An integrated approach to structural synthesis and analysis

Abstract

The structural synthesis problem, which is currently viewed as an inequality constrained minimization problem in design variable space, is transformed into an unconstrained minimization problem in a space such that each point represents a set of values for the design variables as well as for each behavior variable in each load condition. Using penalty functions and a trial value of the optimum weight (W0)^ rather than slack variables and Lagrange multipliers, a positive function i/' is constructed such that any point where \[/ = 0 represents an acceptable design of weight W0 or less. This integrated formulation is used to seek optimum designs by systematically reducing W0, thus generating a sequence of acceptable designs with decreasing weight. Numerical examples of optimum designs, based on a nonlinear analysis for a one node m-bar planar truss, are presented together with computer running times. These results are obtained using a steep-descent-type procedure in conjunction with the \//function formulation. The results indicate that the integrated approach offers the prospect of making substantial improvements in the efficiency of the structural synthesis process, particularly when linearization of the structural analysis is inappropriate.