Mixed Variational Formulation of Coupled Plates
Abstract
This paper proposes a mixed variational formulation for the problem of two coupled plates with a rigid {junction}. The proposed mixed {formulation} introduces {the union of} stresses and moments as {an auxiliary variable}, which {are} commonly of great interest in practical applications. The primary challenge lies in determining a suitable {space involving} both boundary and junction conditions of the auxiliary variable. The {theory} of densely defined operators in Hilbert spaces is employed to define {a nonstandard Sobolev space} without the use of trace operators. The well-posedness is established for the mixed formulation. Based on these conditions, this paper provides a framework {of} conforming {mixed} finite element methods. Numerical experiments are given to validate the theoretical results.
Cite
@article{arxiv.2403.18217,
title = {Mixed Variational Formulation of Coupled Plates},
author = {Jun Hu and Zhen Liu and Rui Ma and Ruishu Wang},
journal= {arXiv preprint arXiv:2403.18217},
year = {2024}
}