Multi-scale Parallel Topology Optimization For Time Domain Dynamics Of Continuum Structures

Structures with enhanced damping capacity are widely used in engineering.Structures are usually excited by periodic or generally time-dependent loads.In these applications,viscoelastic damping structures are often used to attenuate unexpected responses.Most viscoelastic materials exhibit low stiffness in practical applications.Therefore,a typical damping structure is composed of viscoelastic materials and structural materials to have high damping and desired stiffness.In this thesis,the composite structure is taken as the research object.Using the variable density method and the energy based homogenization method,the multiphase material structure and the time-domain dynamics multi-scale topology optimization are studied in depth to achieve the multi-scale design considering both the macroscopic and microscopic material distribution.Firstly,a topology optimization design model based on the time domain dynamic stiffness problem of dual scale hierarchical structures is proposed.Aiming at the dynamic stiffness optimization problem of macro/micro scale in time domain,the energy homogenization method is used to evaluate the macro equivalent properties of materials.Based on the variable density method and the energy homogenization method,with the objective of minimizing the dynamic flexibility of multi-scale structures,and with the macro and micro structure volumes as constraints,a topology optimization design model for time domain dynamic stiffness problems of dual scale hierarchical structures is established.The validity of the model is verified by numerical examples for 2D cases.Secondly,a multi-scale optimal design model considering the microstructure of multiphase materials is proposed.On the basis of the proposed two-scale structure topology optimization design model,the microstructure topology optimization design of multiphase materials was introduced.For the microstructure containing multiphase materials,the structure/material multi-scale topology optimization design model was established by using the variable density topology optimization method and the energy homogenization method.In order to maximize dissipative energy without considering inertia,the effectiveness of the proposed model is proved by numerical cases under different loads.The parallel topological design of macrostructure and microstructure of multiphase materials is realized,and the performance of macrostructure is further improved.Then,on the basis of the proposed multi-scale topology optimization model of multiphase material microstructure and considering the effect of inertia,a structure/material multi-scale topology optimization design model based on the multi-phase material microstructure under the action of inertia is proposed.The effectiveness of the model is verified by numerical examples,and the macro/micro scale collaborative optimization is achieved to obtain the topology structure with better performance.Finally,a new multi-scale parallel topology optimization method is proposed to optimize the structure of the periodic filling of multiple cells.This method has good structural performance and does not need to pretreat the initial design domain,which improves the degree of freedom of structural optimization design to a certain extent.On the macroscopic scale,a new piecewise projection is proposed to distinguish microstructural blocks.Then,an improved ordered solid isotropic material penalty method(SIMP)was used to optimize the spatial distribution of different microstructures at a reasonable computational cost.On the micro scale,the numerical homogenization method is used to generate the micro structure.Finally,the problem of compliance minimization under the volume fraction constraint is studied,and the sensitivity analysis is carried out.Numerical examples are given to verify the effectiveness of the proposed method.