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.




    Computational Issues in Large Strain Elasto-Plasticity: An Algorithm for Mixed Hardening and Plastic Spin

    Montáns, Francisco Javier; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical Methods in Eng., v 63, 159-196, 2005.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: In this paper an algorithm for large strain elasto-plasticity with isotropic hyperelasticity based on the Multiplicative decomposition is formulated. The algorithm includes a (possible) constitutive equation for the plastic spin and mixed hardening in which the principal stress and principal backstress directions are not necessarily preserved. It is shown that if the principal trial stress directions are preserved during the plastic flow (as assumed in some algorithms) a plastic spin is inadvertently introduced for the kinematic/mixed hardening case. If the formulation is performed in the principal stress space, a rotation of the backstress is inadvertently introduced as well. The consistent linearization of the algorithm is also addressed in detail.

    Keywords: large strains, computational plasticity, plastic spin, kinematic hardening, cyclic plasticity, logarithmic strains




    3D-Shell Elements and Their Underlying Mathematical Model

    Chapelle, Dominique; Ferent, A.; Bathe, Klaus-Jürgen. Source: Mathematical Models & Methods in Applied Sciences, v 14, 105-142, 2004.

    ISSN: 0218-2025

    Publisher: World Scientific Publishing Company

    Abstract: We focus on a family of shell elements which are a direct generalization of the shell elements most commonly used in engineering practice. The elements in the family include the effects of the through-the-thickness normal stress and can be employed to couple directly with surrounding media on either surfaces of the shell. We establish the "underlying" mathematical model of the shell discretization scheme, and we show that this mathematical model features the same asymptotic behaviors - when the shell thickness becomes increasingly smaller - as classical shell models. The question of "locking" of the finite element discretization is also briefly addressed and we point out that, for an effective finite element scheme, the MITC approach of interpolation is available.

    Keywords: shells, general shell elements, asymptotic behaviors, locking




    On Modeling Mixed Hardening in Computational Plasticity

    Bathe, Klaus-Jürgen; Montáns, Francisco Javier. Source: Computers & Structures, v 82, 535-539, 2004.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We address herein the calculation of Prager’s hardening parameter in computational plasticity when mixed hardening is considered. We consider two approaches to evaluate the mixed hardening response; namely, based on splitting the plastic strains and based on splitting the plastic modulus. For a one-dimensional stress–strain curve with nonlinear hardening, the proper calculation of Prager’s hardening parameter is demonstrated and some comparisons and insight are provided.

    Keywords: Computational plasticity, cyclic response, Prager’s rule, Mixed hardening




    Finite Element Developments for General Fluid Flows with Structural Interactions

    Bathe, Klaus-Jürgen; Zhang, Hou. Source: Int. J. for Numerical Methods in Eng., v 60, 213-232, 2004.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd.

    Abstract: The objective in this paper is to present some developments for the analysis of Navier-Stokes incompressible and compressible fluid flows with structural interactions. The incompressible fluid is discretized with a new solution approach, a flow-condition-based interpolation finite element scheme. The high-speed compressible fluids are solved using standard finite volume methods. The fluids are fully coupled to general structures that can undergo highly non-linear response due to large deformations, inelasticity, contact and temperature. Particular focus is given on the scheme used to couple the fluid media with the structures. The fluids can also be modelled as low-speed compressible or slightly compressible media, which are important models in engineering practice. Some solutions obtained using ADINA are presented to indicate the analyses that can be performed.

    Keywords: fluid flow, incompressible, compressible, FSI, ADINA




    On the Method of Finite Spheres in Applications: Towards the Use with ADINA and in a Surgical Simulator

    De, Suvranu; Hong, Jung-Wuk; Bathe, Klaus-Jürgen. Source: Computational Mechanics, v 31, 27-37, 2003

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

    Publisher: Springer

    Abstract: In this paper we report some recent advances regarding applications using the method of finite spheres; a truly meshfree numerical technique developed for the solution of boundary value problems on geometrically complex domains. First, we present the development of a preprocessor for the generation of nodal points on two-dimensional computational domains. Then, the development of a specialized version of the method of finite spheres using point collocation and moving least squares approximation functions and singular weight functions is reported for rapid computations in virtual environments involving multi-sensory (visual and touch) interactions.

