The hybrid‐Trefftz stress element is used to emulate conventional finite elements for analysis of Kirchhoff and Mindlin‐Reissner plate bending problems. The element is hybrid because it is based on the independent approximation of the stress‐resultant and boundary displacement fields. The Trefftz variant is consequent on the use of the formal solutions of the governing Lagrange equation to approximate the stress‐resultant field. In order to emulate conventional elements, nodal functions are used to approximate the displacements on the boundary of the element. Duality is used to set up the element solving system. The associated variational statements and conditions for existence and uniqueness of solutions are recovered. Triangular and quadrilateral elements are tested and characterized in terms of convergence, sensitivity to shear‐locking, and shape distortion. Their relative performance is assessed using assumed strain Mixed Interpolation of Tensorial Components (MITC) elements and recently proposed Trefftz‐based elements. This relative assessment is extended to a hypersingular problem to illustrate the effect of enriching the domain and boundary approximation bases.

中文翻译：

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用于板弯曲的Hybrid-Trefftz应力元素

混合-Trefftz应力单元用于模拟常规有限元，用于分析Kirchhoff和Mindlin-Reissner板的弯曲问题。单元是混合的，因为它基于应力结果和边界位移场的独立近似。因此，使用控制拉格朗日方程式的形式解来逼近应力结果场时，Trefftz变体就出现了。为了模拟常规元素，节点函数用于近似元素边界上的位移。对偶用于建立元素求解系统。恢复了相关的变式陈述和解的存在性和唯一性的条件。测试了三角形和四边形元素，并根据收敛性，对剪切锁定的敏感性，和形状变形。使用假定的张量分量混合混合插值（MITC）元素和最近提出的基于Trefftz的元素对它们的相对性能进行了评估。此相对评估扩展到一个超奇异的问题，以说明丰富域和边界近似基础的效果。