Research On Topology Optimization Method Of Multi-material Structure Under Inertial Load

At present,topology optimization has been widely used in automotive,marine,aerospace,mechanical equipment,building structures and other engineering fields,creating huge economic benefits by saving materials or improving structural performance.As people's demands increase,structural topology optimization under fixed loads and structural topology optimization of single materials have been unable to meet the increasingly demanding needs of people.Therefore,topology optimization and multi-material topology optimization under the design-dependent load have been developed.For the topology optimization under the design-dependent load,there are already researches on structural topology optimization under the influence of design load such as inertial load,surface pressure,thermal load and electromagnetic force.For multi-material topology optimization,there are also methods such as relative density method,level set method,ICM independent continuous mapping method and block coordinate descent method to solve the problem of structural topology optimization of multi-materials.However,there are very few studies on topology optimization of multi-material structures under design-dependent loads.At present,there is no research on topology optimization of multi-material structures under inertial loads.Working conditions and materials are two important dimensions of structure.Structural topology optimization under inertial loads requires corresponding optimization methods.Structural optimization of multi-materials also requires corresponding optimization methods.Multi-material structural topology optimization under inertial loads is more A special optimization method is needed to solve both the topology-optimized design-dependent load problem and the multi-material problem.This thesis is devoted to the study of multi-material structure topology optimization method under the action of inertial load.Taking the maximum structural stiffness as the goal and the structural quality as the constraint,the single material and multi-material structure topology optimization methods under inertial load are studied successively,and the correctness of the method is verified by an example.This paper mainly studies from the following aspects:1.A multi-material structure topology optimization method based on guide-weight method and block coordinate descent method under self-weight load is proposed.The corresponding mathematical model is established,and the multi-material optimization problem is decomposed by the block coordinate descent method.Then the guide-weight method is used to solve the block variable topologyoptimization problem under self-weight load.Finally,the simply supported beam,cantilever beam,L-beam and digging structure are used for numerical verification and comparative analysis.2.A multi-material structure topology optimization method under the action of centrifugal load and centrifugal load and inertial load is proposed.The corresponding mathematical model is established,and the multi-material optimization problem is decomposed by the block coordinate descent method.Then the guide-weight method is used to solve the block variable topology optimization problem under the action of centrifugal load or centrifugal force and gravity.Finally,the cantilever beam model is used for numerical verification and comparative analysis.3.The RAMP interpolation model and the method of applying mass points are developed to solve the problem of intermediate density element and fuzzy structure.The rational approximation interpolation model RAMP is used to replace the traditional SIMP interpolation model to express the nonlinear function relationship between density and elastic modulus,which solves the problem of a large number of intermediate density units in the optimization results.For the problem that the fuzzy structure exists at the end of the cantilever beam,the method of applying the mass point is proposed to improve the optimization effect.