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Crustal motions in Alaska are computed by calculating the finite element solution for an elastic spherical shell problem. Very long baseline interferometry and geologic data are used and seem to be in rough agreement.
Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.
Solutions for the axially symmetric motion of an elastic spherical sandwich shell have been obtained from a theory of shells which includes the effects of transverse shear deformation and rotary inertia. Frequency equations and mode shapes are derived for the full vibrations of a closed spherical shell.
Elastic buckling equations for calculating plastic buckling of plates and shells under biaxial loading
Approximate solution for elastic equilibrium of hinge-supported shallow spherical shell
Matrix displacement method for nonlinear elastic analysis of shells of revolution under symmetrical and asymmetrical loadings
Computer programs for elastic analysis of shells of revolution under arbitrary loading with asymmetrical stiffness properties
Matrix displacement method for nonlinear elastic analysis of shells of revolution under symmetrical and asymmetrical loadings
Elastic buckling load of cylindrical shells with dimple imperfections under external pressure, applying perturbation expansion to Karman-Donnell equations
Effect of curvature and elastic-plastic material behavior of cylindrical thin shell under critical load
Plane wave impulse approximation for deriving momentum distribution for nucleon in atomic nucleus
Finite difference method stability analysis of deformed eccentrically stiffened shells of revolution, accounting for finite prebuckling rotations
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The equation for the equilibrium of cylindrical shells introduced by Donnell in NACA Technical Report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. It is shown that by this method solutions may be obtained very easily and the results in each case may be expressed in terms of two nondimensional parameters, one dependent on the critical stress and the other essentially determined by the geometry of the cylinder. The influence of boundary conditions related to edge displacements in the shell median surface is discussed. The accuracy of the solutions found is established by comparing them with previous theoretical solutions and with test results. The solutions to a number of problems concerned with the buckling of cylinders with simply supported edges on the basis of a unified viewpoint are presented in a convenient form for practical use. (author)
This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. In part I, the equation for the equilibrium of cylindrical shells introduced by Donnell in NACA report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The question of implicit boundary conditions is also considered.
Effect of face sheet flexural stiffness on buckling of elastic curved plates and cylindrical shells of sandwich construction in axial compression
Elastic buckling loads of shallow spherical shells supported by edge rings including nonlinear prebuckling effects
A theoretical investigation of the factors controlling the stress rupture life of the National Aeronautics and Space Agency's (NASA) composite overwrapped pressure vessels (COPVs) continues. Kevlar(TradeMark) fiber overwrapped tanks are of particular concern due to their long usage and the poorly understood stress rupture process in Kevlar(TradeMark) filaments. Existing long term data show that the rupture process is a function of stress, temperature and time. However, due to the presence of a load sharing liner, the manufacturing induced residual stresses and the complex mechanical response, the state of actual fiber stress in flight hardware and test articles is not clearly known. This paper is a companion to the experimental investigation reported in [1] and develops a theoretical framework necessary to design full-scale pathfinder experiments and accurately interpret the experimentally observed deformation and failure mechanisms leading up to static burst in COPVs. The fundamental mechanical response of COPVs is described using linear elasticity and thin shell theory and discussed in comparison to existing experimental observations. These comparisons reveal discrepancies between physical data and the current analytical results and suggest that the vessel's residual stress state and the spatial stress distribution as a function of pressure may be completely different from predictions based upon existing linear elastic analyses. The 3D elasticity of transversely isotropic spherical shells demonstrates that an overly compliant transverse stiffness relative to membrane stiffness can account for some of this by shifting a thin shell problem well into the realm of thick shell response. The use of calibration procedures are demonstrated as calibrated thin shell model results and finite element results are shown to be in good agreement with the experimental results. The successes reported here have lead to continuing work with full scale testing of larger NASA COPV hardware.