Optimization of submerged funicular arches

Abstract

This paper is concerned with the least weight design of fully stressed, funicular arches subjected to hydrostatic forces and selfweight and having supporting points on different elevations. The optimization problem is posed as the minimization of the arch weight with respect to the axial force parameter, the initial slope of the arch shape and the total curved arch length. To be satisfied is the inequality constraint that is constructed from the error norm to be within a specified tolerance value. This error norm is the sum of the absolute values of the differences between the desired terminal boundary conditions and the computed ones obtained from performing a forward integration of the governing set of first-order differential equations defining the funicular arch shape. The generalized reduced gradient nonlinear optimization method was adopted for the optimization process. Optimal funicular shapes of submerged arches are presented for various water depths, selfweight parameters, and ground slopes. The relationships between the pertinent design parameters are investigated.