新疆大学学报（自然科学版中英文）2026，Vol.43Issue(2)：223-237,15.DOI:10.13568/j.cnki.651094.651316.2025.12.10.0001
协调与非协调元在板弯曲问题中的数值模拟及应用
Numerical Simulation and Applications of Conforming and Non-Conforming Finite Elements in Plate Bending Problems
摘要
Abstract
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 bihar-monic equations.In this work,we perform numerical simulations for clamped and simply supported plates using both con-forming 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 conver-gence rates.Finally,the proposed methods are successfully applied to a practical plate problem,yielding efficient and accurate simulation results.关键词
板问题/重调和方程/协调元/非协调元/数值模拟Key words
plate problems/biharmonic equations/conforming elements/non-conforming elements/numerical simulation分类
数理科学引用本文复制引用
李哲,吴帮民,杨泽琨..协调与非协调元在板弯曲问题中的数值模拟及应用[J].新疆大学学报（自然科学版中英文）,2026,43(2):223-237,15.基金项目
新疆维吾尔自治区科技计划项目-自然科学基金-青年基金"磨损接触问题的虚拟元方法研究"(2024D01C227). （2024D01C227）
