Topology Optimization of Graded Truss Lattices Based on On-the-Fly Homogenization

TL;DR

This paper presents a novel computational framework for optimizing graded truss lattices with spatially varying architecture using on-the-fly homogenization, enabling smooth, fabricable designs with tunable length scales.

Contribution

It introduces a homogenization-based topology optimization method for graded cellular structures, allowing continuous variation of architecture and unit cell properties in 2D and 3D.

Findings

Successfully optimized graded truss lattices with smooth variation.

Demonstrated the method's effectiveness through benchmark problems.

Enables fabrication of complex, tunable architectures.

Abstract

We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order homogenization approach, which replaces the discrete truss by an effective continuum description to be treated by finite elements in a macroscale boundary value problem. By defining the local truss architecture through a set of Bravais vectors, we formulate the optimization problem with regards to the spatially varying basis vectors and demonstrate its feasibility and performance through a series of benchmark problems in 2D (though the method is sufficiently general to also apply in 3D, as discussed). Both the displacement field and the topology are continuously varying unknown fields on the macroscale, and a regularization is included for well-posedness. We argue that prior solutions obtained from aligning trusses along the directions of principal stresses are included as a special case. The outlined approach results in heterogeneous truss architectures with a smoothly varying unit cell, enabling easy fabrication with a tunable length scale (the latter avoiding the ill-posedness stemming from classical nonconvex methods without an intrinsic length scale).