A State-Space-Based Stress Analysis of a Multilayered Spherical Shell With Spherical Isotropy

This paper presents an exact static stress analysis of a multilayered elastic spherical shell(hollow sphere) completely based on three-dimensional elasticity for spherical isotropy.Two independent state equations are derived after introducing three displacement func-tions and two stress functions. In particular, a variable substitution technique is used toderive the state equations with constant coefficients. Matrix theory is then employed toobtain the relationships between the state variables at the upper and lower surfaces ofeach lamina. By virtue of the continuity conditions between two adjacent layers, a second-order linear algebraic equation and a fourth-order one about the boundary variables atthe inner and outer surfaces of a multilayered spherical shell are obtained. Numericalexamples are presented to show the effectiveness of the present method.@DOI: 10.1115/1.1343913#

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