CRITICAL BUCKLING LOAD CALCULATION OF RIBBED PLATES BY THE FIRST-ORDER SHEAR DEFORMATION THEORY AND THE MOVING-LEAST SQUARE APPROXIMATION

In order to obtain the critical buckling load of ribbed plates, a meshfree method based on the first-order shear deformation theory (FSDT) and the moving-least square (MLS) approximation is introduced. The plate and the ribs of a ribbed plate are considered separately and the ribs are simulated with a beam model. The approximated displacement fields of the plate and the ribs are determined according to the FSDT and MLS approximation. Employing the displacement compatible conditions along the interface between the plate and ribs, the formula that transforms the nodal parameters of the ribs to those of the plate is derived. Superposing the potential energy of the plate and ribs, the governing equation for the buckling behavior of the entire ribbed plate is established by the principle of minimum potential energy. Compared with the FEM, the introduced method has such advantages that the ribs need not to be fitted along the mesh lines of the plate and remeshing is avoided if the rib position changes. The solutions given by the proposed method about several numerical examples are compared with those from ANSYS using solid elements. A close agreement has been observed, which proves the validity of the introduced method.