Weight optimum arch structures

Abstract

This investigation is concerned with the optimization of arch structures. The DOT optimization code is used to minimize the volume of such arch structures which are constrained by limits on stress, design geometry, and section dimensions. Modeling the arch structure by a series of bar-beam elements, the finite elements method is used to compute element stresses. The DOT optimization code selects section dimensions to prevent failure due to element stresses exceeding the material yield stress. Specifically, through coordinate transformations between local element coordinates and global systems coordinates the element stiffness matrices transform into the global stiffness matrix. The resulting system matrix equations are then solved for the system degrees of freedom, that is, displacements and slopes. The system degrees of freedom, in turn, are then transformed back to the element level to computer the internal forces and moments and hence, the stresses. Results are presented for a number of cases with regard to optimization scheme and stress analysis.