Thesis (M. Eng.(Mechanical and aeronautical engineering))-University of Pretoria, 2005. / Includes bibliographical references. Available on the Internet via the World Wide Web.

The large ductile deformation response of stiffened plates subjected to blast loads is investigated and simplified methods of analysis of such response are developed. Simplification is derived from modelling stiffened plates as singly symmetric beams or as grillages thereof. These beams are further assumed to behave in a rigid, perfectly plastic manner and to have piecewise linear bending moment-axial force capacity interaction relations, otherwise known as yield curves. A blast loaded, one-way stiffened plate is modelled as a singly symmetric beam comprised of one stiffener and its tributary plating, and subjected to a uniformly distributed line load. For a stiffened plate having edges fully restrained against rotations and translations, both transverse and in-plane, use of the piecewise linear yield curve divides the response of the beam model into two distinct phases: an initial small displacement phase wherein the beam responds as a plastic hinge mechanism, and a final large displacement phase wherein the beam responds as a plastic string. If the line load is restricted to be a blast-type pulse, such response is governed by linear differential equations and so may be solved in closed form. Examples of a one-way stiffened plate subjected to various blast-type pulses demonstrate good agreement between the present rigid-plastic formulation and elastic-plastic beam finite element and finite strip solutions. The response of a one-way stiffened plate is alternatively analysed by approximating it as a sequence of instantaneous mode responses. An instantaneous mode is analogous to a normal mode of linear vibration, but because of system nonlinearity exists for only the instant and deformed configuration considered. The instantaneous mode shapes are determined by an extremum principle which maximizes the rate of change of the stiffened plate's kinetic energy. This approximate rigid-plastic response is not solved in closed form but rather by a semi-analytical time-stepping algorithm. Instantaneous mode solutions compare very well with the closed-form results. The instantaneous mode analysis is extended to the case of two-way stiffened plates, which are modelled by grillages of singly symmetric beams. For two examples of blast loaded two-way stiffened plates, instantaneous mode solutions are compared to results from super finite element analyses. In one of these examples the comparison between analyses is extremely good; in the other, although the magnitudes of displacement response differ between the analyses, the predicted durations and mechanisms of response are in agreement. Incomplete fixity of a stiffened plate's edges is accounted for in the beam and grillage models by way of rigid-plastic links connecting the beams to their rigid supports. Like the beams, these links are assumed to have piecewise linear yield curves, but with reduced bending moment and axial force capacities. The instantaneous mode solution is modified accordingly, and its results again compare well with those of beam finite element analyses. Modifications to the closed-form and instantaneous mode solutions to account for strain rate sensitivity of the panel material are presented. In the closed-form solution, such modification takes the form of an effective dynamic yield stress to be used throughout the rigid-plastic analysis. In the time-stepping instantaneous mode solution, a dynamic yield stress is calculated at each time step and used within that time step only. With these modifications in place, the responses of rate-sensitive one-way stiffened plates predicted by the present analyses once again compare well with finite element and finite strip solutions. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

An experimental study is presented on the non-linear twisting of plates with free edges, through the application of self-equilibrating corner loads. A simple apparatus was designed and various sizes of plates were twisted while measuring the surface strains on both sides at the centre. Initial difficulty was encountered due to unwanted deflection of the plate under its own weight. The Rayleigh-Ritz method is used to determine an analytical relationship between midsurface strains and curvatures in the pre- and post-bifurcation regions of twisting. In both the experimental and analytical results, the midsurface strains are found to vary linearly with the Gaussian curvature. Non-dimensional groups are identified which collapse the experimental load-strain, load-curvature and midsurface strain-Gaussian curvature relationships. These non-dimensional groups collapse the results in both the linear and non-linear regions. The curvature at the point of bifurcation is identified as a function of plate dimensional parameters. Also shown are the expressions for critical surface strain and corner load at which bifurcation occurs. The experimental load-curvature relationship and point of bifurcation are compared with analytical results found in the literature. A large discrepancy in the literature is resolved for the theoretical point of bifurcation. The present results form a basis for verification of future analytical results, and are important in the measurement of constitutive relationships using the twisted plate test. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

