结构振动分析中的无网格方法

Vibration analysis by an effective meshless method

无网格法采用移动最小二乘法构造位移函数,采用罚方法满足本征边界条件,对弹性体的振动问题进行了分析。首先,对权函数中的参数进行了讨论并优化,给出了参数最优值的确定方法;在此基础上对不同边界条件下梁和板的模态进行了分析;最后计算了受突加荷载作用的简支梁以及具有初位移的简支方板的动力响应。计算结果表明该方法在动力问题的分析中有较高的精度。

Based on the moving least squares method, an effective meshless method is developed for the vibration analysis of elastic bodies. The penalty method is employed to impose the essential boundary conditions. As the accuracy of the scheme will depend on the parameters of the weight functions, parameters study has been carried out to determine their best values. Then modal analyses of the beams and plates with different boundaries have been put forward. In addition, the responses of these structures under dynamic excitation have been analyzed. The examples including simply supported beams subjected to sudden excitations and simply supported plates subjected to initial displacements. Numerical examples show that this method has high accuracy in the vibrate analysis.