Using FORM for minimizing the uncertain cost of structural designs

Abstract

This chapter demonstrates the use of the first-order reliability method (FORM) for minimizing expected cost, when the cost is a continuously differen- tiable function of many random variables and models. The models include con- struction cost and cost of damage, and typically a finite element model. Assuming these costs are non-negative, the expected cost is the area underneath the com- plementary cumulative distribution function on the positive cost axis. Points on this distribution function are determined by FORM and numerical integration is employed to calculate the area. Exact derivatives of responses and costs with respect to random variables are propagated through the models and used in FORM. Moreover, exact derivatives of responses and costs with respect to design variables are propagated through FORM in order to have exact derivatives of the expected cost available in the optimization analysis. This framework for minimizing expected cost is implemented in a computer program and illustrated by means of a demonstration example.