Topology and geometry optimization of grid-shells under self-weight loading

TL;DR

This paper introduces a convex optimization approach for designing grid-shell structures that simultaneously optimizes topology and elevation under self-weight and external loads, ensuring globally optimal solutions.

Contribution

It presents a novel second-order cone optimization method for simultaneous topology and geometry optimization of grid-shells, improving accuracy and computational efficiency.

Findings

Optimal structures change significantly with self-weight influence.

The method achieves higher accuracy than standard topology optimization.

Solutions are obtained several orders of magnitude faster.

Abstract

This manuscript presents an approach for simultaneously optimizing the connectivity and elevation of grid-shell structures acting in pure compression (or pure tension) under the combined effects of a prescribed external loading and the design-dependent self-weight of the structure itself. The method derived herein involves solving a second-order cone optimization problem, thereby ensuring convexity and obtaining globally optimal results for a given discretization of the design domain. Several numerical examples are presented, illustrating characteristics of this class of optimal structures. It is found that, as self-weight becomes more significant, both the optimal topology and the optimal elevation profile of the structure change, highlighting the importance of optimizing both topology and geometry simultaneously from the earliest stages of design. It is shown that this approach can obtain solutions with greater accuracy and several orders of magnitude more quickly than a standard 3D layout/truss topology optimization approach.