Research On Explicit Topology Optimization Considering Constraints On Structural Length Scale And Local Stress

As one of the most efficient tools for structure design,topology optimization has drawn widespread attention from various industrial fields,and created huge economic profit due to its application in aerospace,vehicles and so on.However,since traditional topology optimization approaches have adopted implicit expression of structural topology,there exist some problems such as difficulties in extracting structural geometric information,too many design variables,too heavy computational cost and low accuracy in stress evaluation.All these have influenced remarkably further application of topology optimization.For the aforementioned problems,topology optimization framework based on explicit expression of structural boundary can be a proper solution.Under explicit topology optimization framework,structural boundaries are expressed explicitly by specific functions from which geometric information of boundary can be obtained by using tools of analytic geometry.Additionally,those functions used to describe structural boundary can be built by only a few parameters,which leads to great reduction of the number of design variables.Explicit topology optimization is also advantageous by using adaptive mesh to decrease FE computation and increase accuracy of stress evaluation.In this thesis,effective 2D and 3D topology optimization approaches under the explicit Moving Morphable Components/Voids(MMCs/MMVs)frameworks are developed,and the topology optimization problems considering structural length scale control and local stress control are investigated.Minimum length scale of a structure has significant influence on the manufacturability,stability and robustness of the structure.Unreasonable structure design can bring to local stress concentration which will be amplified by crack propagation,fatigue etc.and cause serious harm to the whole structure.In the present study,tools and techniques such as constraint integration,boundary smoothing,adaptive mesh and the XFEM(eXtended Finite Element Method)are adopted.This thesis will be developed in the following aspects.Firstly,in this thesis,a 3D topology optimization approach using components with the quasi hyper-ellipsoidal shape is put forward under the MMCs framework,and a 2D topology optimization approach using voids described by B-spline curves is put forward under the MMVs framework.These two approaches perfect further the MMCs/MMVs frameworks,and can give satisfactory results in the present study.Secondly,based on the trapezoid-shape approach under the MMCs framework,this thesis gives a mathematical definition on structural minimum length scale and develops the corresponding control method.In most cases,minimum length scale can be controlled conveniently by the upper/lower bound constraints of design variables;in other cases where components intersect,an integrated geometric constraint will be introduced to control the minimum length scale.Compared with traditional control methods,the present one is more advanced because it is explicit,local and straightforward.Thirdly,considering the characteristics of explicit topology optimization frameworks that a large amount of weak material is included and the integrals in sensitivity analysis are implemented only along structural boundary,the present study introduces an h-adaptive mesh to the MMCs/MMVs topology optimization frameworks.This quadtree/octree mesh only refines areas near the structural boundaries,and adopts the scaled boundary finite element and piecewise linear finite element to implement FE analysis,respectively.Numerical examples indicate that quadtree-based adaptive mesh in 2D case contributes to reducing dramatically computational cost of FE and sensitivity analysis and saving massive computational time.The last,the problem of local stress level control is investigated under the MMVs topology optimization framework.The technique of reorganization of B-spline control point is used to obtain smooth structural boundary and prevent cusps and sharp corners.By introducing mean compliance to normalize the original stress-related problem,the singular solution can be avoided.Besides,the application of quadtree/octree-based adaptive mesh improves the efficiency and accuracy of stress evaluation.The present study develops and perfects topology optimization approaches based on the explicit MMCs/MMVs frameworks,and demonstrates their effectiveness on aspects of structural length scale control and local stress level control.The present study indicates that due to its own special features,the explicit MMCs/MMVs topology optimization frameworks exhibit great research significance and application value.