T-Splines Based Isogeometric Topology Optimization with Arbitrarily Shaped Design Domains

In this paper,a new isogeometric topology optimization(ITO)method is proposed by using T-splines based isogeometric analysis(IGA).The arbitrarily shaped design domains,directly obtained from CAD,are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline(NURBS).The coefficients correlated with control points are directly used as design variables.Therefore,the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution.Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures.The optimized results are free of checkerboard patterns without additional stabilization and filtering techniques due to the properties of T-splines,which also simplified the post-processing.In addition,through performing local refinement,we can easily achieve multiresolution optimization and infill optimization within the T-splines based framework.In general,the proposed method provides a possibility to design,analyze,and optimize engineering structures in a uniform model,which has the potential to improve design efficiency and reduce the cost of product development.

T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems

Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.