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A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams

机译:用于3-D梁几何非线性动力学分析的一致同向旋转有限元公式

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A co-rotational total Lagrangian finite element formulation for the geometrically nonlinear dynamic analysis of spatial Euler beam with large rotations but small strain, is presented. The nodal coordinates, displacements, rotations, velocities, accelerations, and the equations of motion of the structure are defined in a fixed global set of coordinates. The beam element has two nodes with six degrees of freedom per node. The element nodal forces are conventional forces and moments. The kinematics of beam element are defined in terms of element coordinates, which are constructed at the current configuration of the beam element. Both the element deformation nodal forces and inertia nodal forces are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using the d'Alembert principle and the virtual work principle in the current element coordinates. An incremental-iterative method based on the Newmark direct integration method and the Newton--Raphson method is employed here for the solution of the nonlinear equations of motion. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.
机译:提出了一种共旋转的总拉格朗日有限元公式,用于大旋转但小应变的空间欧拉梁的几何非线性动力学分析。结构的节点坐标,位移,旋转,速度,加速度和运动方程式在一组固定的全局坐标中定义。梁单元有两个节点,每个节点有六个自由度。单元节点力是常规力和力矩。梁单元的运动学是根据单元坐标定义的,单元坐标是在梁单元的当前配置下构造的。单元变形节点力和惯性节点力都是通过在当前单元坐标系中使用d'Alembert原理和虚拟功原理对完全几何非线性梁理论进行一致的线性化来系统得出的。这里采用基于Newmark直接积分法和Newton-Raphson方法的增量迭代法来求解非线性运动方程。数值算例表明了该方法的准确性和有效性。

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