Exact sensitivity analysis of stresses and lightweight design of Timoshenko composite beams

Abstract

The paper describes the novel optimization techniques for lightweight design of composite beams. The optimization model is to find width and depth of composite beams to minimize the mass of beams under the stiffness, strength and delamination failure constraints. The exact formulae for displacements, stresses and their sensitivities with respect to width and depth are derived using Timoshenko continuous beam theory. The analytical stiffness, strength and delamination failure functions, and their gradients are obtained using the exact expressions of displacements and stresses, and their sensitivities. The mass and its gradient are also expressed analytically. The standard gradient-based nonlinear programming algorithms are employed to solve lightweight design problems of composite beams. The lightweight designs of composite beams are performed using the proposed optimization techniques. Three standard gradient-based optimization methods (SQP, interior-point and active-set) using exact derivatives converge to the same lightweight design. However, gradient-based algorithms using finite difference sensitivities may not lead to optimal lightweight designs. It is necessary to develop exact sensitivity analysis method instead of the difference methods for gradient-based algorithms.