Li Zhe,Wu Bangmin,Yang Zekun.Numerical simulation and applications of conforming and non-conforming finite elements in plate bending problems[J].Journal of Xinjiang University(Natural Science Edition in Chinese and English),2026,43(2):223-237.
Li Zhe,Wu Bangmin,Yang Zekun.Numerical simulation and applications of conforming and non-conforming finite elements in plate bending problems[J].Journal of Xinjiang University(Natural Science Edition in Chinese and English),2026,43(2):223-237. DOI: 10.13568/j.cnki.651094.651316.2025.12.10.0001.
Numerical Simulation and Applications of Conforming and Non-Conforming Finite Elements in Plate Bending Problems
The study of plate problems plays a crucial role in understanding the load-bearing capacity
deformation
stability
and vibration behavior of plate structures. Mathematically
such problems are typically formulated as the solution of biharmonic equations. In this work
we perform numerical simulations for clamped and simply supported plates using both conforming and non-conforming finite elements on rectangular and triangular meshes. The conforming elements adopted include the Bogner-Fox-Schmit (BFS) element and the Argyris element
while the non-conforming elements consist of the Adini and Morley elements. Numerical results demonstrate that all employed elements achieve the theoretically optimal error convergence rates. Finally
the proposed methods are successfully applied to a practical plate problem
yielding efficient and accurate simulation results.
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references
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