe, Klaus-Jürgen; Nitikitpaiboon, C; and Wang, Xiaodong. Source: Computers & Structures, v 56, No. 2/3, 225-237, 1995.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The solutions of fluid-structure interaction problems, using displacement-based finite element formulations for acoustic fluids, may contain spurious non-zero frequencies. To remove this deficiency, we present here a new formulation based on a three-field discretization using displacements, pressure and a ''vorticity moment'' as variables with an appropriate treatment of the boundary conditions. We propose specific finite element discretizations and give the numerical results of various example problems. 

    Keywords: fluid structure interaction, mixed finite element




    Finite Element Analysis of Incompressible and Compressible Fluid Flows with Free Surfaces and Structural Interactions

    Bathe, Klaus-Jürgen; Zhang, Hou; Wang, M. H. Source: Computers & Structures, v 56, No. 2/3, 193-213, 1995.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We present the current ADINA-F capabilities for fluid flow analysis. The fluid can be considered to be an incompressible or compressible medium. Free surfaces and the full interactions with structures in two- and three-dimensional conditions can be analyzed. The basic formulations and finite element discretizations used are described, the techniques for the solution of the finite element equations are briefly discussed, and the results of various demonstrative analyses are given.

    Keywords: finite element, fluid structure interaction




    An Iterative Finite Element Procedure for the Analysis of Piezoelectric Continua

    Gaudenzi, P; Bathe, Klaus-Jürgen. Source: J. of Intelligent Material Systems and Structures, v 6, No. 2, 266-273, 1995.

    ISSN: 1045-389X (print); 1530-8138 (online)

    Publisher: SAGE Publications

    Abstract: In this paper an iterative finite element procedure is presented for the analysis of two-and three-dimensional piezoelectric continua. The procedure is applied to the steady-state analysis of two-dimensional media subjected to mechanical and electrical loading. 

    Keywords: piezoelectric continua, finite element




    Error Indicators and Adaptive Remeshing in Large Deformation Finite Element Analysis

    Lee, Nam-Sua; Bathe, Klaus-Jürgen. Source: Finite Elements in Analysis and Design, v 16, 99-139, 1994

    ISSN: 0168-874X

    Publisher: Elsevier Science Publishers B. V.

    Abstract: We present and use a system of adaptive procedures for large-deformation finite element analysis of elastic and elastoplastic problems using the h-refinement approach. The procedures include a pointwise indicator for error in stresses, a pointwise indicator for error in plastic strain increments, a quadrilateral element mesh generator for generating completely new meshes on the deformed configuration of the body, and several mapping schemes for transferring state variables and history-dependent variables accurately across models. These procedures constitute the ingredients of a proposed adaptive scheme that is demonstrated to be effective in solutions of two-dimensional stress analysis problems including contact conditions. An important observation is that with coarse finite element meshes and no error indicator used, crucial physical phenomena may be completely missed in the analysis.

    Keywords: error indicator, adaptive remeshing, finite element




    Stability and Patch Test Performance of Contact Discretizations and a New Solution Algorithm

    Elabbasi, Nagi; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 79, 1473-1486, 2001.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Stability and patch test performance are two important issues influencing the selection of discretization algorithms for flexible body contact problems. The patch test performance is dictated by the accuracy of evaluation of the contact integrals, not by the specific form of the gap, contact pressure, or contact surface definitions. Stability on the other hand, is related to the form of the assumed contact pressure distribution. In this paper, several commonly used contact algorithms are briefly summarized, and their stability in an inf-sup test and performance in a contact patch test are assessed. The existing algorithms do not satisfy both requirements. This fact has motivated the development of a new algorithm for flexible body contact problems that results in a symmetric coefficient matrix and satisfies both the stability and the contact patch conditions.

    Keywords: contact, finite element solution, stability, patch test




    The Inf-Sup Condition and its Evaluation for Mixed Finite Element Methods

    Bathe, Klaus-Jürgen. Source: Computers & Structures, v 79, 243-252, 971, 2001.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The objective of this paper is to review the general inf-sup condition for mixed finite element methods and summarize numerical procedures (inf-sup tests) for the evaluation of the inf-sup expressions specific to various problem areas. The inf sup testing of a given mixed finite element discretization is most important in order to assess its reliability and solution effectiveness. The problem areas considered are (almost) incompressible analysis of solids and fluids, acoustic fluids, the analysis of plates and shells, and the solution of convection-dominated flows.

    Keywords: inf-sup condition, mixed finite element method




    On the Inf-Sup Condition of Mixed Finite Element Formulations for Acoustic Fluids

    Bao, Weizhu; Wang, Xiaodong; Bathe, Klaus-Jürgen. Source: Mathematical Models & Methods in Applied Sciences, v 11, no. 5, 883-901, 2001.

    ISSN: 0218-2025

    Publisher: World Scientific Publishing Company

    Abstract: The objective of this paper is to present a study of the solvability, stability and optimal error bounds of certain mixed finite element formulations for acoustic fluids. An analytical proof of the stability and optimal error bounds of a set of three-field mixed finite element discretizations is given, and the interrelationship between the inf-sup condition, including the numerical inf-sup test, and the eigenvalue problem pertaining to the natural frequencies is discussed. 

