弹性地基梁板的径向基函数逼近求解方法  

Solution Method of Radial Basis Function Approximation for Elastic Foundation Beam and Plate

作　　者：林军志[1,2] 杨笛 徐绩青 LIN Junzhi;YANG Di;XU Jiqing(School of River and Ocean Engineering,Chongqing Jiaotong University,Chongqing 400074,China;Key Laboratory of Chongqing Municipal Education Commission for Geological Disaster Reduction of Mountain Highway Water Transportation,Chongqing 400074,China;Key Laboratory of Hydraulic and Waterway Engineering of the Ministry of Education,National Engineering Technology Research Center for Inland Waterway Regulation,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学河海学院,重庆400074 [2]山区公路水运交通地质减灾重庆市教委重点实验室,重庆400074 [3]重庆交通大学国家内河航道整治工程技术研究中心水利水运工程教育部重点实验室,重庆400074

出　　处：《重庆交通大学学报（自然科学版）》2023年第7期69-75,112,共8页Journal of Chongqing Jiaotong University(Natural Science)

摘　　要：基于Winkler模型对弹性地基梁和弹性地基板的挠度求解提出了一种新方法。利用加权余量法中的配点法结合径向基函数逼近得到挠度近似解,该方法无需划分网格且无需积分是未知数与方程数目一一对应的强形式解法。数值实验表明:该近似解结果与理论解基本吻合,计算效果与杂交边界法相当,优于滑动最小二乘法;此外,根据边界条件可赋予附加未知量物理意义,将部分特征矩阵构造成单位阵从而降低了待求方程组的求解难度,减小误差,为特征矩阵附加行的编写提供了新思路。Based on Winkler model,a new method was proposed to solve the deflection of elastic foundation beam and plate.The approximate solution of deflection was obtained by using the collocation method of weighted residual method combined with radial basis function approximation.The proposed method didn't need mesh and integration,which was a strong form solution of one-to-one correspondence between the number of unknowns and the number of equations.The numerical results show that the approximate solution is in good agreement with the theoretical solution,and the computational effect is equivalent to that of the hybrid boundary method,which is superior to that of the sliding least square method.In addition,according to the boundary conditions,the physical meaning of the additional unknown quantity is given,and part of the characteristic matrix is constructed into the unit matrix,to reduce the difficulty of solving the equations to be solved and the error,which provides a new idea for the compilation of the additional rows of the characteristic matrix.

关 键 词：岩土工程 径向基函数 加权余量配点法 弹性地基梁 弹性地基板 

分 类 号：U656.1[交通运输工程—港口、海岸及近海工程]