节点参数含应变的空间几何非线性样条梁单元

A Spatial Geometric Nonlinearity Spline Beam Element With Nodal Parameters Containing Strains

工程中很多细长杆件可以抽象为Euler-Bernoulli梁,分析其动态行为时需要对其进行柔性多体系统动力学建模.以绝对节点坐标参数为代表的几何非线性梁单元解决了大量柔性梁动力学问题,但仍然面临诸如剪切闭锁、节点应力不连续、计算效率低下等问题.鉴于此,以大变形梁虚功率方程为理论基础,建立了转动参数和位移参数间的转换方程,满足Euler-Bernoulli梁变形耦合关系,推导了这种情况下可描述梁几何非线性效应的广义应变;保证应力连续的情况下,采用样条插值实现单元间缩减自由度式组装;将边界节点部分参数替换为轴向应变和截面曲率,得到了更加准确简洁的施加外力的约束方式;对梁结构的运动方程进行降噪处理,来滤除高频分量,提高求解效率;并通过数值算例验证了所提单元的有效性.

Many slender rods in engineering can be modeled as Euler-Bernoulli beams.For the analysis of their dynamic behaviors,it is necessary to establish the dynamic models for the flexible multi-body systems.Geometric nonlinear elements with absolute nodal coordinates help solve a large number of dynamic problems of flexible beams,but they still face such problems as shear locking,nodal stress discontinuity and low computation efficiency.Based on the theory of large deformation beams’virtual power equations,the functional formulas between displacements and rotation angles at the nodes were established,which can satisfy the deformation coupling relationships.The generalized strains to describe geometric nonlinear effects in this case were derived.Some parameters of boundary nodes were replaced by axial strains and sectional curvatures to obtain a more accurate and concise constraint method for applying external forces.To improve the numerical efficiency and stability of the system’s motion equations,a model-smoothing method was used to filter high frequencies out of the model.The numerical examples verify the rationality and effectiveness of the proposed element.