Displacement based multilevel structural optimization: beams, trusses, and frames

TLDR: In this paper, a finite element based multilevel optimization is performed on large three-dimensional trusses, to one-dimensional beams, and to two-dimensional frames, where the weight of each element is minimized under the action of nonlinear stress constraints.

Abstract: When attempting to perform true multidisciplinary design optimization (MDO) in a realistic and complex environment, economy of time and effort are two of the most desirable attributes of any approach, in the overall optimization and in the sub-disciplines. A new and efficient methodology for the MDO subset of structural optimization was recently developed and applied to the minimum weight optimization of small two- and three-dimensional statically indeterminate truss structures under size, strength, and displacement constraints. In this paper, the approach is extended to large three-dimensional trusses, to one- and two-dimensional beams, and to two-dimensional frames. Specifically, finite element based multilevel optimization is performed on these structures. In the system level optimization, the load unbalance resulting from the substitution of approximate displacements into the stiffness equations is minimized. These approximate displacements are obtained from assumed polynomially based global displacement functions whose coefficients are the design variables. In the subsystem level optimizations, the weight of each element is minimized under the action of nonlinear stress constraints. Here, the cross sectional dimensions of the individual elements are the design variables. The approach is quite effective since the optimization task is distributed and broken down into a number of small and efficient subtasks, each with a rather limited number of variables, making it amenable to distributed and parallel computing.