TY - JOUR
T1 - Multi-patch isogeometric topology optimization for cellular structures with flexible designs using Nitsche's method
AU - Gao, Jie
AU - Wu, Xiaomeng
AU - Xiao, Mi
AU - Nguyen, Vinh Phu
AU - Gao, Liang
AU - Rabczuk, Timon
N1 - Funding Information:
This work was partially supported by the National Natural Science Foundation of China (No. 52105255 ), the National Key R&D Program of China (No. 2020YFB1708300 and No. 2022YFB3302900 ), the Tencent Foundation or XPLORER PRIZE , the Knowledge Innovation Program of Wuhan-Shuguang, China and the Fundamental Research Funds for Central Universities of Huazhong University of Science and Technology, China (No. 5003123025 ).
Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/5/15
Y1 - 2023/5/15
N2 - Cellular structures have recently been received a tremendous growth in discussions and applications in the engineering due to their several fascinating structural properties, such as the ultra-lightweight, high stiffness and crashworthiness. However, the discussions on the design of cellular structures in the complex structural domain with the non-conforming mesh are still unavailable, resulting from the fact that the non-conforming mesh causes several difficulties in numerical analysis and design optimization. Hence, the main purpose of the work is to propose a Multi-Patch Isogeometric Topology Optimization (MP-ITO) method with powerful capabilities for periodic or graded cellular structures. Firstly, the Nitsche's method is applied to couple non-conforming meshes in multiple NURBS patches and conduct multi-patch isogeometric analysis. Secondly, a multi-patch topology description model is developed, in which a local smoothing mechanism and the two-resolution scheme of discretization meshes are constructed to avoid terrible structural features and improve smoothness and continuity of boundaries at the interfaces within adjacent subdomains. The separation and independency of the Density Distribution Function (DDF) at each subdomain can offer high flexibility for cellular designs with the imposing of several kinds of periodic constraints. Thirdly, the MP-ITO method is proposed for complex structures and the mathematical formulation for cellular designs considering periodic constraints is developed. Finally, the effectiveness and indispensability of the local smoothing mechanism and the two-resolution scheme in the MP-ITO are discussed, and several numerical examples are addressed to present the compelling effectiveness and capabilities of the MP-ITO method with the high flexibility on the designs of periodic and graded cellular structures.
AB - Cellular structures have recently been received a tremendous growth in discussions and applications in the engineering due to their several fascinating structural properties, such as the ultra-lightweight, high stiffness and crashworthiness. However, the discussions on the design of cellular structures in the complex structural domain with the non-conforming mesh are still unavailable, resulting from the fact that the non-conforming mesh causes several difficulties in numerical analysis and design optimization. Hence, the main purpose of the work is to propose a Multi-Patch Isogeometric Topology Optimization (MP-ITO) method with powerful capabilities for periodic or graded cellular structures. Firstly, the Nitsche's method is applied to couple non-conforming meshes in multiple NURBS patches and conduct multi-patch isogeometric analysis. Secondly, a multi-patch topology description model is developed, in which a local smoothing mechanism and the two-resolution scheme of discretization meshes are constructed to avoid terrible structural features and improve smoothness and continuity of boundaries at the interfaces within adjacent subdomains. The separation and independency of the Density Distribution Function (DDF) at each subdomain can offer high flexibility for cellular designs with the imposing of several kinds of periodic constraints. Thirdly, the MP-ITO method is proposed for complex structures and the mathematical formulation for cellular designs considering periodic constraints is developed. Finally, the effectiveness and indispensability of the local smoothing mechanism and the two-resolution scheme in the MP-ITO are discussed, and several numerical examples are addressed to present the compelling effectiveness and capabilities of the MP-ITO method with the high flexibility on the designs of periodic and graded cellular structures.
KW - Cellular structures
KW - Isogeometric topology optimization
KW - Multi-patch isogeometric analysis
KW - Nitsche's method
UR - http://www.scopus.com/inward/record.url?scp=85152597641&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2023.116036
DO - 10.1016/j.cma.2023.116036
M3 - Article
AN - SCOPUS:85152597641
SN - 0045-7825
VL - 410
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 116036
ER -