Periodic Implicit Representation, Design and Optimization of Porous Structures Using Periodic B-splines

TL;DR

The paper proposes a periodic implicit representation for porous structures based on periodic B-spline functions to enable infinite tiling of a unit cell with symmetry. A voxel-based porous sample is converted to a discrete distance field, which is then approximated by a periodic B-spline using a constrained least squares progressive-iterative algorithm to produce an implicit porous unit. The implicit unit can be optimized to improve connectivity and used in topology optimization to increase stiffness while maintaining periodicity or symmetry. Experimental results show potential for creating complex, high-performance porous architectures, with applicability to biomimetic and artificial design in engineering.

Abstract

Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming and tedious process.In this study, we propose a novel representation method and design approach for porous units that can be infinitely spliced to form a porous structure. We use periodic B-spline functions to represent periodic or symmetric porous units. Starting from a voxel representation of a porous sample, the discrete distance field is computed. To fit the discrete distance field with a periodic B-spline, we introduce the constrained least squares progressive-iterative approximation algorithm, which results in an implicit porous unit. This unit can be subject to optimization to enhance connectivity and utilized for topology optimization, thereby improving the model's stiffness while maintaining periodicity or symmetry. The experimental results demonstrate the potential of the designed complex porous units in enhancing the mechanical performance of the model. Consequently, this study has the potential to incorporate remarkable structures derived from artificial design or nature into the design of high-performing models, showing the promise for biomimetic applications.