Some shortcomings in Michell's truss theory

Regenerative Topology Optimization of Fine Lattice Structures

We present a generative approach for creating three-dimensional lattice structures optimized for mass and deflection composed of thousands of one-dimensional strut primitives. Our approach draws inspiration from topology optimization principles. The proposed method iteratively determines unnecessary lattice struts through stress analysis, erodes those struts, and then randomly generates new struts across the entire structure. The objects resulting from this distributed optimization technique demonstrate high strength-to-weight ratios that are at par with state-of-the-art topology optimization approaches, but are qualitatively very different. We use a dynamics simulator that allows optimization of structures subject to dynamic load cases, such as vibrating structures and robotic components. Because optimization is performed simultaneously with simulation, the process scales efficiently on massively parallel graphics processing units. The intricate nature of the output lattices contributes to a new class of objects intended specifically for additive manufacturing. Our work contributes a highly parallel simulation method and simultaneous algorithm for analyzing and optimizing lattices with thousands of struts. In this study, we validate multiple versions of our algorithm across sample load cases, to show its potential for creating high-resolution objects with implicit optimized microstructural patterns.

Optimum structure to carry a uniform load between pinned supports: exact analytical solution

Recent numerical evidence indicates that a parabolic funicular is not necessarily the optimal structural form to carry a uniform load between pinned supports. When the constituent material is capable of resisting equal limiting tensile and compressive stresses, a more efficient structure can be identified, comprising a central parabolic section and networks of truss bars emerging from the supports. In the current article, a precise geometry for this latter structure is identified, avoiding the inconsistencies that render the parabolic form non-optimal. Explicit analytical expressions for the geometry, stress and virtual-displacement fields within and above the structure are presented. Furthermore, a suitable displacement field below the structure is computed numerically and shown to satisfy the Michell–Hemp optimality criteria, hence formally establishing the global optimality of this new structural form.