An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework

Abstract

Summary An efficient optimization framework is developed in this study by integrating auxiliary projection‐based multigrid isogeometric reanalysis (MG‐IGR) and metaheuristic searching techniques. It is well known that the inherent characteristics of isogeometric analysis (IGA) are superior in shape optimization problems. Inheriting the characteristics of IGA, an auxiliary projection‐based MG reanalysis (MGR) is proposed to construct mapping between the mesh before modification and after modification during the optimization process. Subsequently, MG‐IGR is utilized to reanalyze the modified design efficiently by reusing the initial evaluated results. Moreover, the proposed MG‐IGR also eliminates the restriction of mesh consistency. In this framework, the structure can be designed directly through parameterized control of the non‐uniform rational B‐spline (NURBS) model, and the MG‐IGR fast solver enables any metaheuristic algorithm to perform the optimization procedure. Moreover, the accuracy of the simulation can be guaranteed by the NURBS model and the convergence criterion of the MG. Finally, two geometric optimization examples are presented to validate the performance of the developed framework.

New insight into multilevel local refinement in adaptive isogeometric analysis

“…Higher order continuity and exact geometry representation of CAD basis functions have shown superior solution accuracy of IGA compared with the traditional C 0 FEA. In this way, many researchers have implemented the IGA in various classes of problems, that is, fluid mechanics, [3][4][5][6] fluid-structure interaction, [7][8][9] optimization, [10][11][12][13] shell problems, 14,15 and cracks. [16][17][18][19][20] However, a drawback of NURBS basis functions stems from their tensor-product structure which prohibits a truly local refinement in multidimensional analysis.…”