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Shape optimization using the boundary element method with substructuring
Author(s) -
Sandgren Eric,
Wu ShyueJian
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260903
Subject(s) - shape optimization , linearization , boundary element method , mathematics , plane stress , boundary (topology) , mathematical optimization , finite element method , linear elasticity , optimization problem , elasticity (physics) , boundary knot method , geometry , mathematical analysis , structural engineering , nonlinear system , engineering , materials science , physics , quantum mechanics , composite material
Applications of the boundary element method for two‐ and three‐dimensional structural shape optimization are presented. The displacements and stresses are computed using the boundary element method. Sub‐structuring is used to isolate the portion of the structure undergoing geometric change. The corresponding non‐linear programming problem for the optimization is solved by the generalized reduced gradient method. B ‐spline curves and surfaces are introduced to describe the shape of the design. The control points on these curves or surfaces are selected as design variables. The design objective may be either to minimize the weight or a peak stress of the component by determining the optimum shape subject to geometrical and stress constraints. The use of substructuring allows for problem solution without requiring traditional simplifications such as linearization of the constraints. The method has been successfully applied to the structural shape optimization of plane stress, plane strain and three‐dimensional elasticity problems.