Mapping an irregular domain into a square one is a common technique in analyzing problems of plates and shells with irregular shapes. For the irregular shape without four corners such as the elliptical shape, the difficulty arises that the Jacobian determinant is zero at the corner points. An efficient quadrature method is presented to analyze the transverse vibration of thin plates with an elliptical shape. To circumvent the above-mentioned difficulty, Gauss quadrature is used in numerical integration. Besides, derivative degrees of freedom are not used, and a boundary point is modeled by two nodes separated by a very small distance. Since the nodes are not coinciding with integration points, a way indirectly using the differential quadrature law is employed to derive the explicit formulas to ease the programming. A convergence study is performed. Free vibration of elliptical plates with continuous and discontinuous edge conditions is analyzed to demonstrate the efficiency of the developed rotation-free weak-form quadrature method.

将不规则区域映射到正方形区域是分析具有不规则形状的板和壳问题的常用技术。对于没有四个角的不规则形状（例如椭圆形），出现的困难是雅可比行列式在角点处为零。提出了一种有效的正交方法来分析椭圆形薄板的横向振动。为了避免上述困难，在数值积分中使用了高斯正交。此外，不使用导数自由度，并且边界点是由相隔非常小的距离的两个节点建模的。由于节点与积分点不一致，因此采用间接使用差分正交定律的方法来导出显式，以简化编程。进行收敛研究。