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Equivalent displacement based formulations for maximum strength truss topology design. (English) Zbl 0769.73054

Maximum strength elastic truss structural design is conveniently formulated in terms of displacements and bar volumes. The resulting problem is nonconvex, and for topology design very large, as one seeks the optimal topology as a subset of a large number of potential bars connecting all nodal points of an initially chosen set. In this paper we present a number of equivalent formulations in the displacements only, taking full advantage of the structure of the optimization problem. The equivalent formulations are of min-max type or are quadratic programming problems in the displacements, reducing in some cases even to linear programming problems.

MSC:

74P99 Optimization problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
90C90 Applications of mathematical programming
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