<p>In modern engineering there is a considerable interest in predicting the behavior of post-buckled structures. With current lightweight, aerospace, and high performance applications, structural elements frequently operate beyond their buckled load. This is especially true of plates, which are capable of maintaining stability at loads several times their critical buckling load. Additionally, even structures such as cylindrical shells may be pushed into a post-buckled range in these extreme applications. </p><p>Because of the nature of these problems, continuation methods are particularly well suited as a solution method. Continuation methods have been extensively applied to a range of problems in mathematics and physics but have been used to a lesser extent in engineering problems. In the present work, continuation methods are used to solve a variety of buckling and stability problems of discrete dynamical systems, plates and cylinders. The continuation methods, when applied to dynamic mechanical systems, also provide very useful information regarding the modal behavior of the structure, including linearized natural frequencies and mode shapes as a by-product of the solution method.</p><p>To verify the results of the continuation calculations, the commercial finite element code ANSYS is used as an independent check. To confirm previously unseen stable equilibrium shapes for square plates, a set of experiments on polycarbonate plates is also presented.</p> / Dissertation

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In the present study, the buckling behavior of beams is analyzed by a plane strain finite element. The displacement-type finite element formulation is based on elasticity and has no any other simplification and assumption except that the beam is of moderate depth. Also all the displacement boundary conditions can be imposed exactly. These are the advantages that beam theories of conventional approach, which simulate beams with neutral plane behaviors, do not have. Therefore the present analyses should be able to obtain buckling load and buckling mode more accurately than conventional method. Numerical values of buckling loads of the present approach will be compared with previously published results of the Euler-Bernoulli beam theory and the Timoshenko beam theory, and further with the high order beam theory to reveal their differences. The effects of the geometry ratio, the distribution of axial loads and the displacement boundary conditions on buckling of beams are also discussed.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 154-158). Also available via the Internet.

The aim of this study was to investigate the dynamic collapse of composite shells in a constant external pressure water environment that is representative of a naval underwater structure. Laminated carbon/epoxy composite shells with diameters of 1.735 in., wall thickness of 0.041 in, length-to-diameter ratios ranging for 2.8 to 12 and [55/-55/(90)3/-55/55] layup were collapsed in a custom pressure testing facility that provided a constant pressure water environment. Buckling was sudden, dynamic, led to failure and fragmentation of the shells; the whole event lasted only a couple of ms. The dynamic collapse of the shells was recorded using high-speed digital imaging and dynamic pressure sensors synchronized with the camera were used to monitor the emanating pressure waves. All shells buckled in mode 2 at pressure levels predicted by models adopted. Collapse led to a localization zone in the central section of the shells, approximately spanning on a 4D length for the longer ones, and shorter for the shorter shells. A single axial crack developed in the collapsing section, which propagated 2 to 4 diameters depending on the length of the specimen. The axial crack was located on the extrados for long shells, and on the intrados for shorter ones. Helical cracks initiated from the tips of the axial crack, propagated outwards, and were responsible for the collapse and fragmentation of the two outer sections. The receding walls of the central localizing zone caused a dynamic drop in pressure that lasted until the inward motion was arrested by contact. This was followed by a sharp, short duration positive pressure pulse associated with an outward expansion wave. The pressure pulse varied to some degree around the circumference with the highest peak occurring opposite the initial crack. The final result of such dynamic events was catastrophic failure and fragmentation of the shell into small shreds. / text

A finite element analysis approach is used to determine the susceptibility to wrinkles for thin sheets with clamped ends when subjected to tensile loading. The model problem chosen to do this analysis is the stretching of a thin sheet with clamped-ends. In the preliminary analysis, a stress analysis of thin sheets is done to study the stresses that develop under these boundary conditions. The analysis shows that there is a stretch-induced compressive stress in the transverse direction to the applied load that causes wrinkles. Then, the parametric study is conducted to determine the effect of aspect ratio and strain on the compressive stress. Based on the results of the parametric study, a critical strain value for each aspect ratio is determined for which the corresponding compressive stress is zero. Further buckling analysis is performed to find the buckling modes of the model problem that shows a limit of aspect ratio below which buckling is not possible under given conditions. Finally, post-buckling analysis shows the nature of wrinkles observed in the model problem for different aspect ratios. / text

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