Study On The Reliability-based Robust Design Of Composite Structures And The Optimization Algorithm

The existing reliability analysis and reliability based design have focused mainly on the effect of random uncertainty on the structural response. Little has been done considering the non-probabilistic or the mixed uncertainty. Meanwhile, Many achievements have been made in robust design optimization based on robustness of objective function, which is achieved by reducing the change of the objective with respect to the change of tolerance for the design variables, but the robustness of constraints has gained little attention, which means that all the constraints are satisfied within the change of tolerance for the design variables. On the other hand, since the reliability based design problem and robust design optimization problem for structures usually involve the solution to a several-loop optimization problem, the computational cost is very expensive in general. Therefore, it is necessary to develop an effective optimization algorithm, establish a theoretical framework of reliability based robust design optimization (RBRDO) and a corresponding optimization strategy which can effectively solve the RBRDO problems.Aiming at the problems mentioned above, the main contents and achievements in this paper are listed as follows:(1) A feasible robust design model is established and then two sequential optimization algorithms are presented. In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some constraints in a structural optimization problem. It is important to ensure that all constraints at the optimum are insensitive to the variations of design variables. However, it is difficult to measure this disparity by probability theory in the absence of data or conditions. In this paper, a tolerance region model is introduced to measure the disparity and a feasible robustness index is defined originally. In order to reduce the computational burden, two sequential sing-loop procedures are proposed to replace the computationally expensive trip-loop procedure for the feasible robust design optimization problems.(2) In practical engineering applications, random uncertainty and epistemic uncertainty are usually mixed together. To make the theoretical model truly reflect the objective reality and avoid the risk induced by artificial assumption, effect of the mixed uncertainties should be considered reasonably. In this paper, a RBRDO is established in accord with the mixture of epistemic uncertainty of design variables and random uncertainty. To reduce the computational burden, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables.(3) Hybrid surrogate model (HSM) is proposed, in which radial basis function (RBF) is first established to interpolate residual errors between the existing data and the estimate values by response surface method at the sample points, and then the derived RBF approximation is added to the response surface approximation. The HSM can provide approximations with equivalent accuracy as RSM surrogate model for linear and low nonlinear problems, and with equivalent accuracy as standard RBF surrogate model for high nonlinear problems, since HSM is constructed by combining linear regression fit and RBF interpolation. Since intelligent optimization algorithm is a population based algorithm, a large population needs to be initiated at the beginning for a simple mathematical problem. For complex engineering structure, one simulation involving multiple disciplines may take several hours or days. This greatly limits the extensive application of intelligent optimization algorithms on the optimization of engineering structures. Therefore, we propose an effective SBPSO. It combines the merits of traditional optimization algorithms and particle swarm optimization, only a small number of particles are needed to achieve the optimal position after several iterations.(4) For solving the optimization problems of complex structures, it is important to ensure the optimal results with good accuracy and make the computational cost reasonable. In order to achieve the requirement, a method combing SBPSO and finite element method is proposed and applied to the reliability-based design optimization of composite lamination and the reliability based robust design optimization of composite pressure vessel with metal liner. In the method, ANSYS/APDL is employed to construct the finite element model and accurately calculate the response of structures, and SBPSO is used to solve the optimization problems with expensive functions. With the method, a global optimum can be found while the computational cost is reduced considerably. For the reliability-based design optimization of composite lamination, both in-plane damage and delamination were taken into account. For composite pressure vessel with metal liner, Tsai-Wu failure criterion and Mises failure are employed to predict failure of the composite plies and metal ply, respectively. The deterministic optimization, reliability based sign optimization and reliability based robust design optimization are solved respectively. It is demonstrated that the proposed method has the property of solving structural optimization of complex structures.