Large Displacement Analysis of Internally Pressurized Multi-Segmented Spherical Shells with Lagrange’s Multiplier Technique
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Abstract
This paper presents a large displacement analysis of internally pressurized multi-segmented spherical shells with Lagrange’s multiplier technique. Multi-segmented spherical shells are modeled using differential geometry to compute the first and second surface fundamental forms. The energy functional of multi-segmented spherical shells can be derived from the variational formulation, and it is written in the appropriate forms for nonlinear analysis. The numerical results in terms of large displacement of the multi-segmented spherical shells can be obtained by nonlinear finite element method via the fifth-order polynomial shape function described in spherical polar coordinates, and are solved by the iterative procedure. Since the multi-segmented spherical shells have two different radii of curvatures, the Lagrange’s multiplier technique is required in the present formulation to handle the discontinuity effect. The numerical results indicate that the deformed configuration of the present formulation is accurate when compared to those from the commercial finite element software. The effects of the internal pressure, radius ratio, support angle, and thickness on the large displacement responses of the multi-segmented spherical shells are presented in this paper. Finally, the results indicate that all displacement responses of the internally pressurized multi-segmented spherical shells change rapidly near the shell edge junctions. The analytical models obtained in this study can be applied to other shell structures with complex patterns. Additionally the most efficient structure's surface-area-to-volume ratio can be defined.
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