Abstract

In this pioneering study, the cross-sectional warping included transient response and normal/shear stress components of composite elliptical and elliptical cone helices over exact axis geometry are investigated using a mixed FEM. The transient analysis is performed using the Newmark time integration algorithm with or without the amplitude decay factor. The constitutive equations of composite curved rods are derived from three-dimensional elasticity theory. A displacement-type finite element formulation computing the warping-included torsional rigidity is incorporated with the mixed finite element formulation. The curvatures and displacement-type finite elements are used to estimate the normal and shear stress distributions on the respective cross-sections. The maximum normal/shear stresses of a composite straight beam are compared with the literature. An excellent agreement is obtained for the results of an exact elliptical cone helix under dynamic loads compared to the results of 3D solid finite elements. During the implementation of the time integration scheme, the first and second time derivatives of forces and moments are preserved, and their time histories are discussed. Finally, the influences of helix geometry, lamination, and the ratios of material constants on the transient response besides the stresses are investigated. All the numerical examples in this paper are original for the literature.

摘要

在这项开创性的研究中，使用混合 FEM 研究了在精确轴几何上的复合椭圆和椭圆锥螺旋的瞬态响应和法向/剪切应力分量的横截面翘曲。瞬态分析使用 Newmark 时间积分算法进行，有或没有幅度衰减因子。复合弯曲杆的本构方程来源于三维弹性理论。计算包含翘曲的扭转刚度的位移型有限元公式与混合有限元公式相结合。曲率和位移型有限元用于估计各个横截面上的法向和剪切应力分布。将复合直梁的最大法向/剪切应力与文献进行了比较。与 3D 实体有限元的结果相比，动态载荷下精确椭圆锥螺旋的结果获得了极好的一致性。在时间积分方案的实施过程中，保留了力和力矩的一阶和二阶时间导数，并讨论了它们的时程。最后，除了应力之外，还研究了螺旋几何形状、层压和材料常数比对瞬态响应的影响。本文中的所有数值示例均为文献原创。在时间积分方案的实施过程中，保留了力和力矩的一阶和二阶时间导数，并讨论了它们的时程。最后，除了应力之外，还研究了螺旋几何形状、层压和材料常数比对瞬态响应的影响。本文中的所有数值示例均为文献原创。在时间积分方案的实施过程中，保留了力和力矩的一阶和二阶时间导数，并讨论了它们的时程。最后，除了应力之外，还研究了螺旋几何形状、层压和材料常数比对瞬态响应的影响。本文中的所有数值示例均为文献原创。