Abstract
Topology Optimization (TO) is a powerful numerical technique to determine the optimal material layout in a design domain, which has accepted considerable developments in recent years. The classic Finite Element Method (FEM) is applied to compute the unknown structural responses in TO. However, several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO. In order to eliminate the negative influence of the FEM on TO, IsoGeometric Analysis (IGA) has become a promising alternative due to its unique feature that the Computer-Aided Design (CAD) model and Computer-Aided Engineering (CAE) model can be unified into a same mathematical model. In the paper, the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization (ITO) in methods and applications. Finally, some prospects for the developments of ITO in the future are also presented.
Highlights
Structural optimization [1] has attracted considerable attentions among researchers ranging from theoretical research to engineering applications, which aims to solve the optimal design of the load-carrying structures with the reasonable structural features, like the connectivity of holes, the shapes of boundaries
An extensive work [53] used the trimmed spline surfaces to present structural boundaries and proposed a novel Isogeometric Topology Optimization (ITO) framework based on TO and IsoGeometric Analysis (IGA), which opens up a new window for the development of TO in the future
The introducing of IGA into topology optimization for the rational design of auxetic metamaterials can track to Ref. [78], which used the SIMPbased ITO method proposed in Ref. [69] and numerically implemented the energy-based homogenization method to evaluate the effective macroscopic
Summary
Structural optimization [1] has attracted considerable attentions among researchers ranging from theoretical research to engineering applications, which aims to solve the optimal design of the load-carrying structures with the reasonable structural features, like the connectivity of holes, the shapes of boundaries. It is known that the FEM features several deficiencies in numerical analysis, like (1) the finite element mesh is just an approximant of the structural geometry, rather than the exact representation; (2) The neighboring finite elements have the loworder (C0) continuity of the structural responses, and the deficiency exists in the higher-order finite elements; (3) The lower efficiency to gain a high quality of the finite element mesh These drawbacks mainly stem from the use of different mathematical languages in geometric model and numerical analysis model: spline basis functions are used in the former whereas Lagrangian and Hermitian polynomials in the latter. An extensive work [53] used the trimmed spline surfaces to present structural boundaries and proposed a novel Isogeometric Topology Optimization (ITO) framework based on TO and IGA, which opens up a new window for the development of TO in the future. Many research works have been performed to sufficiently consider the positive features of IGA into TO, which can develop more and more efficient and effective ITO methods for many numerical problems. We will provide the detailed discussions about the ITO methods in three different types, including the density-based, level set-based and MMC/V-based, respectively
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