Application Of The Fixed Grids/mesh Method In Planar Continuum Structural Shape Optimization

The objective of structural shape optimization is to improve the performance of a structureby changing the geometry shape of its boundaries. This may include reducing stressconcentration and increasing stiffness of the structure. The effective use of the technology canimprove utilization efficiency of material and the mechanical performance of structure. Thedistortion of mesh presented in the process of structural shape optimization can be avoided byintegrating the fixed grids/mesh method into shape optimization. The main research work ofthis thesis is on the application of fixed grids/mesh method in planar continuum structuralshape optimization.First of all, the frame work of structural shape optimization based on fixed finite elementanalysis is presented in this dissertation. The structure boundary is represented by uniformB-spline curves. The coordinates of control points are selected as design variables. Theanalysis method of structure is the fixed grids FE. Expressions for sensitivity analysis of theobjective and constraint function have been presented. The algorithm for smooth optimaldesign has been implemented and numerical examples are presented.Secondly, finite element analysis using structured mesh and implicit boundary method isintroduced and studied. Unlike in traditional FEM, there may not be nodes present on theboundary of domain when a structured grids/mesh is used. This poses a challenge of imposingboundary condition for structured mesh. A solution structure is constructed using approximateHeaviside step function of implicit equations of the boundaries such that the essentialboundary condition is satisfied automatically. The numerical implementation of elementstiffness matrix and computation of load vector are investigated.Thirdly, finite element analysis using uniform B-spline approximation and implicitboundary method are introduced and discussed. The uniform B-spline basis function which islack of Kronocker-delta property poses a challenge in imposition of essential boundarycondition. The implicit boundary method can solve the problem. B-spline elements studied inthis part not only provide smooth solution with continuous stress and strain throughout theanalysis domain, but also exhibited good convergence behavior.Fourthly, shape optimization based on B-spline finite element and implicit boundary method is presented in this part. The analysis method is B-spline finite element instead offixed grids/mesh FEM on the frame of shape optimization. Numerical examples show thereliability and applicability of the proposed method.Finally, the research work is summarized. Several conclusions are drawn from the presentstudy. The some topics for future work are also suggested.