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
(6 volumes)
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
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Keywords: mixed finite element formulation, Stokes flow problem, error bound
Nonlinear
Analysis of Concrete Structures
Bathe, Klaus-Jürgen; Walczak, Jan; Welch, Alan; Mistry, Nagin. Source: J. Computers & Structures, v 32, No. 3/4, 563-590, 1989.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract: Solution capabilities for two- and three-dimensional nonlinear finite element analysis of concrete structures are presented. The concrete material is modeled including the triaxial nonlinear stress-strain behavior, tensile cracking, tension-stiffening, compression crushing and strain-softening. The results of various sample analyses are given to demonstrate the constitutive model and the solution strategies. These analyses include the response predictions of a test beam and of small scale models of two reactor vessels.
Keywords: nonlinear analysis, concrete structure, constitutive model
Some
Advances in the Analysis of Semi-deformable Media
Sussman, Theodore; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 30, No. 1/2, 105-112, 1988.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract: Semi-deformable media are materials in which certain modes of deformation are prohibited (for example, incompressible materials). The displacement/pressure (u/p) finite element formulation can be used to effectively analyze semi-deformable media. We summarize the basic characteristics of the formulation and present some representative numerical examples in linear and nonlinear analysis.
Keywords: semi-deformable media, finite element
A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis
Sussman, Theodore; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 26, 357-409, 1987.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract: We introduce a displacement-pressure (u/p) finite element formulation for the geometrically and materially nonlinear analysis of compressible and almost incompressible solids. The (u/p) formulation features the a priori replacement of the pressure computed from the displacement field by a separately interpolated pressure; this replacement is performed without reference to any specific material description. Considerations for incremental nonlinear analysis (including contact boundary conditions) are discussed and various (u/p) elements are studied. Numerical examples show the performance of the (u/p) formulation for two- and three-dimensional problems involving isotropic, orthotropic, rubber-like and elasto-plastic materials.
Keywords: finite element, nonlinear analysis, isotropic material; orthotropic material, rubber-like material, elasto-plastic material
Studies
of Finite Element Procedures—Stress Solution of a Closed
Elastic Strain Path with Stretching and Shearing Using the Updated
Lagrangian Jaumann Formulation
Kojić, Miloš; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 26, 175-179, 1987.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract: The updated Lagrangian Jaumann formulation is used for the analysis of an elastic closed strain path involving stretching and shearing. The analytical stress solution for each phase of the strain path is given and the final stresses at zero strain are calculated.
We do not present any new concept or procedures but study an interesting example solution that gives insight into the use of the updated Lagrangian Jaumann formulation.
Keywords: finite element, strain path, updated Lagrangian Jaumann formulation
Thermo-Elastic-Plastic
and Creep Analysis of Shell Structures
Kojić, Miloš; Bathe, Klaus-Jürgen. Source: J. Computers & Structures, v 26, 135-143, 1987.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract: The effectivc-stress-function algorithm previously proposed for general 2-D and 3-D thermo-elastic-plastic and creep analysis is specialized to the stress and strain conditions of shell and beam structures. Von Mises plasticity with isotropic and kinematic hardening assumptions and the potential theory of creep are considered. The governing equations to compute the plastic and creep effects are given, and the numerical results obtained in the analysis of some demonstrative beam and shell problems are presented.
Keywords: shell structure, creep analysis, thermo-elastic-plastic analysis
The
'Effective-Stress-Function' Algorithm for Thermo-Elasto-Plasticity
and Creep
Kojić, Miloš; Bathe, Klaus-Jürgen. Source: Int. Journal for Numerical Methods in Engineering, v 24, 1509-1532, 1987.
ISSN: 0029-5981 CODEN: IJNMBH
Publisher: John Wiley & Sons, Ltd.
Abstract: An algorithm for stable and accurate computations of stresses in finite element thermo-elastic-plastic and creep analysis of metals is presented. The effective-stress-function algorithm solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective-stress-function: a functional relationship which involves as unknown only the effective stress. The derivation of the effective-stress-function for thermo-elasto-plasticity conditions, including creep, for 2-D and 3-D analysis is presented, and the algorithmic steps of the stress solution are discussed. For use in the stiffness matrix a tangent material stress-strain relationship is evaluated consistent with the effective-stress-function algorithm. The solution of some demonstrative problems shows the effectiveness of the solution procedure
Keywords: effective-stress-function algorithm, finite element, thermo-elastic-plastic analysis, creep analysis
Causes
and Consequences of Nonuniqueness in an Elastic-Perfectly-Plastic
Truss
Hodge, P. G. Jr.; Bathe, Klaus-Jürgen; Dvorkin, Eduardo N. Source: Journal of Applied Mechanics, v 53, 235-241, 1986.
ISSN: 0021-8936 (print); 1528-9036 (online)
Publisher: American Society of Mechanical Engineers
Abstract: A complete solution to collapse is given for a three-bar symmetric truss made of an elastic/perfectly-plastic material, using linear statics and kinematics, and the solution is found to be partially nonunique in the range of contained plastic deformation. The introduction of a first-order deviation from symmetry and/or the inclusion of first order nonlinear terms in the equilibrium equations is found to restore uniqueness. The significance of these effects is analyzed and discussed from mathematical, physical, modeling, computational and engineering points of view.
Keywords: elasto-plasticity, collapse analysis, uniqueness of solution, truss structure
Finite
Elements in CAD and ADINA
Bathe, Klaus-Jürgen. Source: Nuclear Engineering and Design, 57-67, 1986.
ISSN: 0029-5493 (print); 1872-759X (online)
Publisher: Elsevier Science B.V.
Abstract: The use of finite element methods in computer-aided-design — CAD — is discussed. Some current capabilities are presented and important future developments are outlined. The discussion focusses on the use of the ADINA program in CAD applications.
Keywords: finite element, CAD, ADINA
Studies
of Finite Element Procedures - Stress Band Plots and the Evaluation
of Finite Element Meshes
Sussman, Theodore; Bathe, Klaus-Jürgen. Source: J. Engineering Computations, v 3, No. 3, 178-191, 1986.
ISSN: 0264-4401
Publisher: MCB UP Ltd
Abstract: We describe a visual method—stress band plots—for displaying the stress solution within a two-dimensional finite element mesh. The stress band plots differ from conventional stress contour plots because stress band plots display unaveraged stresses (the stresses are computed directly from the solution variables) and stress discontinuities in the finite element solution are directly displayed. Stress band plots are useful in judging the accuracy of a finite element solution, in the comparison of different finite element solutions and during mesh refinement. These uses are demonstrated in an axisymmetric pressure vessel analysis.
Keywords: finite element, stress band plot
A
Formulation of General Shell Elements—The Use of Mixed
Interpolation of Tensorial Components
Bathe, Klaus-Jürgen; Dvorkin, Eduardo N. Source: Int. Journal for Numerical Methods in Engineering, v 22, 697-722, 1986.
ISSN: 0029-5981 CODEN: IJNMBH
Publisher: John Wiley & Sons, Ltd.
Abstract: We briefly discuss the requirements on general shell elements for linear and nonlinear analysis in practical engineering environments, and present our approach to meet these needs. We summarize and give further insight into our formulation of a 4-node shell element using a mixed interpolation of tensorial components, and present a new 8-node element using this approach. Specific attention is given to the general applicability of the elements and their efficient use in practice.
Keywords: shell element, mixed interpolation of tensorial components
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