- The mathematical shell model underlying general shell elements
- D. Chapelle ; K.J. Bathe
- Book Title / Journal: International Journal for Numerical Methods in Engineering
- Year: 2000 , Volume: , Series:
- Structural Analysis
- Keywords: shell model ; finite element discretization ; degenerated solid
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- Finite element analysis of fluid flows fully coupled with structural interactions
- K.J. Bathe ; H. Zhang ; S. Ji
- Book Title / Journal: Computers and Structures
- Year: 1999 , Volume: 72 , Series:
- Structural Analysis
- Keywords: Finite element analysis ; coupled analysis ; fluid flow
- Description
- 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.
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- Fundamental Considerations for the Finite Element Analysis of Shell Structures
- D. Chapelle ; K.J. Bathe
- Book Title / Journal: Computers & Structures
- Year: 1998 , Volume: 66 , Series:
- Structural Analysis
- Keywords: shells ; Finite element analysis
- Description
- 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.
An effective finite element scheme should be applicable to both categories of shell behaviour and the rate of convergence in either case should be optimal and independent of the shell thickness. Such a finite element scheme is difficult to achieve but it is important that existing procedures be analysed and measured with due regard to these considerations. To this end, we present theoretical considerations and we propose appropriate shell analysis test cases for numerical evaluations.
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- Mixed-Interpolated Elements for Reissner-Mindlin Plates
- F. Brezzi ; K.J. Bathe ; M. Fortin
- Book Title / Journal: International Journal for Numerical Methods in Engineering
- Year: 1989 , Volume: 28 , Series:
- Structural Analysis
- Description
- We present in this paper a procedure to establish Reissner-Mindlin plate bending elements. The procedure is based on the idea to combine known resuits on the approximation of Stokes problems with known results on the approximation of elliptic problems. The proposed elements satisfy the mathematical conditions of stability and convergence, and some of them promise to provide efficient elements for practical solutions.
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- An Accelerated Subspace Iteration Method
- K.J. Bathe ; S. Ramaswamy
- Book Title / Journal: Computer Methods in Applied Mechanics and Engineering
- Year: 1980 , Volume: 23 , Series:
- Structural Analysis
- Description
- The subspace iteration method for solving symmetric eigenproblems in computational mechanics is considered. Effective procedures for accelerating the convergence of the basic subspace iteration method are presented. The accelerated subspace iteration method has been implemented and the results of some demonstrative sample solutions are presented and discussed.
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