Explicit isogeometric topology optimization based on moving morphable voids with closed B-spline boundary curves

Abstract

In this paper, we propose an explicit isogeometric topology optimization approach based on moving morphable voids (MMVs) with closed B-spline boundary curves, named TOP-IGA-MMV in short. We model the design domain by a non-uniform rational B-spline (NURBS) patch, and then employ the NURBS-based isogeometric analysis (IGA) for structural response and the well-established adjoint approach for sensitivity analysis. As for the geometry representation of structural topology, we utilize MMVs to describe boundaries of void material regions and model MMVs by closed star-like B-spline curves. Design variables consist of the coordinates of the central points and the distances from the central points to their corresponding independent control points of these closed B-spline MMVs. We perform structure analysis on a coarse mesh in which four identification schemes (control points, nodal points, Gaussian points, and Greville points) are adopted to form the Young’s modulus and volume fraction of a NURBS element and plot the structural topology on a high-resolution mesh after obtaining explicit boundaries. Three benchmark numerical examples are presented, demonstrating the effectiveness of TOP-IGA-MMV for topology optimization with different initial design and identification schemes and comparing numerical efficiency with the solid isotropic material with penalization (SIMP) method and the TOP-IGA-MMC method.