Modeling and discretization methods for the numerical simulation of elastic frame structures

Abstract

A new model description for the numerical simulation of elastic frame structures is proposed. Instead of resolving algebraic constraints at frame nodes and incorporating them into the finite element spaces, the constraints are included explicitly in the model via new variables and enforced via Lagrange multipliers. Based on the new formulation, an inf-sup inequality for the continuous-time formulation and the finite element discretization is proved. Despite the increased number of variables in the model and the discretization, the new formulation leads to faster simulations for the stationary problem and simplifies the analysis and the numerical solution of the evolution problem describing the movement of the frame structure under external forces. The results are illustrated via numerical examples for the modeling and simulation of elastic stents.