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Title: Numerical development in meshfree method for stiffened plates and plate assemblies
Other Titles: Jia lei ban yu ban ji de wu wang ge fang fa jin zhan
Authors: Peng, Linxin (彭林欣)
Department: Dept. of Building and Construction
Degree: Doctor of Philosophy
Issue Date: 2006
Publisher: City University of Hong Kong
Subjects: Elastic plates and shells
Galerkin methods
Meshfree methods (Numerical analysis)
Notes: CityU Call Number: QA935.P46 2006
Includes bibliographical references (leaves 235-248)
Thesis (Ph.D.)--City University of Hong Kong, 2006
xxxii, 248 leaves : ill. ; 30 cm.
Type: Thesis
Abstract: This thesis presents a study on the simulation of stiffened plates, stiffened or un-stiffened corrugated plates, and folded plates with a meshfree Galerkin method based on the first-order shear deformation theory (FSDT). It is believed to be the first time that a meshfree method has been successfully implemented in the study of the elastic bending, free vibration, and elastic buckling problems of these structures. The computational results of a number of examples prove that the proposed method is more flexible and applicable than the finite element methods (FEM), but maintains the same degree of accuracy. Numerous studies on meshfree methods are reviewed to give the reader a comprehensive view of these methods and their origin and development. Several representative meshfree methods are introduced to demonstrate their advantages and disadvantages. A detailed derivation of the moving least-squares (MLS) approximation is described, and a meshfree Galerkin method is formed by incorporating the approximation with the Galerkin weak formulation. The difficulties of meshfree methods and the solutions to these difficulties are also presented. The meshfree formulations for the elastic bending, free vibration, and elastic buckling of concentrically and eccentrically stiffened plates are derived. The stiffened plates are regarded as composite structures of plates and beams. By imposing displacement-compatible conditions between the plate and the stiffener, the displacement field of the stiffener can be expressed in terms of the mid-surface displacement of the plate, and thus the strain energy of the plate and stiffener can be superimposed to obtain the stiffness matrix of the stiffened plate. Because no elements are used in the meshless model of the plate, the stiffeners need not be placed along the mesh lines, as is the case in most FEMs, and thus a change in position of the stiffener does not lead to the remeshing of the plate. The convergence and accuracy of the proposed method in studying stiffened plate problems is demonstrated by considering several concentrically and eccentrically stiffened plate problems. The present results show good agreement with the existing analytical and finite element solutions. The influences of support size and the completeness order of the basis function on the numerical accuracy are investigated. The elastic bending, free vibration, and elastic buckling behavior of stiffened and un-stiffened corrugated plates are also studied. The corrugated plates are approximated by orthotropic plates of uniform thickness and different elastic properties along two perpendicular directions. The key to the approximation is the equivalent elastic properties of the orthotropic plates, which are derived by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plates are analyzed as stiffened orthotropic plates, and thus the achievements of the research for stiffened plates can be extended to the study of stiffened corrugated plates. The stiffeners are modeled as beams, and the stiffness matrix of the stiffened corrugated plate is approximately obtained by superimposing the strain energy of the equivalent orthotropic plate and the beams after implementing displacement compatibility conditions between the plate and the beams. The meshfree characteristic of the proposed method guarantees that the stiffeners can be placed anywhere on the plate, and that remeshing is avoided when the stiffener positions change. Some selected examples are studied to demonstrate the accuracy and convergence of the proposed method. The results are compared with those from literatures and the finite element software ANSYS. Meshfree solutions for the elastic bending, free vibration, and elastic buckling problems of stiffened and un-stiffened folded plates are obtained. In the case of elastic buckling, stiffened and un-stiffened folded plates that are subjected to in-plane partial edge loading are investigated. In this analysis, the un-stiffened folded plates are modeled as assemblies of flat plates, and the stiffness matrices of the flat plates are derived by the meshfree Galerkin method. A treatment is implemented to modify the stiffness matrices, and the matrices are then superposed to obtain the stiffness matrix of the entire folded plate. The analytical process for the stiffened folded plates is similar. After the stiffness matrices from the results of the stiffened plate research are modified by the aforementioned treatment, they are superposed to give the stiffness matrix of the entire stiffened folded plate. Some numerical examples are computed using the proposed method to demonstrate its accuracy and convergence, and the results agree well with the results that are given by ANSYS and other researchers. The geometrically nonlinear meshfree Galerkin formulation for corrugated plates and folded plates is derived. The corrugated plates are still approximated by stiffened and un-stiffened orthotropic plates, and the folded plates are regarded as assemblies of stiffened or un-stiffened flat plates. The large deflection theory of von Karman is employed, and the strains are assumed to be small. Several numerical examples are presented to verify the formulation. The solutions that are given by the proposed method, including the post-buckling curve of a shallow shell, agree well with those from ANSYS and other studies. To the author’s knowledge, this thesis is the first attempt to employ a meshfree method in studying stiffened plate, corrugated plate, and folded plate problems, and the corresponding formulations are derived to make the meshfree method applicable to the structures. Although the author has adopted the meshfree Galerkin method as the analysis tool, any of the meshfree methods could be employed to analyze the structures with the meshfree formulations that are presented in this thesis. The thesis provides a basis from which subsequent researchers can study crack propagation and drastic large deformation in stiffened plates, corrugated plates, and folded plates, for which the superiority of meshfree methods are more evident.
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