A simple approach for finite element simulation of reinforced plates

TL;DR

This paper introduces a straightforward finite element method for simulating reinforced plates by integrating Bernoulli beam reinforcements using a CutFEM approach, enabling efficient support assessment and optimization.

Contribution

It presents a novel finite element discretization combining Kirchhoff plates with Bernoulli beams via CutFEM, simplifying reinforcement modeling.

Findings

Efficient integration of beams into plate finite element models.

Facilitates rapid support placement and optimization.

Compatible with standard finite element spaces.

Abstract

We present a new approach for adding Bernoulli beam reinforcements to Kirchhoff plates. The plate is discretised using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces. The beams are discretised by the CutFEM technique of letting the basis functions of the plate represent also the beams which are allowed to pass through the plate elements. This allows for a fast and easy way of assessing where the plate should be supported, for instance, in an optimization loop.