The parametrized superelement approach for lattice joint modelling and simulation

Abstract

From large scale structures such as bridges and cranes to small-scale structures such as lattices, mechanical structures today increasingly consist of “tuneable parts”: parts with a simple geometry described by a small set of strongly varying parameters. For example, although a bridge is a macroscale structure with a complex geometry, it is made from simple beams, bolts and plates, all of which depend on spatially varying, geometrical parameters such as their length-to-width ratio. Accelerating this trend is the concurrent improvement of, on one hand, Additive Manufacturing techniques that allow for increasingly complex parts to be manufactured and, on the other, structural optimization techniques that exploit this expanded design space. However, this trend also poses a challenge to current simulation techniques, as for example the Finite Element Method requires large amounts of elements to represent such structures. We propose to exploit the large conformity between parts inside the mechanical structure through construction of semi-analytic “Parametrized Superelements”, built by meshing with solid elements, reduction to a fixed interface and approximation of the reduced stiffness matrices. These new elements can be employed next to standard elements, enabling the simulation of more complex geometries. The technique we propose is applied to lattice structures and provides a flexible, differentiable, more accurate but still efficient way to simulate their elastic response. A net gain in total computation time occurs after simulating more than twenty lattices. As such, the proposed method enables large-scale parameter exploration and optimization of lattice structures for improved energy absorption, mass and/or stiffness.