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Composites have been applied more and more in aviation, which leads to a need of aeroelasticity design of composite structures. In this paper, the aeroelasticity and strength optimization design of composite structures is explored. In view of the low efficiency of the traditional aeroelasticity and strength optimization process, a sequential optimization process of aeroelasticity and strength is proposed, which decouples the aeroelastic analysis from the optimization process, reduces the number of calls of the aeroelastic analysis program, and thus shortens the optimization cycle and improves the optimization efficiency. The reliability design method is compared with the traditional deterministic design method. Considering the dispersion of composite materials, the reliability-based aeroelasticity/strength optimization method of composite structures is established. The uncertainty is introduced into the multidisciplinary optimization of composite structures. In the reliability optimization design, the double-layer sequential method is used to decouple the reliability analysis and aeroelastic analysis from the optimization process, which reduces the number of calls of aeroelastic analysis program and reliability analysis program, and improves the optimization efficiency. Compared with the traditional optimization method based on b-reference value and safety factor, better design results are obtained.

Directly solving time-dependent reliability-based design optimization (TRBDO) with aleatory and epistemic uncertainties is time-demanding, which limits its engineering application. By treating aleatory and epistemic uncertainties with probability and evidence variables respectively, an advanced decoupling method named sequential optimization and unified time-dependent reliability analysis (SOUTRA) is proposed in this work. By the SOUTRA, the original nested optimization process is solved by a sequence of unified time-dependent reliability analysis, updated reliability index target estimation and deterministic optimization. Only few numbers of the unified time-dependent reliability analysis are required to derive the optimum by the SOUTRA; thus, it is highly efficient. Furthermore, in order to construct the deterministic optimization, a new probability transformation method named focal element midpoint (FEM) is established to convert the evidence variable into a random one. FEM can avoid the issues of uniformity approach and equal areas method, and both are used in the existing probability transformation. Several numerical and engineering applications are introduced to illustrate the effectiveness of the proposed SOUTRA.

Based on decoupling strategy, a novel efficient method is proposed to solve the nonlinear interval uncertainty optimization problem with correlated interval design variables or parameters. This method is applicable to cases where both objective function and constraints are nonlinear with uncertain parameters, and design variables and parameters can be correlated or independent. The uncertainty of design variables and interval parameters is expressed by a multidimensional parallelepiped model, with which the correlated variables and parameters can be converted into independent interval parameters, thus constituting the traditional interval optimization model for independent interval parameters. Based on the idea of sequential optimization and reliability assessment (SORA), the two-layer nested optimization involved in the above interval optimization model can be converted into a single loop problem which can be solved efficiently by the sequential deterministic optimization algorithm. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed model.

To meet the rising demand for high reliability in complex multidisciplinary engineering systems, more attention has been paid to reliability-based multidisciplinary design optimization (RBMDO). In this paper, a sequential optimization and fuzzy reliability analysis (SOFRA) method for multidisciplinary systems is developed to decouple the fuzzy reliability analysis from the optimization. In SOFRA, the multidisciplinary design optimization (MDO) and fuzzy reliability analysis are conducted in a sequential manner. Furthermore, a novel adaptive collocation method (ACM) is proposed to conduct the fuzzy reliability analysis for multidisciplinary systems. The ACM arranges points adaptively at the axis of the membership to obtain more accurate results. The shifting distance of the constraint is calculated by the bi-section method. Both numerical and engineering examples are used to demonstrate the validity of the proposed method.

Sequential optimization and reliability assessment (SORA) is one of the most popular decoupled approaches to solve reliability-based design optimization (RBDO) problem because of its efficiency and robustness. In SORA, the double loop structure is decoupled through a serial of cycles of deterministic optimization and reliability assessment. In each cycle, the deterministic optimization and reliability assessment are performed sequentially and the boundaries of violated constraints are shifted to the feasible direction according to the reliability information obtained in the previous cycle. In this paper, based on the concept of SORA, approximate most probable target point (MPTP) and approximate probabilistic performance measure (PPM) are adopted in reliability assessment. In each cycle, the approximate MPTP needs to be reserved, which will be used to obtain new approximate MPTP in the next cycle. There is no need to evaluate the performance function in the deterministic optimization since the approximate PPM and its sensitivity are used to formulate the linear Taylor expansion of the constraint function. One example is used to illustrate that the approximate MPTP will approach the accurate MPTP with the iteration. The design variables and the approximate MPTP converge simultaneously. Numerical results of several examples indicate the proposed method is robust and more efficient than SORA and other common RBDO methods.

