Semi-analytical Methods For Stress And Stability Analyses Of Perforated Plates

Various perforated plates are commonly used in practical engineering structures. The stress concentration and stability of the plates are highly concerned in structure design due to the presence of holes. The study on the stress distribution and stability problems of perforated plates is of great importance for theoretical development and practical application.A novel semi-analytical method for solving the plane stress distribution and bending stress distribution problems of a finite plate with an arbitrary hole and a new semi-analytical method for elastic stability of perforated plates and stiffened plates with a hole are developed. The main works in the study are as follows:Firstly, based on the Kolossov-Muskhelishvili’s complex variable method, a novel semi-analytical method, named as stress functions reconstruction method, is proposed for determining the stress distribution of a finite isotropic plate with an arbitrary hole under in-plane loading. The first stage is to analyze the stress distribution of an infinite plate with a hole. An arbitrary hole in z-plane is represented by a unit circle in ζ-plane by using mapping function, while the corresponding area external to the given hole in z-plane is represented by the area outside the unit circle. Then the stress functions of an infinite plate with a hole, expressed as the complex variable in ζ-plane, is obtained by Cauchy integral. The second stage is to obtain the stress distribution of a finite perforated plate. The stress functions, obtained in the first stage, are reconstructed by extending sufficient terms of series in mapped area (ζ-plane). Then the reconstructed functions are used as the stress functions of a finite plate with a hole. The third stage is to determine the unknown constants of the reconstructed functions by using the least square boundary collocation method. Then the stress field of a finite plate with a hole is determined.Then verification and parameter analysis are conducted. Infinite and finite plates with seven different types of hole are considered respectively. The stress distributions around the holes are calculated by the proposed method, and the results are compared with those obtained by ANSYS and given in literature. It is shown that, when the hole size is large enough, the plane stress theory for the infinite plate is not applicable. The stress functions reconstruction method proposed in this thesis has strong applicability, good accuracy and simplicity. It can be used for the plane stress analysis of infinite plates and finite plates with an arbitrary hole. The stress distribution and stress concentration around the hole of a plate under uniaxial tension, biaxial tension, shear loading respectively are studied. The shapes of hole include circular shape, elliptical shape, triangular shape, maize shape, parabolic shape and bat shape. Moreover, the effects of hole size, hole orientation and plate’s aspect ratio on the stress distribution and stress concentration factor of a plate with a rectangular hole are conducted.Next, based on the complex variable method for bending theory of thin plates, a novel semi-analytical method is proposed for determining the bending stress distribution of a finite isotropic plate with an arbitrary hole subjected to anti-plane loading. Similarly to the plane stress problem, the proposed method for bending stress analysis can be named as stress functions reconstruction method. The bending stress of a finite plate with four different shapes of hole is calculated respectively by proposed method. Verification is conducted by comparing the results obtained by this method with those obtained by ANSYS and given in literature. It is shown that developed method has strong applicability, good accuracy and simplicity. It can be used for bending stress analysis of the infinite plates and finite plates with an arbitrary hole. For a plate with two opposite edges subjected to moment, parametric studies for the bending stress around four different holes are respectively conducted.Afterwards, semi-analytical studies for the overall stability of rectangular plates with a rectangular hole are carried out. In the study, the stress distribution of the plate is firstly conducted by using stress functions reconstruction method. A deflection shape function, satisfying not only the outer boundary conditions but also the inner boundary conditions of hole edges, is obtained by using domain decomposition method. Finally the buckling load of the plate using energy method is calculated based on the stress distribution and the reasonable deflection shape function obtained. The results obtained by this method are compared with those obtained by ANSYS. It is shown that this semi-analytical method has good accuracy. The effect of hole size on the stability of the plate is discussed for four different boundary conditions. They are all four edges simply supported, all four edges clamped, the two loaded edges simply supported and other two non-loaded edges free, the two loaded edges clamped and other two non-loaded edges free.Finally, semi-analytical studies for the overall stability of stiffened plates with rectangular holes are carried out. The stiffened plate is treated as the collections of plate and beam elements in this study. The calculation method is similar to that of perforated flat plate. The stress distribution of perforated flat plate obtained by stress functions reconstruction method is approximately used. A deflection shape function, satisfying not only the outer boundary conditions but also the inner boundary conditions of hole edges, is obtained by using domain decomposition method. Then the bending strain energy and external works of the plate and beam elements are achieved. The buckling load of the stiffened plate using energy method is obtained. The results obtained by this method are compared with those obtained by ANSYS. It is shown that, when the hole size is not larger than a certain value for the chosen stiffened plates, this semi-analytical method has reasonable accuracy. The effect of hole size on the stability of the stiffened plate is discussed for different boundary conditions.It is certainly that the investigation done possess reference value to the theoretical research and engineering design of perforated plates.