Thesis (Ph. D.)--University of Wisconsin--Madison, 1962. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Bibliography: leaves 61-63.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1955. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Cylindrical shells are used for a variety of engineering applications such as undersea vehicles and aircraft. The models currently used to determine the vibration characteristics of these shells are often approximated by assuming the shell is infinitely long or has shear-diaphragm boundary conditions. These models also ignore complex loading conditions such as plane waves in favor of point forces or free vibration models. This work expands on the capabilities of these models by examining the acoustic response of a finite length cylinder with flat plate endcaps to multiple types of distributed loading conditions. Starting with the Donnell equations of motion for thin cylinders and the classical plate theory equations of motion for the endcaps, spacial domain displacement field solutions for the shell and plates take an assumed form that includes unknown wave propagation coefficients. These solutions are substituted into stress boundary conditions and continuity equations evaluated at the intersections between the shell and plates. An infinite summation is contained within the boundary conditions and continuity equations which is decoupled, truncated, and compiled in matrix form to allow for the propagation coefficients to be found via a convergent sum of vectors. System responses due to a ring loading and multiple cases of plane waves are studied and validated using a finite element analysis of the system. It is shown that the analytical model matches the finite element model well. / Master of Science / Cylindrical shells are used for a variety of engineering applications such as undersea vehicles and aircraft. The mathematical models currently used to determine the motion of the shell use approximate methods that can be inaccurate. Often, these models do not apply to forces such as those involved in sonar signals. This work analyses a new model that examines the vibration of a finite length cylinder with flat plate endcaps to multiple types of forces. Standard theories are used to calculate the vibration of the shell and endcaps where the motion of the shell and plates is assumed to follow a specific pattern. Linear algebra techniques are then used to produce the formulas for the motion of the shell. The vibration of the system is validated using a finite element analysis. It is shown that the mathematical model matches the finite element model well.

This paper presents the layout optimization of passive constrained layer damping (PCLD) treatment for vibration control of cylindrical shells under a broadband force excitation. The equations governing the vibration responses are derived using the energy approach and assumed-mode method. These equations provided relationship between the integrated displacement response over the whole structural volume, i.e. the structural volume displacement (SVD), of a cylindrical shell to structural parameters of base structure and multiple PCLD patches, Genetic algorithms (GAs) based penalty function method is employed to find the optimal layout of rectangular PCLD patches with minimize the maximum displacement response of PCLD-treated cylindrical shells. Optimization solutions of PCLD patches’ locations and shape are obtained under the constraint of total amount of PCLD in terms of percentage added weight to the base structure. Examination of the optimal layouts reveals that the patches tend to increase their coverage in the axial direction and distribute over the whole surface of the cylindrical shell for optimal control of the structural volume displacement. / Singapore-MIT Alliance (SMA)

No / This paper considers both the linear elastic and creep buckling of polymeric pipe linings used for the rehabilitation of gravity pipes, for which external groundwater pressure has been identified as the prime source of loading. Theoretically perfect and imperfect conditions are considered, with the imperfections taken to be in the form of a concentric or eccentric annulus between the rigid host pipe (cylindrical constraint) and polymeric lining. Under these conditions two recently obtained mathematical procedures for the prediction of linearly and non-linearly elastic buckling are compared with the results of complementary laboratory testing. Linear elastic conditions are shown to be well approximated by undertaking short-term (¿30 min) testing under increasing pressure to failure. Controlled imperfections are introduced into the laboratory tests and excellent correlation with the theoretical predictions is obtained. In particular, the dominant geometrical imperfections are shown to be major influences on the obtained buckling pressure. The mathematical models are then adapted to simulate the creep buckling process under long-term constant pressure. The results obtained are again compared with those provided by complementary physical testing, and appropriate conclusions are made.

Solid rocket motors consist of a thin metallic or composite shell filled with a soft rubbery propellant. Such motors are vulnerable and prone to buckling due to sudden external pressures produced by nearby detonation. The stability conditions of rocket motors subjected toaxisymmetric, external pressure loading are examined. The outer cases of motors are considered as isotropic (metallic) or anisotropic (composite), thin and high-strength shells, which are the main structures of interest in the stability analyses. The inner, low-strength elastic cores are modeled as linear and nonlinear elastic foundations. A general, refined, Sanders' nonlinear shell theory, which accounts for geometric nonlinearity in the form of von Karman type of nonlinear strain-displacement relations, is used to model thin-walled, laminated,composite cylindrical shells. The first order shear deformable concept is adopted in the analyses to include the transverse shear flexibility of composites. A winkler-type of linear and nonlinear elastic foundation is applied to model the internal foundations. Pasternak-foundation constants are also chosen tomodify the proposed elastic foundation model for the purpose of shear interactions. A set of displacement-based finite element codes have been formulated to determine critical buckling loads and mode shapes. The effect of initial imperfections on the structural responses are also incorporated in the formulations. A variety of numerical examples are investigated to demonstrate the validity and efficiency of the purposed theory under various boundary condiitions and loading cases. First, linear eigenvalue analysis is used to examine approximate buckling loads and buckling modes as well as symmetric conditions. An iterative solution procedure, either Newton-Raphson or Riks-Wempner method is employed to trace the nonlinear equilibrium paths for the cases of stress, buckling and post-buckling analyses. Both ring and shell-type models are applied for the structural analyses with different internal elastic foundations and initial imperfections. / Ph. D.

