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首页> 外文期刊>Meccanica: Journal of the Italian Association of Theoretical and Applied Mechanics >Analysis of curved beams using a new differential transformation based curved beam element
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Analysis of curved beams using a new differential transformation based curved beam element

机译：使用基于微分变换的新型弯曲梁单元分析弯曲梁

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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 beam element including the effects of shear deformation considering axially functionally graded material. The proposed shape functions depend on the variations in crosssectional area, moment of inertia, curvature and material properties along the axis of the curved beam element. The static and free vibration of axially functionally graded tapered curved beams including shear deformation and rotary inertia are studied through solving several examples. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal beams (both forms--prime and quadratic) with hinged-hinged, hinged-clamped and clampedclamped and clamped-free end restraints. Three general taper types (depth taper, breadth taper and square taper) for rectangular cross section are studied. Out of plane vibration is studied and the lowest natural frequencies are calculated and compared with the published results. Out of plane buckling is investigated for circular beams due to radial load.
机译：微分变换方法用于获得任意不均匀弯曲梁单元的节点变量的形状函数，包括考虑轴向功能渐变材料的剪切变形的影响。所提出的形状函数取决于横截面，惯性矩，曲率和沿弯曲梁单元轴的材料特性的变化。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曲梁的静态和自由振动。数值结果给出了圆形，抛物线形，悬链形，椭圆形和正弦形梁（初学者和二次方两种形式）的结果，这些梁带有铰链，铰链夹紧，夹紧和自由夹紧端部约束。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）。研究了平面外振动，并计算了最低固有频率，并将其与已发布的结果进行了比较。对于圆形梁由于径向载荷而引起的平面外屈曲进行了研究。

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