An interpretation for min-max structural design problems including a method for relaxing constraints. (English) Zbl 0531.73062

Taylor, J. E.; Bendsøe; Martin, P.

Int. J. Solids Struct. 20, 301-314 (1984).

Summary: Min-max type problems arise in structural design when the objective is to minimize the maximum value of some local measure of system response, e.g. design to minimize the maximum stress or displacement. A method is described whereby the min-max problem is interpreted as a simple min problem. Governing equations for the adjoint structure are derived directly from the Lagrangian for this min problem by using the generalized multiplier rule on the original state equations. Also certain advantages are demonstrated for a modified form of the min-max problem, a form obtained by introducing a relaxation on the local constraints. The analysis is applied for examples of structural design with stress and displacement criteria, and for the design of an elastic foundation to minimize support pressure.

MSC:

74P99

Optimization problems in solid mechanics

Keywords:

min-max structural design problems; governing equations for adjoint structure derived directly from Lagrangian; generalized multiplier rule on original state equations; relaxation on local constraints; design to minimize the maximum stress or displacement; simple min problem; elastic foundation to minimize support pressure