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 functions and two stress functions. In particular, a variable substitution technique is used to derive the state equations with constant coefficients. Matrix theory is then employed to obtain the relationships between the state variables at the upper and lower surfaces of each 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 at the inner and outer surfaces of a multilayered spherical shell are obtained. Numerical examples are presented to show the effectiveness of the present method.
A State-Space-Based Stress Analysis of a Multilayered Spherical Shell With Spherical Isotropy
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, August 26, 1999; final revision, June 7, 2000. Associate Technical Editor: R. C. Benson. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Chen, W. Q., and Ding, H. J. (June 7, 2000). "A State-Space-Based Stress Analysis of a Multilayered Spherical Shell With Spherical Isotropy ." ASME. J. Appl. Mech. January 2001; 68(1): 109–114. https://doi.org/10.1115/1.1343913
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