Finite Element Applications to the Internal Pressure Loadings on Spherical Shells and other Shells of Revolution

FLORES FERNANDO G.; GODOY LUIS A

Finite Element Analysis of Thin Walled Structures

Elsevier Applied Science

Lugar: Barking; Año: 1990; p. 259 - 296

In this chapter the finite element method is employed to study equilibrium and stability configurations in shells of revolution under internal pressure loading. In the first part of this chapter, a specific semi-analytical curved shell element is presented, and its characteristics compared with other existing elements. The present element is based on shell theory and uses Kirchhoff-Love hypothesis to define the fundamental equations. The formulation is capable of handling both axisymmetric and non-axisymmetric loading conditions, while the computed load displacement path may be linear or non-linear (only geometric non-linearities are considered). Bifurcation loads can also be computed from both load-displacement paths. In the second part the element is used to investigate the linear and non-linear behavior of thin spherical shells. In particular, local stresses are studied in relation to geometric imperfections, to changes in thickness, and to intersection with tubes. The final example studied is an ellipsoidal head. In all cases, it is shown that the shell has a non-linear stiffening behavior, and that a linear solution yields an upper bound to the stresses. When instability under internal pressure is a practical problem, it is shown that geometric non-linearity has the effect of increasing the bifurcation loads.