OPTIMAL SHAPE OF ARCHES UNDER BENDING AND AXIAL COMPRESSION.

Abstract

This note investigates the optimal shape of plastically designed nonfunicular arches under a uniformly distributed load. Unlike an earlier study that restricted the arch shape to be a prescribed family of centroidal axes, the arch axis is now made free to take on any shape so as to minimize the weight. This optimization problem is challenging as it involves a nonsmooth objective function and the arch shape is unknown a priori. The proposed method for solving the problem consists of parameterization of the unspecified arch axis using spline functions and employment of a smoothing function to approximate the nonsmooth objective function. The resulting problem can then be solved by any standard nonlinear optimization technique.