无单元法求解欧拉梁及梁系的自由振动问题

双变量无单元法以广义移动最小二乘法为理论基础,同时考虑挠度和转角双变量.采用双变量无单元法建立了欧拉粱的质量矩阵和刚度矩阵,并进行自由振动的计算.不同边界条件欧拉梁动力特性的算例表明:双变量无单元法比与只考虑挠度的单变量无单元法具有更高的插值精度,并能在高阶振型计算中获得明显优于有限元的计算精度.通过试算法对影响半径中的scale乘子进行了讨论,认为在动力计算中Scale取3.5较合理.最后在欧拉粱的基础上,将无单元法应用于梁系模型的自由振动计算,显示了该法在复杂模型中的精确性.

Solution to free vibration of Euler beam and girder system with Element-Free Galerkin method

An effective method called Appended Massless Constraint Element (AMCE) method is presented and proposed, which is adopted to settle the problem, easy but not to be neglected, inherent in the displacement input model for calculating the structural responses under earthquake-induced ground motion. Based on the comprehensive and intensive analysis of the displacement input model in this paper, it points out explicitly that there is the unstability and extreme irrationality of the calculation results while adopting the displacement input model. To solve the problem, the RMCE method is presented. Then, the rationality and accuracy of the proposed method are further verified. Theoretical analysis and numerical results demonstrate that the proposed method is simple, feasible and possesses high accuracy.