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User Oriented Mesh Refinements in the Discrete Element Analysis Technique
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English
Abstract
Much of the recent work by the author [1, 2, 3, 4 and 5] as well as others [6, 7, 8, 9, 10, 11 and 12] has focused on the need to consider idealization geometry a variable in the finite element solution procedure. Such solutions, in which grid geometry is included as a solution variable, have become known as optimum grid solutions.
To date, considerable emphasis has been placed on establishing criteria for the selection of optimum grid solutions. Criteria have been successfully established for the elastostatic, elastodynamic and the elastic stability problem [5]. Focus is now being directed at exploring the benefits of utilizing optimum grid solutions. Several papers have communicated techniques for determining “near optimum” meshes [4,12].
The purpose of this paper is to consolidate and present the recent advanced made in the area of optimum grid solutions.
The author has arranged this talk into three subareas that serve as objectives:
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(1)To present the user of the finite element method with a basic understanding of the theoretical foundation of the optimum grid solution. The formulation of the elastostatic problem will be reviewed. A method for formulating the elastodynamic and elastic stability problem will be indicated. The physical characteristics indicative of the optimum grid solution for the later class of problems will be indicated.
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(2)To present the user with a compendium of user oriented guidelines that have been presented in the published literature. As mentioned, methods for generating “near optimum” solutions have recently received attention. The purpose of this section will be to perform a comparative evaluation of criteria used to direct mesh refinement.
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(3)To indicate to the user the benefits and pitfalls (cost) of full grid optimization versus the near optimum solution. Experience the author has had in operating a program capable of either “mode” shall serve as the basis of this section.
Throughout this talk simple example problems will be presented that demonstrate the nature of the process being discussed.
Guidelines regarding convergence, error analysis, and error detection as they are relevant in the optimum grid context are included.
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Citation
Carroll, W., "User Oriented Mesh Refinements in the Discrete Element Analysis Technique," SAE Technical Paper 770600, 1977, https://doi.org/10.4271/770600.Also In
References
- Carroll W. E. On Optimum Idealizations in Discrete Element Analysis PhD Thesis Virginia Polytechnic Institute and State University Blacksburg 1971
- Carroll W. E. Barker R. M. “A Theorem for Optimum Idealization in Finite Element Analysis,” College of Engineering Report No. VPI-E-72-19 Virginia Polytechnic Institute and State University Blacksburg 1972
- Carroll W. E. Barker R. M. “A Theorem for Finite Element Idealization,” International Journal of Solids and Structures 9 1973
- Carroll W. E. “Ramifications of Optimum Idealization Geometry in Discrete Element Analysis,” Proceedings of the World Congress on Finite Element in Structural Mechanics Bournemouth, England 1975
- Carroll W. E. “Inclusive Criteria for Optimum Grid Generation in the Discrete Analysis Technique,” Second National Symposium on Computerized Structural Analysis and Design Washington, DC 1976 Computers and Structures
- Taig I. C. “Modeling and Interpretation of Results in Finite Element Structural Analysis,” Proceedings of the World Congress on Finite Element in Structural Mechanics Bournemouth, England 1975
- McNeice B. M. Marcal P. V. Optimization of Finite Element Grids Based on Minimum Potential Energy Technical Report No. 7 Brown University 1971
- Oliveria E. R. A. Theoretical Foundations of the Finite Element Method International Journal of Solids and Structures 4 1968
- Turcke D. J. McNeice G. M. A Variational Approach to Grid Optimization International Conference on Variational Methods in Mechanics Southhampton, England 1971
- Fried I. “Note on the Finite Element Analysis of the Axisymmetric Elastic Solids,” International Journal of Solids and Structures 10 1974
- Turcke D. J. McNeice G. M. “Guidelines for Selecting Finite Element Grids Based on an Optimization Study,” Computers and Structures 4 1974
- Melosh R. J. Killian D. E. “Adaptive Mesh Refinement in Finite Element Analysis,” Second National Symposium on Computerized Structural Analysis and Design Washington, DC 1976