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

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In this work, several studies into the dynamic response of structures are made. In all the studies there is an interaction between the theoretical and experimental work that lead to important results. In the first study, previous theoretical results for the single-mode response of a parametrically excited cantilever beam are validated. Of special interest is that the often ignored nonlinear curvature is stronger than the nonlinear inertia for the first mode. Also, the addition of quadratic damping to the model improves the agreement between the theoretical and experimental results. In the second study, multi-mode responses of a slender cantilever beam are observed and characterized. Here, frequency spectra, pseudo-phase planes, Poincare sections, and dimension values are used to distinguish among periodic, quasi-periodic, and chaotic motions. Also, physical interpretations of the modal interactions are made. In the third study, a theoretical investigation into a previously unreported modal interaction between high-frequency and low-frequency modes that is observed in some experiments is conducted. This modal interaction involves the complete response of the first mode and modulations associated with the third and fourth modes of the beam. A model that captures this type of modal interaction is developed. In the fourth study, the natural frequencies and mode shapes of several composite plates are experimentally determined and compared with a linear finite-element analysis. The objective of the work is to provide accurate experimental natural frequencies of several composite plates that can be used to validate future theoretical developments. / Ph. D.

The nonlinear dynamical behavior of a laterally compressed, flat, composite panel subjected to a high supersonic flow is analyzed. The structural model considers a higher-order shear deformation theory which also includes the effect of the transverse normal stress and satisfies the traction-free condition on both faces of the panel. The possibility of small initial imperfections and in-plane edge restraints are also considered. Aerodynamic loads based on the third-order piston theory are used and the panel flutter equations are derived via Galerkin’s method. Periodic solutions and their bifurcations are obtained by using a predictor-corrector type of numerical integration method, i.e., the Shooting Method, in conjunction with the Arclength Continuation Method for the static solution. For the perfect panel, the amplitudes and frequency of flutter obtained by the Shooting Method are shown to compare well with results from the Method of Multiple Scales when linear aerodynamics is considered and compressive loads are absent. It is seen that the presence of aerodynamic nonlinearities could result in the hard flutter phenomenon, i.e., a violent transition from the undisturbed equilibrium state to that of finite motions which may occur for pre-critical speeds also. Results show that linear aerodynamics correctly predicts the immediate post-flutter behavior of thin panels only. When compressive edge loads or edge restraints are applied, in certain cases multiple periodic solutions are found to coexist with the stable static solution, or multiple buckled states are possible. Thus it is seen that the panel may remain buckled beyond the flutter boundary, or it may flutter within the region where buck-led states exist. Furthermore, the presence of edge restraints normal to the flow tends to stabilize the panel by decreasing the flutter amplitudes and the possibility of hard flutter. Nonperiodic motions (i.e., quasiperiodic and chaotic) of the buckled panel are found to exist, and their associated Lyapunov exponents are calculated. The effects of transverse shear flexibility, aerodynamic nonlinearities, initial imperfections, and in-plane edge restraints on the stability boundaries are also studied. It is observed that the classical plate theory over-predicts the instability loads, and only the shear deformation theory correctly models the panel which is flexible in transverse shear. When aerodynamic nonlinearities are considered, multiple flutter speeds may exist. / Ph. D.

The Layerwise Shell Theory is used to model discretely stiffened laminated composite cylindrical shells for stress, vibration, pre-buckling and post-buckling analysis. The layerwise theory reduces a three-dimensional problem to a two-dimensional problem by expanding the three-dimensional displacement field as a function of a surface-wise two-dimensional displacement field and a one-dimensional interpolation through the shell thickness. Any required degree of accuracy can be obtained by an appropriate, independent selection of the one-dimensional interpolation functions through the thickness and the two-dimensional interpolation of the variables on the surface. Using a layerwise format, discrete axial and circumferential stiffeners are modeled as two-dimensional beam elements. Similar displacement fields are prescribed for both the stiffener and shell elements. The contribution of the stiffeners to the membrane stretching, bending and twisting stiffnesses of the laminated shell is accounted for by forcing compatibility of strains and equilibrium of forces between the stiffeners and the shell skin. The layerwise theory is also used to model initial imperfections of the unstressed configuration. A finite element scheme of the layerwise model is developed and applied here to investigate the effect of imperfections on the response of laminated cylindrical shells. Using a finite element model of the layerwise theory for shells and shell stiffener elements, the accuracy and reliability of the elements is investigated through a wide variety of examples. The examples include laminated stiffened and unstiffened plates and shells and stand-alone beams under different types of external destabilizing loads. Finally, the study identifies the particular types of problems where the layerwise elements possess a clear advantage and superiority over the conventional equivalent single-layer models. / Ph. D.