This paper focuses on the formulation and evaluation of a triangular bending plate element, taking into account the shear effect, with 3 DOFs at each corner node. The new element, called DSPM3, is developed from T3γ element by increasing the linear (lower order) rotation function β and β with incomplete quadratic functions (higher-order). An assumed orthogonality condition between lower and higher bending energies is applied using a free formulation approach to pass the bending moment patch test. A discrete shear constraint is applied on each element side to provide a constant shear strain along the side and simultaneously avoid the shear-locking problem. The constant transverse shear strain on each side of the element is then projected to the corner nodes using the Discrete Shear Projection Method (DSPM). The values ​​at each node are then averaged to represent the constant shear strain in the element domain. The element application on static and free vibration analysis of isotropic plates demonstrates excellent convergence behaviour, superiority, and precision compared to the T3γ element on which the development was based.

中文翻译：

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基于不完全二次函数和假定正交条件的 DSPM 的最优三角板单元

本文重点关注三角形弯曲板单元的制定和评估，考虑到剪切效应，每个角节点都有 3 个自由度。新单元称为DSPM3，是在T3γ单元的基础上增加线性（低阶）旋转函数β和不完全二次函数（高阶）β而发展而来。使用自由公式方法应用较低和较高弯曲能之间的假设正交条件来通过弯矩贴片测试。在每个单元侧面应用离散剪切约束，以沿侧面提供恒定的剪切应变，同时避免剪切锁定问题。然后使用离散剪切投影法 (DSPM) 将单元每侧的恒定横向剪切应变投影到角节点。然后对每个节点处的值进行平均，以表示单元域中的恒定剪切应变。与开发所基于的 T3γ 单元相比，该单元在各向同性板静态和自由振动分析中的应用表现出出色的收敛性能、优越性和精度。