基于无网格法的非均匀弹性地基上变厚度加筋板弯曲与固有频率分析

采用基于移动最小二乘近似的无网格方法并结合一阶剪切变形理论,分析了非均匀弹性地基上变厚度加筋板的弯曲和固有频率问题.首先,用节点对变厚度板和筋条分别进行离散,导出变厚度板和筋条的势能;其次,利用筋条与变厚度板之间的位移协调条件将筋条的节点参数转换为板的节点参数,再将两者的势能进行叠加得到变厚度加筋板的总势能,并根据能量法得到其动能;最后,利用最小势能原理及Hamilton原理分别得到弯曲控制方程与振动控制方程.由于采用的方法不能直接施加位移边界,故采用完全转换法处理位移边界.本文先计算变厚度板的弯曲及非均匀弹性地基板的固有频率,与文献对比验证方法的有效性;然后对非均匀弹性地基上变厚度加筋板弯曲与 自由振动进行了计算,并将计算结果与有限元结果进行了对比.结果表明,本文方法计算所得结果与文献解及有限元结果之间的误差均小于5％,验证了该方法在计算非均匀弹性地基上变厚度加筋板弯曲与固有频率问题的有效性.

Bending and natural frequency analysis of variable thickness stiffened plates on non-uniform elastic foundation based on meshless method

The paper analyzed the bending and frequency problems of ribbed plates on the non-uniform elastic foundation with variable thickness by a meshless method based on Moving Least-Squares(MLS) in conjunction with First-order Shear Deformation Theory(FSDT).First,the variable thickness plates and ribs are discretized respectively,and the potential energy functional of the variable thickness plates and ribs is derived.Secondly,the displacement continuity conditions between the rib and the variable thickness plate are used to convert the nodal parameters of the rib to the nodal parameters of the plate,and then the potential energy functional of the two are superimposed to obtain the total potential energy functional of the variable thickness stiffened plate.Finally,the governing equations of bending and frequency are acquired using the minimum energy theory and Hamilton theory respectively.The full transformation method is used while the displacement boundary is solved because the method mentioned above cannot apply the boundary condition directly.Bending of the variable thickness plate and frequency of the plate with variable thickness on the non-uniform elastic foundation are validated by comparing the results with those of the literatures.Variable thickness ribbed plates with different parameters are analyzed,which are analyzed with the FEM results.They show that the error between the results of the meshless method and the FEM and the error between the results of the meshless method and the literature are both less than 5%,which validates the effectiveness of the meshless method in calculating the bending and frequency of variable thickness ribbed plates on the non-uniform elastic foundation.