A double stage sequential optimization algorithm for finding the optimal fiber content and its distribution in solid composites, considering uncertain design parameters, is presented. In the first stage, the optimal amount of fiber in a Fiber Reinforced Composite (FRC) structure with uniformly distributed fibers is conducted in the framework of a Reliability Based Design Optimization (RBDO) problem. In the second stage, the fiber distribution optimization having the aim to more increase in structural reliability is performed by defining a fiber distribution function through a Non-Uniform Rational B-Spline (NURBS) surface. The output of stage 1(optimal fiber content for homogeneously distributed fibers) is considered as the input of stage 2. The output of stage 2 is Reliability Index (RI) of the structure with optimal fiber content and optimal fiber distribution. First order reliability method in order to approximate the limit state function and a homogenization approach, based on the assumption of random orientation of fibers in the matrix, are implemented. The proposed combined model is able to capture the role of available uncertainties in FRC structures through a computationally efficient algorithm using all sequential, NURBS and sensitivity based techniques. Performed case studies show as an increase in model uncertainties yields to structural unreliability. Moreover, when system unreliability increases fiber distribution optimization becomes more influential.

The coupling of finite element simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a generally applicable strategy for modeling and efficiently solving robust optimization problems based on time consuming simulations. Noise variables and their effect on the responses are taken into account explicitly. The robust optimization strategy consists of four main stages: modeling, sensitivity analysis, robust optimization and sequential robust optimization. Use is made of a metamodel-based optimization approach to couple the computationally expensive finite element simulations with the robust optimization procedure. The initial metamodel approximation will only serve to find a first estimate of the robust optimum. Sequential optimization steps are subsequently applied to efficiently increase the accuracy of the response prediction at regions of interest containing the optimal robust design. The applicability of the proposed robust optimization strategy is demonstrated by the sequential robust optimization of an analytical test function and an industrial V-bending process. For the industrial application, several production trial runs have been performed to investigate and validate the robustness of the production process. For both applications, it is shown that the robust optimization strategy accounts for the effect of different sources of uncertainty onto the process responses in a very efficient manner. Moreover, application of the methodology to the industrial V-bending process results in valuable process insights and an improved robust process design.

With higher reliability and safety requirements, reliability-based design has been increasingly applied in multidisciplinary design optimization (MDO). A direct integration of reliability-based design and MDO may present tremendous implementation and numerical difficulties. In this work, a methodology of sequential optimization and reliability assessment for MDO is proposed to improve the efficiency of reliability-based MDO. The central idea is to decouple the reliability analysis from MDO with sequential cycles of reliability analysis and deterministic MDO. The reliability analysis is based on the first-order reliability method (FORM). In the proposed method, the reliability analysis and the deterministic MDO use two MDO strategies, the multidisciplinary feasible approach and the individual disciplinary feasible approach. The effectiveness of the proposed method is illustrated with two example problems.

Response surfaces are frequently used as approximations in sequential optimization techniques, multidisciplinary optimization and reliability oriented analysis. In this paper several techniques will be exploited to construct response surfaces using both function values and corresponding derivatives, i.e. gradient-enhanced response surfaces (GERS). The way response surfaces are constructed on both function values and derivatives is not well crystallized. In particular how information on function values and derivatives must be weighted against each other is a point of discussion. To a certain extent, the best method seems to depend on the purpose of the response surface. The technique that is studied in this paper treats the response surface building as a multi-objective optimization problem. This enables a well-controlled balance between accuracy of the approximate gradients as well as the approximate function values. The method is studied for a series of test problems and compared to other techniques. This paper addresses in particularly the effect of the plan of experiment on accuracy.