Research On Novel Implementation Of Asymptotic Homogenization Based On SiPESC

Due to its excellent properties,composite materials are increasingly used in automobile,aviation,aerospace and other fields.Composite materials tend to have periodic microstructures.The finite element discretization of composite materials with periodic microstructure is directly performed,and the very high number of nodes and elements is large,which is difficult to solve.The equivalent material properties of the microstructure are usually calculated,substituting an equivalent material for the composite.Asymptotic homogenization(AH)is a common method to calculate the equivalent material properties of periodic structures.This method has strict mathematical theory,and the calculation results are accurate,but it needs to write the unit formula of the unit used in the micro structure,which is difficult to realize.Aiming at the difficulty of numerical realization of asymptotic homogenization method,a novel implementation of asymptotic homogenization(NIAH)was proposed by Cheng Gengdong et al.In this method,the finite element software is used as a black box,and the output results of the finite element software are used to calculate the equivalent properties of periodic structures simply and efficiently.SiPESC(Software Integration Platform for Engineering and Scientific Computation)is an integrated analysis engineering computation software independently developed by the Department of Engineering Mechanics of Dalian University of Technology.The software architecture adopts the object-oriented programming idea,which has strong expansibility and can easily integrate new computing functions.Its finite element analysis function has a rich element library and modular calculation process management,which meets the requirements of the NIAH method to call different elements and analysis modules to calculate the microstructure finite element model.Combining the NIAH method with the SiPESC platform can take advantage of both to achieve efficient numerical computation of the equivalent performance of complex periodic structures.The microstructure homogenization module developed in this thesis is consistent with the design goals of Ansys’ Material Designer module.However,it is richer in functions,not only can the microstructure be equivalent to a solid body,but also can be equivalent to a beam and shell structure.At the same time,based on the calculation of the equivalent mechanical properties of the microstructure,the calculation of the equivalent thermodynamic properties is also realized.In this paper,a new numerical method for progressive homogenization is studied.Based on the scientific computing platform SiPESC,the calculation functions of equivalent material performance prediction,transient heat conduction analysis based on NIAH,and microstructure topology optimization are realized.The main contents of this study include:(1)Seven prediction methods for equivalent material properties are introduced,which are the equivalent material constitutive matrix,the equivalent thermal conductivity and the equivalent thermal expansion coefficient of the three-dimensional periodic solid structure,equivalent stiffness and equivalent shear stiffness for periodic beam and shell structures.The calculation process of seven equivalent material properties is summarized,and a unified calculation framework is designed on SiPESC to realize the calculation function of equivalent material properties of periodic complex micro structure.Based on this analysis function,a software analysis tool SiPESC.NIAH is developed to calculate the equivalent material properties,and a GUI analysis interface is provided.It supports parametric modeling of more than ten microstructures,including lattice structures,unidirectional reinforced composites,particle reinforced composites,honeycomb panels and other microstructures.It also supports the import of custom microstructures and post-processing display.Numerical examples verify the correctness of the calculation of seven equivalent material properties,and the feasibility of the calculation module applied to periodic complex micro structure composed of shell elements,beam elements and other elements.(2)Aiming at the problem that the transient nonlinear heat transfer analysis using NIAH needs to calculate the equivalent heat transfer coefficient multiple times,the calculation efficiency is improved by introducing a neural network method.The function of fitting thermally equivalent constitutive matrix by neural network is realized on SiPESC.Numerical examples verify the accuracy of the computational functions.The computational efficiency of the homogenized model is several times higher than that of the original model.(3)The microstructure topology optimization problem is introduced,the sensitivity calculation formula based on NIAH is deduced,and it is verified by comparing with the differential sensitivity.Based on the SiPESC topology optimization module,a computational function that integrates the response and sensitivity of the topology optimization of the microstructure is developed.Numerical examples verify the feasibility and correctness of the optimization method.After topology optimization,the optimization objective has been significantly improved.