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arXiv · 2403.18217

Mixed Variational Formulation of Coupled Plates

Jun Hu·Zhen Liu·Rui Ma·Ruishu Wang
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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.

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Jun Hu, Zhen Liu, Rui Ma, Ruishu Wang. 2024-03-27. Mixed Variational Formulation of Coupled Plates. https://arxiv.org/abs/2403.18217

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