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首页> 外文期刊>Applied Mathematical Modelling >Coupling of h and p finite elements: Application to free vibration analysis of plates with curvilinear plan-forms
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Coupling of h and p finite elements: Application to free vibration analysis of plates with curvilinear plan-forms

机译：h和p有限元的耦合：在曲线平面板的自由振动分析中的应用

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摘要

This paper presents a method for coupling isoparametric cubic quadrilateral h-elements and straight sided serendipity quadrilateral p-elements. The p-elements are used to model the interior of the domain while the h-elements are used to describe accurately the curved boundaries. At a common side shared by a p-element and an arbitrary number of h-elements, the field variables are minimized in the least square sense with respect to the degrees-of-freedom of the h-elements. This leads to a set of equations which relate the degrees-of-freedom of the coupled elements on the shared side. The method is applied to the calculation of frequencies for plates with curvilinear plan-forms. The effects of shear deformation and rotary inertia are taken into account. The frequencies are obtained for a sectorial plate with simply supported radial edges and free circular edge, an annular sec-torial plate with simply supported radial edges and clamped circular edges, and a circular plate with one concentric ring support. Furthermore, new accurate frequencies are given for a fully clamped square plate with a corner cut-out. Constant meshes are used and convergence is sought by increasing progressively the degree p of the interpolating polynomial. The fast convergence and high accuracy of the method are validated through convergence and comparison studies.
机译：本文提出了一种耦合等参立方四边形h元素和直边奇异四边形p元素的方法。 p元素用于建模区域内部，而h元素用于准确描述弯曲边界。在由p元素和任意数量的h元素共享的公共侧，相对于h元素的自由度，在最小二乘意义上将字段变量最小化。这导致了一组方程，这些方程关联了共享侧耦合元素的自由度。该方法适用于曲线平面板的频率计算。考虑了剪切变形和旋转惯性的影响。对于具有简单支撑的径向边缘和自由圆形边缘的扇形板，具有简单支撑的径向边缘和夹紧的圆形边缘的环形扇形板以及具有一个同心环支撑的圆形板，可以获得频率。此外，对于带有角切口的完全夹紧的正方形板，给出了新的精确频率。使用常数网格，并通过逐渐增加插值多项式的次数p来寻求收敛。通过收敛和比较研究验证了该方法的快速收敛性和高精度。

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