An analysis strategy for swept solids

Abstract

Numerous engineering components such as gears, turbine-blades, splined-shafts, and MEMS devices have a common underlying geometric structure in that they may be represented as a sweep of a 2D cross-section along a 3D trajectory. We consider here boundary value problems over such solids and propose an efficient strategy for solving such problems. The proposed strategy avoids the construction of a 3D finite element mesh, and therefore does not require a 3D mesh generator/solver. Instead a 2D mesh of the cross-section is coupled with an implicit 1D ‘hierarchical mesh’ over the trajectory. The latter is symbolically eliminated prior to computational analysis. This, we show, leads to the reduction of 3D scalar boundary value problems to simpler 2D vector problems over the cross-section. The proposed method is particularly well suited for the design exploration of swept solids, where numerous combinations of trajectories and/or cross-sections must be examined. Its computational superiority over extant 3D strategies is established through theory and numerical experiments.