This paper introduces a new quadrilateral plate element named DSPM4, which improves upon the previous Q4γs element. The DSPM4 element has twelve DOFs and four temporary DOFs at the mid-sides of the element. The rotation functions βs are modified by adding an incomplete quadratic function to improve the bending performance. An orthogonality condition between the lower and higher-order bending energy is assumed to satisfy the constant bending patch test. The element development involves kinematic and mixed transverse shear strains. In the local normal-tangential (n-s) coordinate system of each side, the mixed transverse shear strains are obtained by combining the constitutive law for shear forces, equilibrium equations, the constitutive law for bending, and curvatures. The relationship between the temporary DOFs and the final DOFs at the corner nodes is established by equating the constant kinematic and mixed transverse shear strains in the direction cosines of each side of the element. As in the Q4γs element, the discrete shear projection method is applied to avoid the shear-locking effect. Numerical analyses are conducted for thin and thick isotropic plates, and the results are compared with those of the DKMQ and MITC4 elements. Numerical results prove that the DSPM4 element is free of shear locking in thin and thick plates, has a proper rank, and provides better convergence behaviour than the Q4γs element. Its performance in static and free vibration analyses of isotropic plates is highly comparable to the DKMQ element.

中文翻译：

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使用不完全二次函数、假设 Bergan 自由公式的能量正交性和混合横向剪切应变富集 Q4γs 板有限元


本文介绍了一种新的四边形板元件 DSPM4，它改进了以前的 Q4γs 元件。DSPM4 元件在元件的中侧有 12 个自由度和 4 个临时自由度。通过添加不完全二次函数来修改旋转函数 β 以提高弯曲性能。假设低阶和高阶弯曲能量之间的正交条件满足恒定弯曲斑块试验。单元开发涉及运动和混合横向剪切应变。在每侧的局部法向-切向 （n-s） 坐标系中，通过结合剪切力本构定律、平衡方程、弯曲本构定律和曲率得到混合横向剪切应变。临时自由度和拐角节点处的最终自由度之间的关系是通过使单元每侧的余弦方向上的恒定运动和混合横向剪切应变相等来建立的。与 Q4γs 单元一样，采用离散剪切投影法以避免剪切锁定效应。对薄板和厚各向同性板进行了数值分析，并将结果与 DKMQ 和 MITC4 单元的结果进行了比较。数值结果证明，DSPM4 元件在薄板和厚板中均无剪切锁定，具有适当的等级，并且比 Q4γs 元件具有更好的收敛行为。它在各向同性板的静态和自由振动分析中的性能与 DKMQ 元件高度相似。