Inverse finite element method for large‐displacement beams

Abstract

SUMMARYA finite element model for the inverse analysis of large-displacement beams in the elastic range is presented. The model permits determining the initial shape of a beam such that it attains the given design shape under the effect of service loads. This formulation has immediate applications in various fields such as compliant mechanism design where flexible links can be modeled as large-displacement beams. Numerical tests for validation purposes are given, together with two design applications of flexible mechanisms with distributed compliance: a flexible gripper and a flexible S-type clutch.

Inverse finite element modeling of shells using the degenerate solid approach

“…Further, at the light of the current applications, we observe once again (see our previous works on 3D solids [3] and beams [4,5,6] …”

“…Another remarkable quality of IFEM, already observed in several applications developed in our previous works [3,4,6], is the fast convergence to the solution of the nonlinear equilibrium equation (37). When Sze et al [17] solved the (direct) FEM problem (the one whose solution is the domain of analysis for the current IFEM problem), they reported to need 347 iterations …”

“…This kind of problem -also known as Inverse Design problem-often arises in the design of compliant structures or mechanisms suffering large elastic displacements and/or rotations, for instance: a gasket that deforms to the desired shape under given loads [1]; a rubber seal that closes a given channel under a given pressure [2]; a turbine blade that attains an optimal shape at a certain angular speed [3]; an S-clutch whose shoes exactly engage the friction surface of the given drum at a given angular speed [4,5]; a device that folds an intraocular lens in such a way that facilitates its implantation into the eye [6], among other interesting applications developed in the just-cited works.…”

“…This was illustrated by Albanesi et al [4,5], who used IFEM to design a compliant gripper, originally designed by Lan and Cheng [9] by solving an optimization problem.…”

“…In our previous works, IFEM was introduced for 3D solids [3] and 3D beams [4,5]. The current work is a step towards the completion of our IFEM library by introducing shell elements.…”