Uncertainty Analysis And Wrinkle-free Optimization Design Of Thin Membrane Aerospace Structure

With the advantages of light weight,large deformation,ease of stowing and folding,thin membrane structures have been widely used in aerospace field.However,due to the low bending rigidity of the membrane structures,when compressive stress occurs in some areas,the membrane structures will tend to wrinkle.In most aerospace equipment,the mechanical properties and reliability of membrane structure will be seriously influenced by wrinkles,which may lead to the decrease of the precision of membrane antenna reflector and the uneven illumination of solar sail.How to quantify and suppress wrinkles effectively has become a challenging task in the aerospace field.It is found that the wrinkle amplitude measured in the experiment is often larger than that in the simulation.The main reason is that compared with the perfect geometry in the simulation,the geometric imperfections of the experimental membranes have a great impact on the wrinkle amplitude,so how to quantify the impact of imperfections on the wrinkle has become one of the focuses of this paper.Membrane wrinkle is a highly nonlinear post buckling behavior.In order to resolve the complex problems,it is the main problem to propose a reasonable optimization model and solve the optimization model accurately.In the aspect of optimization algorithm,the main difficulties to be solved in this paper are improving the efficiency and accuracy of optimization calculation,dealing with stress constraints and completing optimization calculation without sensitivity information.Based on the above research background,this paper focus on the algorithm innovation,quantification of wrinkle uncertainty and wrinkle-free optimization design of aerospace membrane.The specific contents of the thesis include:(1)A global optimization algorithm for parallel computing based on Kriging surrogate model is proposed.The purpose is to greatly improve the efficiency of global search and the accuracy of optimization algorithm.According to the Expect Improvement(El)function of Kriging surrogate model having characteristics of multiple peaks,we can search the multiple peaks in one sequence sampling.At the same time,sampling at the peaks and around the peaks to improve the calculation efficiency.In addition,use the design domain reduction strategy to effectively improve the optimization accuracy.Compared with similar algorithms,the accuracy of the optimization algorithm proposed in this paper is enhanced by about an order of magnitude,and the calculation efficiency is improved by nearly three times.(2)Quantify the membrane wrinkle amplitude with considering initial thickness imperfections.It is inevitable that thickness imperfections will occur in the manufacturing process.This paper presents an experimental and numerical investigation on how thickness imperfections affect the wrinkling of stretched membrane structures.With the measured data from a limited number of samples and bounded field method with spatial correlation,imperfections information is described and wrinkle quantification model is established.Based on Kriging surrogate model optimization algorithm effectively solves the wrinkle quantification problem,which is verified by Monte Carlo simulation.(3)Design Wrinkle-free thin membrane structures using stress-based topology optimization.According to the principal stress criterion,the membrane wrinkle-free design topology optimization model is established under the constraint of principal stress.In order to make the optimization problem tractable,the principal stress constraint is transformed into equivalent form and cosine type relaxation function is used for relaxing constraints.Adjoint method sensitivity analysis is used and the modified optimization problem is solved by gradient-based optimization algorithm.Through post buckling simulation and experiments,the effectiveness of the proposed method in membrane wrinkle-free design is verified.(4)Optimize fixtures shape to suppress wrinkles in large-displacement membrane structures.The fixtures provide the loads and boundary conditions for stretching the membrane,so they play a key role in the stress and wrinkle distribution of the membrane structure.In this paper,a global optimization method is proposed to design the shape of fixtures to suppress the membrane wrinkles.The objective of optimization problem is to maximize the minor principal stress of the membrane.The optimization problem is solved by Kriging surrogate model optimization algorithm.Compared with other wrinkle-free design,the proposed method does not reduce the effective working area of the membrane.(5)Based on the material field method and Kriging surrogate model,a non-gradient topology optimization algorithm is proposed.The number of design variables is effectively reduced by the series expansion of material field,and the topology optimization model is established in ?-space.The optimization algorithm based on Kriging surrogate model proposed is used to solve the topology optimization model without derivation of gradient information.The correctness and effectiveness of the proposed method are verified by a variety of topology optimization examples.And the method is extended to the topology-shape combination optimization design.The membrane and fixture designed by this method has better performance to suppress the membrane wrinkle.More importantly,because there is no need to derive gradient information,this method has great potential in solving multi-disciplinary and highly nonlinear topology optimization problems.