Research On Moving Morphable Components Topology Optimization Method And Application Based On Isogeometric Analysis

Structural topology optimization technology is one of the way of implementing the optimization design for industrial products,of which the physical field is calculated by finite element method.Its optimization efficiency and accuracy determine the iterative update period and reliability of industrial products.Due to the inconsistency between CAD and CAE models and the low continuity of shape function of analysis,topology optimization encounters several crucial issues,such as cumbersome model conversion between CAD and CAE,low optimization accuracy.Isogeometric analysis based on NURBS with high continuity,not only can realize the unified description of CAD and CAE model,but also can generate accurate analysis result without geometric discretization errors.In addition,topology optimization method using moving morphable components can obtain the boundary information of optimal results explicitly,of which the optimal result can be converted into CAD model efficiently.To improve the efficiency and accuracy of topology optimization further,a moving morphable components topology optimization method based on isogeometric analysis is studied in this work,of which the contents are as follows:To solve the C~1 discontinuity existing in topological description function and instability of optimization process,an isogeometric topology optimization method using moving morphable components is proposed based on R-functions and NURBS collocation strategy.The aggregation of topological description functions of different basic structural components is implemented by R-functions for the overlap regions of components,which ensures the C~1 continuity for the proposed optimization model.Then,the effects of the robustness and convergence of isogeometric topology optimization are thoroughly discussed for the ersatz material models based on three different NURBS collocation strategies,namely uniform,Gaussian and Greville abscissae.The proposed method improves the convergence and robustness for isogeometric topology optimization method using moving morphable components.Aiming at resolving the low computational efficiency isogeometric topology optimization method,an efficient isogeometric topology optimization method using moving morphable components is put forward based on the adaptive isogeometric analysis,which is implemented by hierarchical B-splines.An uncoupled ersatz material model is proposed based on Gaussian quadrature points of each active element,and a local refining strategy for hierarchical analysis mesh is constructed based on the topological description function values of Gaussian quadrature points.With the aid of the transformation matrix of hierarchical basis functions between different hierarchical levels,the sensitivity formula for the optimization model is derived with a hierarchical characteristic structure.The proposed method can avoid the sharp conflict between efficiency and accuracy,and enhance the computational efficiency dramatically,as well as greatly improve both the convergence and robustness of isogeometric topology optimization.To solve the problems of low computational efficiency and accuracy of adaptive isogeometric topology optimization using hierarchical B-splines,an adaptive isogeometric topology optimization method with high efficiency and accuracy is proposed based on truncated hierarchical B-splines and coarsening manipulation of hierarchical analysis mesh.Based on the topology description values of Gaussian quadrature points and the relative errors of objective function between consecutive iterative steps,a fully adaptive mark strategy is constructed to perform the hierarchical local refinement and coarsening of the analytic mesh simultaneously.Different values of the local coarsening mark parameter are used to investigate the impact of the local coarsening parameter.The proposed method can improve the efficiency,convergence,and robustness of adaptive isogeometric topology optimization.Based on the aforementioned research contents,a prototype system of moving morphable components topology optimization based on isogeometric analysis is implemented and designed in terms of MATLAB,which is verified by an engineering optimization problem of cross section structure of CNC machine tool stiffeners.