Research On Topology Optimization For Multiscale Design Of Structure-Material Based On Parametric Level Set

Topology optimization has been regarded as a scientific and efficient tool to search the optimal material distribution with the best structural performance,subject to the prescribed constraints.It has been accepted a wide array of applications in many fields,like the biology,the mechanical,the medical and etc.However,the conventional works,where the topology optimization is performed on the basis of the homogenized materials,cannot maintain the high requirements of the ultra-lightweight,the specific properties and the integration of the functionals in the modern industrial products.How to explore the performance of material microstructures in improving the functional becomes more and more popular in the research field of the topology optimization,where material layouts and material properties are both considered in the multiscale design of structure-material.In the current work,the parametric level set method(PLSM)combined with the homogenization theory is firstly applied to study the design of mechanical metamaterials and optimize material microstructures.The topology optimization formulation for the multiscale design of structure-material is studied,which is later applied to discuss the single material microstructure,multiple microstructures and the dynamic,respectively.Firstly,the topology optimization formulation for the rational design of mechanical metamterials is proposed based on the parmetric level set.An energy-based homogenization method(EBHM)is developed to evaluate the macroscopic effective properties of material microstructures,which can effectively remove several numerical difficulties of numerical homogenization method,such as the complexity of the theoretical derivations.We adopt the PLSM and the EBHM to develop the topology optimization formulation for the systematic design of mechanical metamaterials.Several numerical examples in 2D and 3D for the maximal bulk modulus,the maximal shear modulus and the negative Poisson's ratio are studied to demonstrate the effectiveness.Secondly,the topology optimization formulation for the multiscale design of structure-material with a kind of microstructures to maximize the stiffness performance is proposed.In the formulation for mechanical metamaterials,we introduce the conventional topology optimization considering the homogenized materials.In terms of the single kind of material microstructures,we employ the PLSM and the EBHM to develop the multiscale topology optimization formulation.The PLSM can ensure the smooth structural boundary and distinct material interface to improve the manufacturability,and the EBHM is beneficial to reduce the computational cost of the finite element analysis.The topologies at the macro and micro are concurrently optimized to improve the stiffness performance.Then,the topology optimization formulation for the multiscale design of structure-material with multiple kinds of microstructures to maximize the stiffness performance is proposed.The macrostructural topology,the topologies of multiple kinds of microstructures and their overall distribution in the macrostructure should be simultaneously considered.A multiscale topology optimization formulation with two stages are proposed,where the first stage employes the variable thickness sheet method to construct the material distribution optimization model for seeking the optimal layout of material microstructures.In the second stage,the topologies of the macrostructure and multiple kinds of material microstructures are concurrently optimized based on the PLSM and the EBHM.Later,the topology optimization formulation for the multiscale design of structure-material with multiple kinds of microstructures for the minimization of frequency responses is proposed,which should consider the macrostructural topology,the topologies of multiple kinds of microstructures and their overall distribution in the macrostructure.Based on the proposed multiscale topology optimization formulation for the stiffness,we propose the multiscale topology optimization formulation with two stages for the frequency responses.The quasi-static Ritz vector is applied to approximate the displacement responses to reduce the computational cost,and the kinematical connectors are pre-defined in microstructures to ensure the connectivity between adjacent microstructures,so that the macrostructure can have a reasonable loading transmission path.Subsequently,we employ the ANSYS engineering software to simulate the mechanical metamaterials and present the auxetic behavior.The proposed materials design formulation and the multiscale topology optimization formulation are applied to the discussions of lattice materials in the aerospace and the main-bearing structures in the satellite,respectively.The effectiveness and the engineering practicability can be presented in the final designs.Finally,the concluded remarks of the current work and the key contributions are both outlined in the final section,and we also provide some prospects for the future works.