Study On The Reliability-based Optimum Design And The Robust Optimization For Laminated Composite Structures

Consisting of the high strength-low density fibers and matrix, the fibrous composite has many excellent properties or special characteristics, for example, high specific strength and high specific modulus, anisotropic and designable. In recent twenty years, it has been widely used in the structures of aircraft, space, marine and automobile, etc. The study on the fibrous composite, especially on its structural optimal design has become an important concern.The mechanical properties of composite materials are correlated with the manufacturing process, and their dispersed degrees are generally larger than metals'. They are sensitive to the change of loads, boundary conditions and surroundings because of the anistropic features. Composite materials are usually used in complex environments and severe conditions. All those need a preferable structural reliability, and the reliability-based optimum design of composite structures has thus become an important developing topic of research.Due to the manufacturing errors, in many ways, the real composite structure may differ from the design in, for example, the fiber orientations and the thickness of the sub-laminates. Performances of the structure will be influenced by the variation of these factors. A robust design is necessary which aims to compensate the loss induced by the variation and gets a stable solution. This is a new theme.Achievements in this paper are listed as follows:The advances in studies on structural reliability analysis, reliability-based optimum design for structures, especially for composite laminate's are summarized and commented. A reliability analysis model of the composite laminate is presented. The first order second moment method is used to estimate the reliability of each ply group, and the system reliability is computed based on first–ply failure (FPF) or last-ply failure (LPF) assumptions. For a lamina, two major failure modes are considered: matrix failure and fiber breakage that are characterized by the proper strength criteria in the literature. For the last-ply failure assumption, system reliability is estimated through the significant failure sequences. Numerical examples are given to compare the results of different assumptions, and show the validity of the method proposed.The optimum design of composite laminates under probabilistic considerations is dealt with. The objective is the maximization of the system reliability index with the total thickness as the constraint. A genetic algorithm (GA) is used to search for the optimum solution. Numerical examples are worked out to demonstrate the accuracy by comparing the results with that obtained from the sequential quadratic programming technique (SQP). It is showed that GA is an efficient method in solving the reliability-based optimum design problem for laminated composites, especially for the case where the last-ply failure assumption is adopted.The robust optimum design for laminated composite plates is bring forward. The ultimate strength is computed by FEM, and based on this, the optimum and robust optimum are analyzed considering both in-plane and out-of-plane loads. For a lamina, two major failure modes are considered: matrix cracking and fiber breakage. When a lamina has failed, the laminate stiffness is modified to reflect the damage, and stresses in the structure are re-analyzed. This procedure is repeatedly performed until the whole structure fails and thus the ultimate strength is determined. A structural optimization problem is solved with the fiber orientation and the lamina thickness as the design variables and the LPF load as the objective. Robust optimum design method for laminates is presented and discussed. A numerical example is put forward to compare robust design with the conventional optimum solution, to show the necessity and the advantage of the robust optimum design.