摘要
将无单元法成功地应用于中厚板的模态分析,推导了无单元法的插值函数,利用权函数构造出了高阶连续的近似场函数,并在权函数中借鉴了自适应影响半径的思想;利用Mindlin-Reissner中厚板理论,从变分原理出发导出了中厚板模态分析的控制方程;同时利用罚函数法引入本质边界条件,给出了不同边界条件下的罚因子矩阵,推导出的系统刚度矩阵具有对称正定和带状分布的特点,可对不同边界条件下的中厚板振动问题进行求解,得到其自振频率及相应振型,并编制了相应的计算程序和后处理程序,可在MATLAB环境下绘制各阶振型图,便于直观、形象地对其振动特性进行定性研究。数值算例表明无单元法用于中厚板模态分析是合理可行的,能适用于较大范围内的剪切系数和长宽比,其结果具有相当高的精度。
The element-free Galerkin method （EFGM） is successfully applied to the modal analysis of moderately thick plates. The shape function of high-order continuity is formulated by means of the weight function. A method to incorporate the adaptive influential radius in the weight fhnction is proposed. Based on the variation principle, the governing equation for modal analysis of plates is derived from the Mindlin-Reissner plate theory, Using the penalty function method, the stiffness matrix, a real symmetric positive definite matrix, is derived, This method may solve the vibration problem of moderately thick plates with different boundary conditions and may obtain its free frequencies and the corresponding vibration mode curves. A computer code of EFGM with post-processing is developed, by means of which, one may obtain the vibration mode curves under the MATLAB software to study the vibration characteristic of the plate. Numerical examples show that the EFGM is feasible and accurate.
出处
《土木工程学报》
EI
CSCD
北大核心
2006年第10期29-33,共5页
China Civil Engineering Journal
关键词
无单元法
中厚板
模态分析
罚函数法
element-free Galerkin method
moderately thick plate
modal analysis
penalty function
