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首页> 外文期刊>International Journal of Mechanical Sciences >Static, stability and free vibration analysis of arches using a new differential transformation-based arch element
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Static, stability and free vibration analysis of arches using a new differential transformation-based arch element

机译：使用新的基于微分变换的拱单元进行拱的静态，稳定性和自由振动分析

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摘要

Differential transformation method is used to obtain the shape functions for nodal variables of an arbitrarily non-uniform curved arch element including the effects of shear deformation and extensibility of the neutral axis, considering axially functionally graded material. The proposed shape functions depend on the variations in cross-sectional area, moment of inertia, curvature and material properties along the axis of the curved arch element. Since the element stiffness, mass and geometric stiffness matrices for an arch element are developed based on the exact displacement shape functions, the arch element developed here is more accurate than the elements developed in the past. By adopting the finite-element method the static, stability and free and forced vibrations of axially functionally graded tapered arches including shear deformation and rotary inertia are studied by solving several examples. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal arches (both forms - prime and quadratic) with hinged-hinged, hinged-clamped and clamped-clamped and clamped-free end restraints. Three general taper types (depth taper, breadth taper and square taper) for rectangular cross-section are studied. The lowest four natural frequencies are calculated and compared with the published results.
机译：考虑到轴向功能渐变材料，使用微分变换方法来获得任意不均匀弯曲拱形拱的节点变量的形状函数，包括剪切变形和中性轴可扩展性的影响。所提出的形状函数取决于横截面积，惯性矩，曲率和沿着弧形拱形元素的轴的材料属性的变化。由于根据精确的位移形状函数开发了拱形单元的单元刚度，质量和几何刚度矩阵，因此此处开发的拱形单元比过去开发的单元更加精确。通过采用有限元方法，通过求解几个实例，研究了包括剪切变形和旋转惯性在内的轴向功能梯度锥形拱的静态，稳定性以及自由振动和强迫振动。数值结果显示了圆形，抛物线形，悬链形，椭圆形和正弦形拱形（素形和二次形），并带有铰链铰链，铰链夹紧，夹紧夹紧和自由夹紧的端部约束。研究了矩形截面的三种常规锥度类型（深度锥度，宽度锥度和方形锥度）。计算出最低的四个固有频率，并将其与已发布的结果进行比较。

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