Analysis of the Hex Cell Discretization for Topology Synthesis of Compliant Mechanisms

We use non-linear finite element simulations to study the convergence behavior of the honeycomb or hex cell design discretization for optimization-based synthesis of compliant mechanisms in this paper. Adjacent elements share exactly one common edge in the hex cell discretization, unlike the square cell discretization in which adjacent elements can be connected by a single node. As the single node connections in bilinear quadrilateral plane stress elements allow strain-free relative rotations, compliant mechanism designs obtained from square cell discretizations with these elements often contain elements with single node connections or point flexures. Point flexures are sites of lumped compliance, and as such, are undesirable as they lead to compliant mechanisms designs which deviate from the ideal of distributed compliance. The hex cell design discretization circumvents the problem of point flexures without any additional computational expense (e.g. filtering, extra constraints, etc.) by exploiting the geometry of the discretization. In this work we compare the elastic response of a group of four cells in which two adjacent cells have the least connectivity in both: the square and the hex discretizations. Simulations show that the hex cell discretization leads to a more accurate modeling of the displacement, stress and strain energy fields in the vicinity of the least connectivity regions than the square cell discretization. Therefore, the hex cell discretization does not suffer from stress singularities that plague the square cell discretization. These properties ensure that continuous optimization-based compliant mechanism synthesis procedures that use the hex cell discretization, exhibit a faster and more stable convergence to designs that can be readily manufactured than those that use the square cell discretization.