Structural optimization utilizing approximated structural behavior

Abstract

This dissertation presents an investigation of the feasibility of using approximated structural behavior in the optimization of plane truss and plane frame structures. Design variables are limited to the cross-sectional areas and/or moments of inertia of members of constant cross-section. Total weight or total volume of material has been taken as the objective function to be minimized. Limitations on members stress and nodal displacements have been imposed on the optimum design. An explicit functional relationship between a nodal displacement and the design variables has been determined, to within a set of unspecified parameters, for plane truss and frame structures. Based on this relationship, a simple approximating functional form is established with which to approximate the displacements of each node in the structure. The structure is then analyzed for a number of sets of values of the design variables (data points) and the computed nodal displacements are used to compute unknown coefficients in the approximating function so that it best fits the known displacements of a given node in the Least Squares sense. A special scheme of choosing data points has been devised for this problem which proves useful in cases where both the approximated and approximating functions are homogenous. These approximating functions are then used in nonlinear mathematical programming formulation of the minimum weight (or volume) design problem to evaluate constrains on member stresses and nodal displacements. Several plane truss and frame structures are optimized to study the feasibility of the method. The solutions obtained are compared with known solutions from the literature and the computer running times for the truss examples are compared with those obtained in solving the problem by the traditional method of incorporating a structural analysis routine in the optimization program to evaluate constraints. The results of these example problems indicate a significant reduction in computer run time to obtain an optimum structure without a significant loss in the accuracy of the optimum point.