- The quadratic MITC plate and MITC shell elements in plate bending
- P.S. Lee ; K.J. Bathe
- Book Title / Journal:
- Year: 2010 , Volume: , Series:
- Structural Analysis
- Keywords: Plate ; shell ; mixed formulation ; Finite elements
- Description
- The analysis of plates can be achieved using the quadratic MITC plate or MITC shell elements. The plate elements have a strong mathematical basis and have been shown to be optimal in their convergence behavior, theoretically and numerically. The shell elements have not (yet) been analyzed mathematically in depth for their rates of convergence, with the plate/shell thickness varying, but have been shown numerically to perform well. Since the shell elements are general and can be used for linear and nonlinear analyses of plates and shells, it is important to identify the differences in the performance of these elements when compared to the plate elements. We briefly review the quadratic quadrilateral and triangular
MITC plate and shell elements and study their performances in linear plate analyses.
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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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- Towards improving the MITC9 shell element
- K.J. Bathe ; P.S. Lee ; J.F. Hiller
- Book Title / Journal: Computers and Structures
- Year: 2003 , Volume: 81 , Series:
- Structural Analysis
- Keywords: Shell elements ; MITC9
- Description
- The 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.
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- 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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