改进移动最小二乘近似（IMLS）采用带权正交多项式基函数，避免了对力矩矩阵的求逆过程，从而比移动最小二乘近似（MLS）节省了计算时间．但是由于其只要求近似函数在各节点处误差的平方和最小，对近似函数导数没有任何限制，使得在处理要求导数连续等问题时产生较大误差．而考虑导数近似的广义移动最小二乘近似（GMLS），虽然提高了近似函数的精度，但由于增加了节点自由度，显著增加了计算时间．结合IMLS和GMLS各自的优点，给出了改进的广义移动最小二乘近似（IGMLS）．该近似在构造函数时要求近似函数在所有节点处误差的平方和与近似函数导数仅在导数边界附近各节点处误差的平方和之和最小．同时，为了节省计算时间，基函数采用加权正交多项式．将IGMLS与无单元Galerkin法（EFG）相结合，给出了基于IGMLS的EFG法．通过对薄板离散建立了相应的薄板自由振动代数方程．通过数值算例证实了IGMLS比IMLS具有更高的精度，所需的运算时间要小于GMLS．%Improved moving least squares approximation(IMLS)use weighted orthogonal polynomial basis functions, avoid the inverse of the moment matrix,so save computing time than the moving least square approximation (MLS).But because it only requires approximate function reach the minimum sum of square of the error at each node,on the approximation of the derivative of the function without any limitation,making large error in the processing requirements of derivative continuous problem.Consider approximations for the derivatives as the generalized moving least squares approximation(GMLS),although improving the accuracy of function approximation,but due to the increased nodal degrees of freedom,significantly increase the computational time.With the IMLS and GMLS respective advantages,gave improved generalized moving least square approximation.IGMLS in construction requires the minimum sum of the square of the approximation functions error of all nodes and the square of derivative error in derivative boundary node.At the same time,in order to save the computing time,basis function uses weighted orthogonal polynomial.Combining IGMLS and the element free Galerkin method(EFG),gave the EFG method based on IGMLS.By discreting plate build the corresponding algebraic equations of vibration.Through numerical calculation examples demonstratedthat IGMLS has higher accuracy than the IMLS,the computational time required too less than GMLS.
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