In the present study, a new tapered finite element is developed by incorporating the in‐plane effect in our recently introduced element for the vibration analysis of internally tapered laminated plates. Stress and strain fields for a laminated plate with varying thickness along two orthogonal directions are expressed through extending classical laminated plate theory. Shape functions regarding bending and membrane behavior are extracted from the bending and axial basic displacement functions of the Euler‐Bernoulli beam, respectively. Several laminated plates with different taper configurations have been studied, and the results obtained from vibration analysis are compared with those of the literature. Since the element can capture the exact form of variation in thickness, the solution has shown to be competitively accurate with considerably fewer total degrees of freedom and elements in comparison with conventional finite elements.Highlight A new finite element for thin, tapered, laminated plates is introduced. Laminates' stiffness matrix is obtained for arbitrary thickness variation. A novel method is adopted to derive in‐plane shape functions. C1 continuity is guaranteed along the edges of elements. Calculation cost is considerably reduced.

中文翻译：

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一种用于锥形层合板振动分析的新型有限元

在本研究中，通过将面内效应纳入我们最近引入的用于内锥形层合板振动分析的单元中，开发了一种新的锥形有限元。通过扩展经典层合板理论，表达了沿两个正交方向变化厚度的层合板的应力和应变场。有关弯曲和膜行为的形状函数分别从欧拉-伯努利梁的弯曲和轴向基本位移函数中提取。研究了几种具有不同锥度配置的层合板，并将振动分析获得的结果与文献的结果进行了比较。由于该单元可以捕获厚度变化的精确形式，因此与传统有限元相比，该解决方案在总自由度和单元数显着减少的情况下具有竞争力。 引入了一种用于薄、锥形、层压板的新有限元。 获得任意厚度变化的层压板的刚度矩阵。 采用一种新颖的方法来推导平面内形函数。 C1 沿元素边缘的连续性得到保证。 计算成本大大降低。