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The incremental structural analysis program NISA83 was used to investigate various parameters affecting the ultimate capacity of square plates with circular perforations subjected to uniform shear stress. Both nonlinear material properties and nonlinear geometry were taken into account in determining the ultimate in-plane capacities and buckling capacities of perforated shear plates. The parameters investigated during this study were the hole size for a concentric location, and the hole location for a constant ratio of hole diameter to plate width of 0.2. In addition various doubler plates were studied to determine the most effective shape to restore a shear plate to its original ultimate in-plane capacity. For the first two parameters, the analysis was separated into three parts. The ultimate in-plane capacity, elastic buckling capacity and the ultimate elastic-plastic buckling capacity was determined for each combination of the two parameters. These were used to identify the importance of both elastic buckling and nonlinear material contribute to the reduced ultimate plate capacities. The results from plates with a concentrically located hole of varying size showed excellent correlation with other published experimental and analytical results for both the in-plane capacity and the 3-dimensional buckling capacities. Variation of the center location of a hole of a standard size provided some significant results. Little change was found in the ultimate in-plane capacity for all hole locations. On the other hand, the elastic buckling capacity was raised by 50% after moving the hole from the plate tension diagonal to the compression diagonal. Finally, from the ultimate elastic-plastic' buckling capacity results it was concluded that the concentric provides lower bound capacity for all other hole locations. The in-plane analysis of the optimum doubler plate size showed wide and thin plates to be more effective than narrow and thick plates. A doubler plate with the same thickness as the plate and twice the diameter of the hole is recommended to restore the perforated plate to its original in-plane capacity. In order to aid in the tedious task of checking the input data and to provide a convenient way of displaying the result, a full graphic post-processor was developed as part of this thesis. The program NISPLOT used color graphics available at the UBC Civil Engineering lab to process the output from NISA83. It was written in FORTRAN 77, utilizing subroutines from a commercial graphics package, DI3000, to obtain device independent graphics. NISPLOT generated plots of the nodes and element mesh for each data check. When a complete analysis was carried out by NISA83, nodes, element mesh, deflected shape, and color stress fill plots were generated. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

A solution procedure based on the finite strip method is presented herein, for the analysis of plate systems exhibiting geometric and material non-linearities. Special emphasis is given to the particular problem of rectangular plates with stiffeners running in a direction parallel to one side of the plate. The finite strip method is selected for the analysis as the geometry of the problem is well suited for the application of this method and also as the problem is too complicated to solve analytically. Large deflection effects are included in the present study, by taking first, order non-linearities in strain-displacement relations into account. Material non-linearities are handled by following von-Mises yield criterion and associated flow rule. A bi-linear stress-strain relationship is assumed for the plate material, if tested under uniaxial conditions. Numerical integration of virtual work equations is performed by employing Gauss quadrature. The number of integration points required in a given direction is determined either by observing the individual terms to be integrated or by previous experience. The final set of non-linear equations is solved via a Newton-Raphson iterative scheme, starting with the linear solution. Numerical investigations are carried out by applying the finite strip computer programme to analyse uniformly loaded rectangular and I beams with both simply supported and clamped ends. Displacements, stresses and moments along the beam are compared with analytical solutions in linear analyses and with finite element solutions in non-linear analyses. Investigations are also extended to determine the response of laterally loaded square plates with simply supported and clamped boundaries. Finally, a uniformly loaded stiffened panel is analysed and the results are compared with finite element results. It was revealed that a single mode in the strip direction was sufficient to yield engineering accuracy for design purposes, with most problems. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

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No description available.

A dissertation submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in fulfiment of the requirements for the degree of Master or Science in Engineering. Johannesburg, 1993. / The stress concentration factors around rectangular holes in carbon-fibre reinforced epoxy plates, subject uniaxial loads, were investigated experimentally and theoretically. To obtain theoretical solutions, two approaches were adopted; the finite element method and the theory of elasticity using the method of complex variable functions. Reflective photoelasticity was used as the experimental method. The determination of the stress concentration factor around a rectangular hole in a glass-fibrereinforced plate was attempted using transmissive photoelasticity, but no meaningful results were obtained. [Abbreviated Abstract. Open document to view full version} / MT2017

A degenerated three-dimensional finite element based on the total Lagrangian, incremental, formulation of a three-dimensional layered anisotropic medium is developed, and its use in the geometrically nonlinear, static as well as dynamic, analysis of layered composite plates and shells is demonstrated via several example problems. For comparison purposes, a two-dimensional finite element based on the Sanders shell theory with the von Karman (nonlinear) strains is also presented. The elements have the following features: • Geometrically linear and nonlinear analysis • Static and transient analyses • Natural vibration (linear) analyses • Plates and shell elements • Arbitrary loading and boundary conditions • Arbitrary lamination scheme and lamina properties The element can be used, with minor changes, in any existing general purpose programs. The 3-D dimensional degenerated element has computational simplicity over a fully three-dimensional element, and the element accounts for full geometric nonlinearities in contrast to the 2-dimensional elements based on the Sanders shell theory. As demonstrated via numerical examples, the deflections obtained by the 2-D shell element deviate from those obtained by the 3-D element for deep shells. Further, the 3-D element can be used to model general shells that are not necessarily doubly-curved. For example, the twisted plates can not be modeled using the 2-D shell element. Of course, the 3-D degenerated element is computationally more demanding than the 2-D shell theory element for a given problem. In summary, the present 3-D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion. / Ph. D.

An exact solution is presented for the large deformation response of a simply supported orthotropic cylindrical panel subjected to a uniform line load along a cylinder generator. The cross section of the cylinder is circular and deformations up to the fully snapped through position are investigated. The orthotropic axes are parallel to the generator and circumferential directions. The governing equations are ·derived using laminated plate theory, nonlinear strain-displacement relations, and applying variational principles. The response is investigated for the case of a panel loaded exactly at midspan and for a panel with the load offset from midspan. The mathematical formulation is one-dimensional in the circumferential coordinate. Solutions are obtained in closed-form. An experimental apparatus was designed to load the panels. Experimental results of displacement controlled tests performed on graphite-epoxy curved panels are compared with analytic predictions. This study demonstrates that panel shallowness, material orthotropy, and stacking sequence can influence the nonlinear static response. Initial geometric imperfections, observed during testing, were found to influence the response of the panels. However, the overall correlation of analytic and experimental results were good. / M.S.

A higher-order shear deformation theory is used to analyze laminated anisotropic composite plates for deflections, stresses, natural frequencies, and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, satisfies the stress-free boundary conditions on the top and bottom planes of the plate, and, as a result, no shear correction coefficients are required. Even though the displacements vary cubically through the thickness, the theory has the same number of dependent unknowns as that of the first-order shear deformation theory of Whitney and Pagano. Exact solutions for cross-ply and anti-symmetric angle-ply laminated plates with all edges simply-supported are presented. A finite element model is also developed to solve the partial differential equations of the theory. The finite element model is validated by comparing the finite element results with the exact solutions. When compared to the classical plate theory and the first-order shear deformation theory, the present theory, in general, predicts deflections, stresses, natural frequencies, and buckling loads closer to those predicted by the three dimensional elasticity theory. / Master of Science