Mixed Variational Formulation of Coupled Plates
<|reference_start|>Mixed Variational Formulation of Coupled Plates: 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.<|reference_end|>
@article{hu2024mixed,
    title={Mixed Variational Formulation of Coupled Plates},
    author={Jun Hu, Zhen Liu, Rui Ma, Ruishu Wang},
    journal={arXiv preprint arXiv:2403.18217},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.18217},
    primaryClass={math.NA cs.NA}
}