Study On Topology Optimization Method Of Fiber Reinforced Laminate Structure

Fiber reinforced Plastic(FRP)have gradually become the preferred alternative materials for lightweight design of metal parts because of their advantages such as light weight,high strength,high modulus,strong designability and good damping properties.Anisotropy is the biggest difference between FRP and traditional metal materials.Because its mechanical properties along the fiber direction are far better than those in other directions,the design of fiber laying angle and laying sequence has always been the most important part to determine the final performance of FRP components.Due to the limitation of manufacturing process,the fiber orientation of traditional composite laminates is consistent in each layer,and the angle change only exists between layers.Although the manufacturing process can be simplified in this way,the load capacity and stiffness performance of FRP are limited because the fiber direction and stress direction can’t be kept consistent in each single layer.However,with the maturity of Automatic Tape Laying(ATL)technology and Automatic Fiber Placement(AFP)technology,the manufacturing of laminated plates with variable stiffness of inner fiber angle has been realized,which makes the research on the design method of variable stiffness laminated plates of fiber reinforced materials particularly important.Topology optimization,as one of the most commonly used methods in lightweight design,can reduce the amount of materials or enhance the overall mechanical properties of the structure by optimizing the distribution of various materials in the design domain.If FRP single-layer board is taken as the design domain,and FRP materials with different fiber orientations are regarded as various independent materials that need to be optimized in distribution,the topology optimization method can be used to optimize the design scheme of FRP variable stiffness overlay.In this paper,the topology optimization method of fiber reinforced variable stiffness laminate structure is taken as the object,and the structural stiffness of FRP laminates is maximized as the research target.an efficient topology optimization program of variable stiffness laminate is compiled by combining the finite element method and topology optimization method,and a new stacking process for variable stiffness laminate is proposed,which has practical engineering significance for further improving the stiffness performance of laminate.The main research contents are as follows:(1)Based on the classical laminated plate theory,the regularized stiffness coefficients of FRP single-layer plate and laminated plate are derived,and the method of solving the overall stiffness matrix and strain energy of FRP single-layer plate structure combined with finite element theory is introduced.Based on the optimization model of discrete composite materials with minimum flexibility,the general idea of using variable density method to solve this kind of problems is introduced,and the manual variable density method for continuous treatment of design variables in this problem,the steepest descent method for iterative updating and the sensitivity filtering method for avoiding numerical instability are introduced in turn.(2)FRP topology optimization program based on MATLAB is written,and the code modification method which is extended to a variety of different loads and boundary conditions is introduced,and the influence of different penalty functions on the program optimization efficiency and optimization results under these working conditions is studied.The results show that in any case,the type of penalty function will not affect the optimization speed of the program and the objective function value obtained by the final optimization,but the overall convergence rate of the program and the specific shape of each paving area obtained by optimization will be affected.(3)The stiffness characteristics of the variable stiffness laminate obtained by topology optimization program and the optimal II constant stiffness laminate obtained by traditional laminate design method under different FRP material types and different loads are compared by simulation and experiment.The results show that under single load,the performance of the laminate obtained by topology optimization method is slightly lower than that of the constant stiffness laminate,the Structural strain energy increases by 4.8%,and the maximum displacement increases by 5.47%.Topology optimization method is more suitable for laminate design under multi-load conditions,compared with the laminate with constant stiffness,the structural strain energy is reduced by 29.45% and the maximum displacement is reduced by 24.18%.Compared with glass fiber prepreg,carbon fiber prepreg,which has a larger E1/E2 value,is more suitable for laying design by topology optimization.(4)Two stacking processes for variable stiffness laminated plates are proposed.Through simulation and test,it is proved that the stacking process of “ intra-layer docking and adjacent layer overlapping”has little effect on the overall stiffness performance of laminated plates,which can be applied to the production of variable stiffness laminated plates.