Full-scale topology optimization for dynamic responses of functionally graded porous infill designs using Nitsche-type multi-patch isogeometric analysis

Abstract

Porous structures, with their outstanding mechanical properties, play a crucial role in engineering applications and are an important consideration in material distribution optimization for structural dynamic performance. Recently, Isogeometric Analysis (IGA) has gained significant interest due to precise geometric representation, high-order continuity, and flexible topology evolution capabilities. Hence, this study proposes a novel infill design approach through a periodic constraint strategy in multiple Non-Uniform Rational B-Splines (NURBS) patches for two dynamic topology optimization problems, namely eigenfrequency maximization and dynamic compliance minimization. By coupling multiple NURBS patches in a conforming mesh, the complexity of the structural design domain is effectively enhanced. The Nitsche-type dynamic formulation is introduced within the IGA framework, and the theoretical analysis of the stabilization condition is performed. Furthermore, the periodic constraint strategy is imposed onto NURBS patches within the specified parameter direction, which controls the sensitivity update values of the objective function across these patches to generate a gradient porous structure. The global topology is described by the Density Distribution Function (DDF) to achieve full-scale topology optimization. The Multi-frequency Quasi-Static Ritz Vector (MQSRV) method is used to reduce the computational cost associated with dynamic problems. The mathematical models for the dynamic compliance minimization and the eigenfrequency maximization are established, where the sensitivity analysis is derived in detail. Finally, the optimized results produced by the work are fully applicable to complex structural design domains and exhibit well-defined boundaries and smooth gradient distributions. Several numerical examples are presented to demonstrate the effectiveness of the proposed multi-patch isogeometric topology optimization infill design method.