Abstract
Based on the first-order shear deformation theory (FSDT) and the moving least-squares approximation, a new meshless model to study the geometric nonlinear problem of ribbed rectangular plates is presented. Considering the plate and the ribs separately, the displacement field, the stress, and strain of the plate and the ribs are obtained according to the moving least-squares approximation, the von Karman large deflection theory, and the FSDT. The ribs are attached to the plate by considering the displacement compatible condition along the connections between the ribs and the plate. The virtual strain energy formulation of the plate and the ribs is derived separately, and the nonlinear equilibrium equation of the entire ribbed plate is given by the virtual work principle. In the new meshless model for ribbed plates, there is no limitation to the rib position; for example, the ribs need not to be placed along the mesh lines of the plate as they need to be in FEM, and the change of rib positions will not lead to remeshing of the plate. The proposed model is compared with the FEM models from pieces of literature and ANSYS in several numerical examples, which proves the accuracy of the model.
Highlights
Ribbed plate has been widely used in engineering, such as bridges, ship hulls, and aviation, and it is a popular structure with obvious advantages
The objective of this paper is to propose a meshless model to study the geometric nonlinear behaviors of ribbed plates from the perspective of composite structure
The nonlinear deflection of the central point of the plate that is obtained by the proposed model under different support sizes and different completeness orders of the basic functions Nc is shown in Figure 3, and is compared with the solution that is given by the finite element software, ANSYS, using SHELL63 element
Summary
Ribbed plate has been widely used in engineering, such as bridges, ship hulls, and aviation, and it is a popular structure with obvious advantages. Based on the fact that the ribs of many ribbed plates are attached to the plate with uniform spacing and close to one another, and that ribbed plates show different elastic characteristics in the two perpendicular directions, early researchers transformed the ribs to an addition layer to the plate and used the orthotropic model to approximate the ribbed plates [1]. The models were simple and fulfilled the demand of fast and easy computation in engineering They are still used in some design environments, where accurate analysis is not the first concern. Several methods have been developed, such as the RayleighRitz method [3,4,5,6,7] and the finite element methods (FEM) [8, 9]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
