Efficient Roll-Forming Simulation Using Non-Conformal Meshes with Hanging Nodes Handled by Lagrange Multipliers

Simulations of industrial roll-forming processes using the finite element method typically
require an extremely fine discretization to obtain accurate results. Running those models using a classical finite element method usually leads to suboptimal meshes where some regions are unnecessarily over-refined. An alternative approach consists in creating non-conformal meshes where a number of nodes, called hanging nodes, do not match the nodes of adjacent elements. Such flexibility allows for more freedom in mesh refinement, which results in the creation of more efficient simulations. Consequently, the computational cost of the models is decreased with little to no impact on the accuracy of
the results. Handling the generated hanging nodes can, however, be challenging. In this work, details are first given about the implementation of these particular meshes in an implicit finite element code with a special focus on the treatment of hanging nodes using Lagrange Multipliers. Standard and non-conformal meshes are then compared to experimental measurements on the forming of a U-channel. A more complex roll-forming simulation—a tubular rocker panel—is then showcased as proof of the potential of the method for industrial uses. Our main results show that the proposed method effectively reduces the computational cost of the roll-forming simulations with a negligible
impact on their accuracy.