The researcher will investigate conditions under which problems in structural design optimization map, without approximation, to linear programming (LP) problems, and to create algorithms which exploit these special properties. The conventional approach is to treat such problems as ones in nonlinear programming (NLP). For large systems, exact solution of the resulting NLP problem is often intractable. It has been shown that a class of structural design problems can be solved much more efficiently. The method requires solution of an LP followed by a system of linear equations. Solution of the LP identifies a canonical structure which possesses the same displacement field as the optimal structure. This displacement field renders the equilibrium equations as a linear system in unknown areas, which can be solved to yield the optimum design. As a consequence, problems can now be solved of practical interest to civil and aerospace engineers several orders of magnitude larger than previously imagined. The goal of this research is to extend the LP methodology to encompass a more general class of structural design optimization problems. Initial numerical evidence indicates that the method is extendable to displacement and frequency constraints. In addition to these constraints, buckling and multiple loads will be considered, and the researchers will define extensions of the method to structures discretized by continuum finite elements. If successful for this broader class of problem, the LP method will greatly reduce the computational effort required for solving these optimization problems, as a consequence of the need to solve an LP rather than a NLP. Such a significant enhancement of efficiency will make optimization more attractive to structural designers.