No / This paper considers both the linear elastic and creep buckling of polymeric pipe linings used for the rehabilitation of gravity pipes, for which external groundwater pressure has been identified as the prime source of loading. Theoretically perfect and imperfect conditions are considered, with the imperfections taken to be in the form of a concentric or eccentric annulus between the rigid host pipe (cylindrical constraint) and polymeric lining. Under these conditions two recently obtained mathematical procedures for the prediction of linearly and non-linearly elastic buckling are compared with the results of complementary laboratory testing. Linear elastic conditions are shown to be well approximated by undertaking short-term (¿30 min) testing under increasing pressure to failure. Controlled imperfections are introduced into the laboratory tests and excellent correlation with the theoretical predictions is obtained. In particular, the dominant geometrical imperfections are shown to be major influences on the obtained buckling pressure. The mathematical models are then adapted to simulate the creep buckling process under long-term constant pressure. The results obtained are again compared with those provided by complementary physical testing, and appropriate conclusions are made.

Cylindrical shells are widely used in civil engineering. Examples include cooling towers, pipelines, nuclear containment vessels, steel silos and tanks for storage of bulk solids and liquids, and pressure vessels. The loading condition for these shells is quite varied depending on the function of the shell. Axial compression, global bending, external or internal pressure and wind loading are some of the most common loading forms for realistic structures. The failure of these cylindrical shell structures is often controlled by elastic or elastic-plastic buckling failure. Yield failure may occur in thick cylinders in some situations. A cylindrical shell under different loading conditions may display quite different buckling behaviour. The objective of this thesis is to investigate the characteristics of different buckling behaviours of cylindrical shell structures under axial compression, global bending, uniform external pressure and wind pressure. Some challenging practical problems in the design of these shell structures are explored. This thesis is expected to have some far-reaching impacts in defining how to design cylindrical shell structures to give them adequate strength to resist extreme events. Many aspects will be based on the latest Eurocode (EN 1993-1-6, 2007) and Recommendations (ECCS EDR5, 2008). The results show both some strength and some weaknesses in the Eurocode in design of shell structures. New methods are proposed for some practical problems. Some new conclusions and suggestions are derived and are expected to provide some useful knowledge for the improvement of the Eurocode in cylindrical shell design in general.

Civil Engineering thin cylindrical shells such as silos and tanks are normally subjected to axial compression that arises from a stored solid, wind, earthquake, self-weight or roof loads. The walls of these shells are very thin, generally of the order of 6 to 25 mm, and massively less than the radius, which is typically 5 to 30 m. They are thus very thin shell structures, like those of rockets, spacecraft, motor vehicles and aircraft. The commonest failure mode is elastic buckling under axial compression. It has long been known that the buckling strength of a thin cylindrical shell under axial compression is very sensitive to tiny deviations of geometry, reducing the buckling strength to perhaps 10 or 20% of the value for the perfect structure. A normal internal pressure usually accompanies the axial compression, caused by stored granular solids or fluids. At relatively low pressures, the elastic buckling strength under axial compression rises, but an elastic-plastic buckling phenomenon intervenes at higher pressures, causing a dramatic decrease in buckling resistance associated with an elephant’s foot collapse mode. To construct such large shells, the fabrication technique is generally the assembly of many rolled plates or panels, joined by short longitudinal welds and continuous circumferential welds. The process of welding produces a distinctive geometric imperfection form at each weld joint, which in turn is extremely detrimental to the shell axial buckling carrying capacity. The strength may be further reduced by slight misalignments between adjacent panels, or in bolted construction, by vertical and horizontal lap splices. Due to the pattern of loading, both the axial compression and internal pressure increase progressively down the wall. Accordingly, practical construction usually uses a stepped wall, formed from panels of uniform thickness, but with larger thicknesses at lower levels. Since the loading varies smoothly, but each panel has constant thickness, the critical location for buckling lies at the base of a panel. But the greater thickness of the lower panel can usefully enhance the buckling strength of the critical panel above it. This thesis presents an extensive computational study that examines all the above influences, divided into chapters that are outlined here. A full exploration of the effect of the cylinder length on the perfect and imperfect elastic buckling strength is presented in Chapter 3. In Chapter 4, the elastic-plastic buckling resistance of imperfect cylinders is described, including strain hardening. These lead to many capacity curves, for which the key parameters are extracted. The effect of internal pressure on the buckling resistance of imperfect elastic cylinders is explored in Chapter 5. Chapter 6 studies the effect of high pressures that produce elastic-plastic elephant’s foot buckling at circumferential welds in imperfect shells. Next, a step change in plate thickness is studied in Chapter 7 for imperfect butt jointed cylinders with and without the internal pressure. Chapter 8 presents an exploration of the effect of plate misalignments at a circumferential joint, as well as the full misalignment of a circumferential lap joint in bolted construction. These are investigated in both the elastic and elastic-plastic domains. The entire thesis is conceived in the context of EN 1993-1-6 (2007) and the ECCS Recommendations on Shell Buckling (2008). This research has shown significant weaknesses in both the concepts and the detailed rules of these standards. Many conditions are found where either the standard is unnecessarily conservative, or its safety margin may be too low. Thus, some new provisions are proposed for each of the above practical problems. These are expected to provide useful knowledge for the design of such structures against buckling in the future.

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