    Keywords: method of finite spheres, meshfree method, ADINA, surgical simulation

    Towards Improving the MITC9 Shell Element

    Bathe, Klaus-Jürgen; Lee, Phill-Seung; Hiller, Jean-François; Source: Computers & Structures, v 81, 477-489, 2003.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: Our objective in this paper is to present some results regarding the predictive capabilities of the MITC9 shell element when the tying points in the element are changed. The MITC9 element is a general nine-node shell element based on the formulation approach of using mixed-interpolated tensorial components. Different tying points are very simple to implement and are not decreasing the computational efficiency of the element. Hence, the use of the “best” tying points is clearly of value.

    Keywords: MITC9 shell element, mixed-interpolated tensorial components, tying points




    Measuring Convergence of Mixed Finite Element Discretizations: An Application to Shell Structures

    Hiller,Jean-François; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 81, 639-654, 2003.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: We consider the problem of assessing the convergence of mixed-formulated finite elements. When displacement-based formulations are considered, convergence measures of finite element solutions to the exact solution of the mathematical problem are well known. However when mixed formulations are considered, there is no well-established method to measure the convergence of the finite element solution. We first review a number of approaches that have been employed and discuss their limitations. After having stated the properties that an ideal error measure would possess, we introduce a new physics-based procedure. The new proposed error measure can be used for many different types of mixed formulations and physical problems. We illustrate its use in an assessment of the performance of the MITC family of shell elements.

    Keywords: mixed-formulated finite elements, error measure, MITC shell elements




    A Shell Problem ‘Highly-Sensitive’ to Thickness Changes

    Bathe, Klaus-Jürgen; Chapelle, Dominique; Lee, Phill-Seung. Source: Int. J. for Numerical Methods in Eng., v 57, 1039-1052, 2003.

    ISSN: 0029-5981 CODEN: IJNMBH

    Publisher: John Wiley & Sons, Ltd

    Abstract: In general, shell structural problems can be identified to fall into one of the categories of membrane-dominated, bending-dominated and mixed shell problems. The asymptotic behaviour with a well-defined load-scaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a well-defined load-scaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes significantly and indeed can fluctuate with changes in shell thickness. We briefly review the different asymptotic behaviours that shell problems can display, and then present the specific problem considered and its numerical solution Using finite element analysis.

    Keywords: shells, asymptotic analysis, finite element solution




    On the Asymptotic Behavior of Shell Structures and the Evaluation in Finite Element Solutions

    Lee,Phill-Seung; Bathe, Klaus-Jürgen. Source: Computers & Structures, v 80, 235-255, 2002.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The objective of this paper is to demonstrate how the asymptotic behavior of a shell structure, as the thickness (t) approaches zero, can be evaluated numerically. We consider three representative shell structural problems; the original Scordelis–Lo roof shell problem, a herein proposed modified Scordelis–Lo roof shell problem and the partly clamped hyperbolic paraboloid shell problem. The asymptotic behavior gives important insight into the shell load bearing capacity. The behavior should also be known when a shell problem is used to test a shell finite element procedure. We briefly review the fundamental theory of the asymptotic behavior of shells, develop our numerical schemes and perform the numerical experiments with the MITC4 shell finite element.

    Keywords: shells, asymptotic behaviors, Ffnite element solutions




    A Flow-Condition-Based Interpolation Finite Element Procedure for Incompressible Fluid Flows

    Bathe, Klaus-Jürgen; Zhang, Hou. Source: Computers & Structures, v 80, 1267-1277, 2002.

    ISSN: 0045-7949 CODEN: CMSTCJ

    Publisher: Elsevier Ltd

    Abstract: The objective of this paper is to demonstrate how the asymptotic behavior of a shell structure, as the thickness (t) approaches zero, can be evaluated numerically. We consider three representative shell structural problems; the original Scordelis–Lo roof shell problem, a herein proposed modified Scordelis–Lo roof shell problem and the partly clamped hyperbolic paraboloid shell problem. The asymptotic behavior gives important insight into the shell load bearing capacity. The behavior should also be known when a shell problem is used to test a shell finite element procedure. We briefly review the fundamental theory of the asymptotic behavior of shells, develop our numerical schemes and perform the numerical experiments with the MITC4 shell finite element.

    Keywords: shells, asymptotic behaviors, finite element solutions




    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 10

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