Probabilistic optimum design of composite laminates

This paper proposes a procedure for the optimum design of composite laminates under probabilistic considerations. The problem is formulated to consider the minimization of laminate weight as the objective function and the reliability requirements as the constraints. Both system-level and element-level reliabilities are considered, The first-order reliability method (FORM) is used to estimate the reliability of each ply group, and system reliability is computed based on series or parallel system assumptions. The Tsai-Wu strength criterion is adopted to derive the limit state function of individual ply groups in the laminate. The gradient and sensitivity information of the objective function and the constraints with respect to the design variables are obtained by using sensitivity analysis based on the composite plate theory. Thus the proposed procedure brings together modern concepts of reliability analysis, composite laminate behavior and nonlinear optimization to develop a rational and practical procedure for the optimum design of composite laminates. Numerical examples are presented to demonstrate the effectiveness of the proposed method.