    Keywords: inf-sup condition, mixed finite element formulation, acoustic fluid




    A Finite Element Procedure for the Analysis of Thermo-Mechanical Solids in Contact

    Pantuso, Daniel; Bathe, Klaus-Jürgen ; Bouzinov, Pavel A. Source: Computers & Structures, v 75, 551-573, 2000.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We present a finite element procedure for the analysis of fully coupled thermo-elasto-plastic response of solids including contact conditions. The continuum mechanics formulation for the solid and contact conditions is summarized and effective finite element techniques for solution are given. The constraint function method is employed to impose the contact conditions at the Gauss points of the contact surface. Other procedures widely used in finite element analysis can be considered as particular cases of the constraint function method discussed herein.

    Keywords: thermo-mechanical analysis, contact, large strains




    The Mathematical Shell Model Underlying General Shell Elements

    Chapelle, Dominique; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical Methods in Eng., v 48, 289-313, 2000.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: We show that although no actual mathematical shell model is explicitly used in general shell element formulations, we can identify an implicit shell model underlying these finite element procedures. This underlying model compares well with classical shell models since it displays the same asymptotic behaviours - when the thickness of the shell becomes very small - as, for example, the Naghdi model. Moreover, we substantiate the connection between general shell element procedures and this underlying model by mathematically proving a convergence result from the finite element solution to the solution of the model.

    Keywords: shell model, finite element discretization, degenerated solid, asymptotic behaviour




    The Method of Finite Spheres

    De, Suvranu; Bathe, Klaus-Jürgen. Source: Computational Mechanics, v 25, 329-345, 2000.

    ISSN: 0178-7675 (Print) 1432-0924 (Online)

    Publisher: Springer Berlin / Heidelberg

    Abstract: The objective of this paper is to present some of our recent developments in meshless methods. In particular, a technique is given – the method of finite spheres – that is truly meshless in nature in the sense that the nodes are placed and the numerical integration is performed without a mesh. The method can be viewed as a special case of the general formulation known as the meshless local Petrov–Galerkin (MLPG) procedure. Some of the novel features of the method of finite spheres are the numerical integration scheme and the way in which the Dirichlet boundary conditions are incorporated. A new way of modeling doubly-connected domains is also presented. Various example problems are solved to demonstrate the method.

    Keywords: method of finite spheres, Petrov–Galerkin procedure, meshless




    On Upwind Methods for Parabolic Finite Elements in Incompressible Flows

    Hendriana, Dena; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical Methods in Engineering, v 47, 317-340, 2000.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: We study the performance of various upwind techniques implemented in parabolic finite element discretizations for incompressible high Reynolds number flow. The characteristics of an 'ideal' upwind procedure are first discussed. Then the streamline upwind Petrov/Galerkin method, a simplified version thereof, the Galerkin least squares technique and a high-order derivative artificial diffusion method are evaluated on test problems. We conclude that none of the methods displays the desired solution characteristics. There is still need for the development of a reliable and efficient upwind method with characteristics close to those of the 'ideal' procedure.

    Keywords: incompressible fluid, upwinding, parabolic elements




    An Inf-Sup Test for Shell Finite Elements

    Bathe, Klaus-Jürgen; Iosilevich, Alexander; Chapelle, Dominque. Source: Computers & Structures, v 75, 439-456, 2000.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We present an inf-sup test for general mixed shell finite element discretizations. The test is useful in the thorough evaluation of a shell finite element discretization scheme. We apply the test to the MITC shell elements and find that these elements pass the test.

    Keywords: shell elements, mixed formulations, MITC elements, inf-sup condition




    An Evaluation of the MITC Shell Elements

    Bathe, Klaus-Jürgen; Iosilevich, Alexander; Chapelle, Dominque. Source: Computers & Structures, v 75, 1-30, 2000.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Based on fundamental considerations for the finite element analysis of shells, we evaluate in the present paper the performance of the MITC general shell elements. We give the results obtained in the analysis of judiciously selected test problems and conclude that the elements are effective for general engineering applications.

    Keywords: shell elements, mixed interpolation, MITC elements, benchmark problems

    Inf-Sup Testing of Upwind Methods

    Bathe, Klaus-Jürgen; Hendriana, Dena; Brezzi, Franco; Sangalli, Giancarlo. Source: Int. J. for Numerical Methods in Engineering, v 48, 745-760, 2000.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: We propose inf-sup testing for finite element methods with upwinding used to solve convection-diffusion problems. The testing evaluates the stability of a method and compactly displays the numerical behaviour as the convection effects increase. Four discretization schemes are considered: the standard Galerkin procedure, the full upwind method, the Galerkin least-squares scheme and a high-order derivative artificial diffusion method. The study shows that, as expected, the standard Galerkin method does not pass the inf-sup tests, whereas the other three methods pass the tests. Of these methods, the high-order derivative artificial diffusion procedure introduces the least amount of artificial diffusion.


    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 8

  • ADINA logo