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Optimal Design of Large Discretized Systems by Iterative Optimality Criteria Methods
Abstract After explaining the discrepancy between analysis and optimization capability of currently available soft- and hardware, a short history of continuum-based optimality criteria (COC) is given and certain fundamental concepts are introduced. The analytical COC approach is illustrated by three simple examples in which the differences between optimal plastic and optimal elastic strength design are also explained and it is shown that the solution is in general not fully stressed for elastic systems with a stress constraint. The third analytical example demonstrates the proposed technique for problems with vanishing members. The rest of the text deals in detail with the COC formulation for elastic systems with stress and displacement constraints and its iterative solution for large discretized systems. It is shown in worked examples that the proposed approach can handle up to one million elements and one million variables and a number of local and global constraints of the same order of magnitude. One particularly ill-conditioned example is chosen to demonstrate that in such problems an accurate solution does require a very large number of elements in the discretization. Other examples include various geometrical constraints, two-dimensional systems, allowance for selfweight and cost of reactions as well as problems with permissible normal and shear stresses.
Optimal Design of Large Discretized Systems by Iterative Optimality Criteria Methods
Abstract After explaining the discrepancy between analysis and optimization capability of currently available soft- and hardware, a short history of continuum-based optimality criteria (COC) is given and certain fundamental concepts are introduced. The analytical COC approach is illustrated by three simple examples in which the differences between optimal plastic and optimal elastic strength design are also explained and it is shown that the solution is in general not fully stressed for elastic systems with a stress constraint. The third analytical example demonstrates the proposed technique for problems with vanishing members. The rest of the text deals in detail with the COC formulation for elastic systems with stress and displacement constraints and its iterative solution for large discretized systems. It is shown in worked examples that the proposed approach can handle up to one million elements and one million variables and a number of local and global constraints of the same order of magnitude. One particularly ill-conditioned example is chosen to demonstrate that in such problems an accurate solution does require a very large number of elements in the discretization. Other examples include various geometrical constraints, two-dimensional systems, allowance for selfweight and cost of reactions as well as problems with permissible normal and shear stresses.
Optimal Design of Large Discretized Systems by Iterative Optimality Criteria Methods
Rozvany, G. I. N. (author) / Gollub, W. (author) / Zhou, M. (author)
1992-01-01
66 pages
Article/Chapter (Book)
Electronic Resource
English
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