A numerical analysis based on the finite element method is developed to simulate the mechanical response of a typical sixteen-ounce plastic drink cup subjected to a lateral compressive load. The aim of the analysis is to simulate a test in which the cup is supported horizontally in a fixture on a testing machine platen, and a loading nose attached to the actuator is displaced downward into the cup. The numerical model is developed using the software packages MSC.Patran, ABAQUS/CAE, and ABAQUS/Standard. The high impact polystyrene material of the cup is modeled as linear elastic, considering isotropic and orthotropic material behavior. The structural model of the cup is a truncated conical shell including a ring at the open end of the cup and circumferential stiffening ribs. The analysis is based on small strain, large rotation shell kinematics, and the loading apparatus of the test is simulated with a rigid, circular cylinder contacting the cup. Coupons cut from the wall of a cup are subjected to tension to determine the ranges of the meridional and circumferential moduli of elasticity. Rings cut from the open end of the cup were tested in diametrical tension to aid in validating the finite element modeling. Reasonable correlation of the simulation to available cup compression test data is achieved. Parametric studies are conducted for several meridional thickness distributions of the cup wall, and for a range of orthotropic material properties. / Master of Science

Excitation of the low frequency vibrational modes of a submerged vessel can generate significant radiated noise levels. Vibrational modes of a submarine hull are excited from the transmission of fluctuating forces through the shaft and thrust bearings due to the propeller rotating in an unsteady fluid. The focus of this work is to investigate the structural and acoustic responses of a submarine hull under axial excitation. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The displacement normal to the surface of the structure in contact with the fluid medium was calculated by assembling the boundary/continuity matrix. The far field radiated sound pressure was then calculated by means of the Helmholtz integral. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model. The individual and combined effects of the various influencing factors, corresponding to the ring stiffeners, bulkheads, conical end closures and fluid loading, on the structural and acoustic responses are characterised by examining the contribution by the circumferential modes. It is shown that equally spaced internal bulkheads generate a periodic structure thus creating a grouping effect for the higher circumferential modes, but do not have strong influence on the sound radiation. Stiffeners are found to have an important effect on both the dynamic and acoustic responses of the hull. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is also clearly observed. This work shows the importance of the bending modes when evaluating the sound pressure radiated by a submarine under harmonic excitation from the propulsion system.

Excitation of the low frequency vibrational modes of a submerged vessel can generate significant radiated noise levels. Vibrational modes of a submarine hull are excited from the transmission of fluctuating forces through the shaft and thrust bearings due to the propeller rotating in an unsteady fluid. The focus of this work is to investigate the structural and acoustic responses of a submarine hull under axial excitation. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The displacement normal to the surface of the structure in contact with the fluid medium was calculated by assembling the boundary/continuity matrix. The far field radiated sound pressure was then calculated by means of the Helmholtz integral. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model. The individual and combined effects of the various influencing factors, corresponding to the ring stiffeners, bulkheads, conical end closures and fluid loading, on the structural and acoustic responses are characterised by examining the contribution by the circumferential modes. It is shown that equally spaced internal bulkheads generate a periodic structure thus creating a grouping effect for the higher circumferential modes, but do not have strong influence on the sound radiation. Stiffeners are found to have an important effect on both the dynamic and acoustic responses of the hull. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is also clearly observed. This work shows the importance of the bending modes when evaluating the sound pressure radiated by a submarine under harmonic excitation from the propulsion system.

<p> Various analytical methods for studying the behaviour of shallow conical shells on Euler-Winkler elastic foundation are presented. </p> <p> To account for the nature of concrete and the geometric properties of the shallow conical shell, Poisson's ratio and certain radial and circumferential deformations of the middle surface are neglected in deriving the basic differential equation. Analytical methods employed in the solution of this shell problem are the GECKELER and asymptotic types of approximations. </p> <p> The presentations of various methods of analysis are made for a representative case of dimensions and loadings of the conical shell to make them as applicable as possible to the cases of thin conical shell commonly encountered in industry. </p> <p> The shell structure studied is a tank in the form of a rotationally symmetrical cylindrical shell supported by a shallow conical shell foundation. The construction joint between the conical shell and the cylindrical shell is either monolithic or hinged. </p> <p> The analytical results of this water tank supported on Euler-Winkler elastic foundation are compared with the corresponding findings of W. Flügge, who assumed a uniform soil bearing pressure acting on the conical shell structure. </p> The method of analysis which possesses obvious advantages over the other methods studied is selected to examine the effect of different elastic stiffness coefficients of the soil. The validity of simplifying the soil bearing pressure to a uniform distribution by most designers can consequently be studied by comparing it to the bearing pressures of an ideal elastic soil which is postulated to react to its deformation like a bed of independent elastic springs. </p> / Thesis / Master of Engineering (ME)