- On the asymptotic behavior of shell structures and the evaluation in finite element solutions
- P.S. Lee ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2002 , Volume: 80 , Series:
- Structural Analysis
- Keywords: shells ; Asymptotic behaviors ; Finite element solutions
- Description
- 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.
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- A shell problem ‘highly sensitive’ to thickness changes
- K.J. Bathe ; D. Chapelle ; P.S. Lee
- Book Title / Journal: International Journal for Numerical Methods in Engineering
- Year: 2003 , Volume: 57 , Series:
- Structural Analysis
- Keywords: shells ; asymptotic analysis ; finite element solution
- Description
- In general, shell structural problems can be identied 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-dened 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 signicantly and indeed can uctuate with changes in shell thickness. We briefly review the dierent asymptotic behaviours that shell problems can display, and then present the specic problem considered and its numerical solution using nite element analysis.
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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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- A triangular six-node shell element
- D-N Kim ; K.J. Bathe
- Book Title / Journal: Computers and Structure
- Year: 2009 , Volume: 87 , Series:
- Structural Analysis
- Keywords: shells ; Finite element ; Triangular element ; Spatial isotropy ; MITC method ; Six-node element
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- Advances in the Multiphysics Analysis of Structures
- K.J. Bathe
- Book Title / Journal:
- Year: 2012 , Volume: , Series:
- Structural Analysis
- Keywords: Finite elements ; wave propagations ; shells ; Large strains ; Maxwell’s equations ; electromechanics
- Description
- In this presentation we survey the advances that we have recently accomplished for the effective analysis of solids and structures, specifically for wave propagations and transient solutions, the analysis of shells, improved stress calculations, the use of interpolation covers, and the solution of the full Maxwell’s equations. The structures may be subjected to complex fluid flows and electromagnetic effects. We briefly give the theoretical developments for the formulations, a few illustrative solutions, and conclude by mentioning some further exciting research challenges.
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