Page 7 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:
You are welcome to download the second edition of the book, 4th printing, however, please note that the book is copyrighted and should only be used in the same manner as a purchased hardcopy of the book. Improved versions will be made available here, from time to time, as the 5th printing, and so on. "Finite Element Procedures", 2nd Edition (.pdf) 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
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
An Arbitrary LagrangianEulerian Velocity Potential Formulation for FluidStructure Interaction Nitikitpaiboon, C.; Bathe, KlausJürgen. Source: J. Computers & Structures, v 47, No, 4/5, 871891, 1993. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: Finite clement formulations for fluidstructure interaction, assuming an inviscid fluid, can be classified into two major categories: displacementbased formulations and potentialbased formulations. Although displacementbased formulations have been used widely, the methods suffer from the presence of spurious circulation modes and locking behavior. Potentialbased formulations are inherently irrotational and do not have the difficulties of the displacementbased formulations. Nevertheless most of the applications of these methods are still limited to cases with relatively small motions. We introduce in this paper an arbitrary LagrangianEulerian formulation using the velocity potential and the density as fluid variables. The formulation can be applied to problems in which the fluid undergoes very large boundary motions and can be used equally well for both compressible and incompressible fluids. Keywords: arbitrary LagrangianEulerian formulation, locking behaviour, fluid structure interaction, finite element
Kato, K.; Lee, NamSua; Bathe, KlausJürgen. Source: J. Computers & Structures, v 47, No. 4/5, 829855, 1993. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: Some basic studies and developments for adaptive procedures in large strain finite element analysis are presented: an evaluation of higherorder elements, two pointwise indicators for errors in stresses, a mesh generator for remeshing on the deformed configuration of the body, and a general mapping scheme for transferring solution variables across models. The methods discussed constitute the ingredients of a proposed adaptive process that is demonstrated in solutions of twodimensional stress analyses of rubberlike materials including contact conditions. Keywords: adaptive finite element analysis, large strain, rubberlike material
Chapelle, Dominique; Bathe, KlausJürgen. Source: J. Computers & Structures, v 47, No. 4/5, 537545, 1993. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: We briefly review the infsup condition for the finite element solution of problems in incompressible elasticity, and then propose a numerical test on whether the infsup condition is passed. The evaluation of elements with this test is simple, and various results are presented. This infsup test will prove useful for many discretizations of constrained variational problems. Keywords: infsup test, constrained variational problem
Bucalem, Miguel Luiz; Bathe, KlausJürgen. Source: Int. J. for Numerical Methods in Engineering, v 36, 37293754, 1993. ISSN: 00295981 CODEN: IJNMBH Publisher: John Wiley & Sons, Ltd. Abstract: Two mixedinterpolated general shell finite elements for nonlinear analysisa 9node element and a 16node elementare presented. The elements are based on the Mixed Interpolation of Tensorial Components (MITC) approach in which the covariant strain component fields for the inplane and shear actions are interpolated and tied to the also interpolated displacement field. Both the 9node element, referred to as the MITC9 element, and the 16node element, referred to as the MITC16 element, are tested numerically and found to have high predictive capabilities. Keywords: Mixed Interpolation of Tensorial Components, MITC, shell element
Lee, NamSua; Bathe, KlausJürgen. Source: Int. J. for Numerical Methods in Engineering, v 36, 35533576, 1993. ISSN: 00295981 CODEN: IJNMBH Publisher: John Wiley & Sons, Ltd. Abstract: We discuss the effects of element distortions on the performance of displacementbased isoparametric quadrilateral finite elements. Suitable example problems for both the Lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions. The effects of angular and curvededge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields. We then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution. The conclusion is that the Lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use. Keywords: isoparametric element, finite element, Lagrangian element
Eterovic, Adrian Luis; Bathe, KlausJürgen. Source: J. Computers & Structures, v 40, No. 2, 203209, 1991. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: Existing methods for the analysis of contact problems deal with the inequality constraints arising from contact conditions by means of an implicit iteration on all constraints. This paper presents a formulation for contact problems with friction for large deformations where all inequality constraints are enforced explicitly. A robust solution technique for the resulting system of nonlinear equations can then be used. This approach admits the use of line search procedures to enlarge the region of convergence. Keywords: finite element, contact condition, line search procedure
Eterovic, Adrian Luis; Bathe, KlausJürgen. Source: J. Comp. Methods in Applied Mech. and Eng., v 93, 3138, 1991. ISSN: 00457825 Publisher: Elsevier Science B.V. Abstract: This note explores some consequences of the assumption of the additive decomposition of the strain tensor in the formulation of constitutive equations for finite deformation inelastic analysis. It is shown that the incremental elastic response can depend on the prior inelastic deformations, and explicit formulas are given that quantify this effect. Keywords: strain tensor, finite deformation elasticity, constitutive equation
Bathe, KlausJürgen; Bucalem, Miguel Luiz; Brezzi, Franco. Source: J. Eng. Computations, v 7, no. 4, 291302, 1990. ISSN: 02644401 Publisher: MCB UP Ltd Abstract: We briefly summarize the theoretical formulations of our MITC plate bending elements and then present numerical convergence results. The elements are based on ReissnerMindlin plate theory and a mixedinterpolation of the transverse displacement, section rotations and transverse shear strain components. We consider our 4, 9 and 16node quadrilateral elements and our 7 and 12node triangular elements. The theoretical and numerical results indicate the high reliability and effectiveness of our elements. Keywords: MITC plate bending element, ReissnerMindlin
Eterovic, Adrian Luis.; Bathe, KlausJürgen. Source: Int. J. Numerical Methods in Engineering, v 30, 10991114, 1990. ISSN: 00295981 CODEN: IJNMBH Publisher: John Wiley & Sons, Ltd. Abstract: This paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity. The combined isotropickinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions: (i) the formulation is hyperelastic based, (ii) the stressstrain law preserves the elastic constants of the infinitesimal theory but is written in terms of the Hencky strain tensor and its elastic work conjugate stress tensor, and (iii) the multiplicative decomposition of the deformation gradient is adopted. Since no stress rates are present, the formulation is, of course, numerically objective in the time integration. It is shown that the model gives adequate physical behaviour, and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor. Keywords: hyperelastic, isotropickinematic hardening
Brezzi, Franco; Bathe, KlausJürgen. Source: J. Computer Methods in Applied Mechanics and Engineering, v 82, 2757, 1990. ISSN: 00457825 Publisher: Elsevier Science B.V. Abstract:
We
discuss the general mathematical conditions for solvability,
stability and optimal error bounds of mixed finite element
discretizations. Our objective is to present these conditions with
relatively simple arguments. We present the conditions for
solvability and stability by considering the general coefficient
matrix of mixed finite element discretizations, and then deduce the
conditions for optimal error bounds for the distance between the
finite element solutions and the exact solution of the mathematical
problem. To exemplify our presentation we consider the solutions of
various example problems. Finally, we also present a numerical test
that is useful to identify numerically whether, for the solution of
the general Stokes flow problem, a given finite element
discretization satisfies the stability and optimal error bound
conditions.
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