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首页> 外文期刊>Proceedings of the Institution of Mechanical Engineers, Part C. Journal of mechanical engineering science >A new formulation based upon trigonometric function for finite circular arch elements
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A new formulation based upon trigonometric function for finite circular arch elements

机译：基于三角函数的有限圆拱单元新公式

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摘要

In this paper, the formulation of the curved beam element by trigonometric functions for the curvature, which is an alternative to the displacement function is presented. Trigonometric function is chosen for the curvature to avoid the shear and membrane locking phenomena. In the developed formulation, the force-curvature relationships in polar coordinate system have been obtained first; then the curvature of the element has been assumed to have a trigonometric function form; and the radial and tangential displacements, and rotation of the cross-section have been found to be a function of the curvature. Moreover, the relationship between the nodal curvatures and the nodal deformations has been calculated and used for determining the deformations in terms of curvature at an arbitrary point. The total potential energy has been calculated accounting for bending, shear, and tangential deformations. Invoking the stationary condition of the system, the force-deformation relationship for the element has been obtained. Using this relationship, the stiffness matrix and the equivalent fixed loads applying at the nodes have been computed. In such an equilibrium equation, the locking phenomenon is eliminated. The formulation is applied to six examples to verify its capabilities. The results demonstrate that the presented element is capable of representing the behaviour of the curved beam with adequate accuracy and efficiency as compared with the previous methods.
机译：在本文中，提出了用三角函数曲率表示弯曲梁单元的方法，该函数可替代位移函数。为曲率选择三角函数，以避免剪切和膜锁定现象。在开发的公式中，首先获得了极坐标系中的力-曲率关系。则假定元素的曲率具有三角函数形式;已经发现，径向和切向位移以及横截面的旋转是曲率的函数。此外，已经计算出节点曲率与节点变形之间的关系，并将其用于确定任意点处的曲率方面的变形。计算了总的势能，说明了弯曲，剪切和切向变形。调用系统的静止状态，已获得元件的力-变形关系。利用这种关系，已经计算了刚度矩阵和施加在节点上的等效固定载荷。在这样的平衡方程中，消除了锁定现象。该公式应用于六个示例以验证其功能。结果表明，与以前的方法相比，所提出的元件能够以足够的精度和效率表示弯曲光束的行为。

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