부산대학교 도서관

Summary: ``In this paper, a novel quasi-smooth tetrahedral numericalmanifold method (NMM) and its two-dimensional (2D) counterpart areproposed. A new topology optimization method is established bycombining the quasi-smooth manifold element (QSME) with theparameterized level set method (PLSM). The QSME introduces aninnovative displacement function characterized by high accuracy andhigh-order continuity, effectively addressing the `linear dependence'(LD) issue inherent in traditional high-order NMM. To integrate QSMEand PLSM, the corresponding optimization formulations and sensitivityanalyses are provided. In order to fully utilize advantages of thisnovel quasi-smooth NMM and the PLSM, an element subdivision techniquebased on model recognition is proposed to accurately capture thephysical boundaries. Additionally, a volume fraction update methodbased on element refinement is proposed. Taking advantage of thecharacteristics of the PLSM, a structure visualization method based onthe sign distance function is developed to accurately describe curveboundary. This method allows for precise visualization of optimizedstructures. This study verifies high efficiency of the QSME-based PLSMfor minimum compliance topology optimization problems in both 2D and 3Dstructures. Some representative structural optimization examples aretested to demonstrate effectiveness of the proposed method in both 2Dand 3D problems, especially in complex design domain.''