Isogeometric topology optimization based on energy penalization for symmetric structure

Abstract

We present an energy penalization method for isogeometric topology optimization using moving morphable components (ITO-MMC), propose an ITO-MMC with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an ITO-MMC with a symmetric constraint. The energy penalization method can solve the problems of numerical instability and convergence for the ITO-MMC and the ITO-MMC subjected to the structural symmetric constraint with asymmetric loads. Topology optimization problems of asymmetric, bilateral symmetric, and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach. Compared with the conventional ITO-MMC, the energy penalization method for the ITO-MMC can improve the convergence rate from 18.6% to 44.5% for the optimization of the asymmetric structure. For the ITO-MMC under a bilateral symmetric constraint, the proposed method can reduce the objective value by 5.6% and obtain a final optimized topology that has a clear boundary with decreased iterations. For the ITO-MMC under a periodic symmetric constraint, the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.

Design method and verification of a hybrid prosthetic mechanism with energy-damper clutchable device for transfemoral amputees

“…To generate the required moment and power for the HTP mechanism when the knee extends Δθ ke of extension, the topology optimization method is used in the development of the customized torsion spring. According to the solid isotropic material penalization [14][15][16], the numerical optimal model of torsion spring can be built.…”

A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

“…[97] to discuss the efficiency of the proposed method, the numerical results show that the current method can improve the convergence rate in a range of 17%-60% for different cases in both FEM and IGA frameworks. This proposed MMC-based ITO method was applied to the topology optimization for the symmetric structures using energy penalization method [98]. After that, Xie et al [99] proposed a new MMC-based ITO method using a hierarchical B-spline which can implement the adaptive IGA to efficiently and accurately assess the structural performance.…”

Adaptive topology optimization under suitably graded THB‐spline refinement and coarsening

“…Therefore, many researchers have dedicated themselves to performing TO under the IGA framework over the last decade. [24][25][26][27][28] Wang et al 29 integrated NURBS-based IGA into parameterized LSM for minimal compliance TO problems, where the LSM function is parameterized by locally supported NURBS basis functions, and developed an IGA based TO method for periodic lattice materials. 30 Liu et al interpreted topology optimization result into stereolithography models and parametric CAD models, in terms of an adaptive B-spline fitting method established on the curvature of the uniform B-spline curve.…”

“…The previous issue can be circumvented by enhancing the continuity of state field, which can be implemented by Isogeometric Analysis (IGA) proposed in the seminal work of Hughes et al 23 By making use of CAD mathematical primitives, for example, B‐splines, NURBS, representing the field unknowns of the PDE, some benefits over traditional Finite Element Method (FEM) are available to IGA, such as higher continuity along with interfaces between adjacent elements, the higher computational efficiency of high order elements, higher accuracy per degree of freedom (DOF), and elimination of geometric discretization errors. Therefore, many researchers have dedicated themselves to performing TO under the IGA framework over the last decade 24–28 . Wang et al 29 integrated NURBS‐based IGA into parameterized LSM for minimal compliance TO problems, where the LSM function is parameterized by locally supported NURBS basis functions, and developed an IGA based TO method for periodic lattice materials 30 .…”