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Alternative lower bounds analysis of elastic thin shells of revolution

Itaru Mutoh (Department of Architecture and Civil Engineering, Gifu National College of Technology, Gifu, Japan)
Shiro Kato (Department of Architecture and Civil Engineering, Toyohashi University of Technology, Tempaku Toyohashi, Japan)
Y. Chiba (Department of Architecture, Hosei University, Koganei, Tokyo, Japan)

Engineering Computations

ISSN: 0264-4401

Article publication date: 1 March 1996


Presents an alternative lower bound to the elastic buckling collapse of thin shells of revolution, in comparison with results from geometrically non‐linear elastic analysis. The numerical finite element method is based on axisymmetric rotational shell elements whose strain‐displacement relations are described by Koiter’s small finite deflection theory, with displacements expanded circumferentially using a Fourier series. First, compares the reduced stiffness linear analysis, based on the buckling equation without incremental linear in‐plane energy components corresponding to the lowest eigenmode (for a particular cylindrical shell under external pressure), with the results obtained by Batista and Croll. Second, the non‐linear astatic (quasi‐static) elastic analysis to clamped spherical caps under uniform external pressure is carried out in order to compare the results from a reduced stiffness analysis from viewpoints of not only buckling loads, but also total potential energy. Argues that the astatic buckling loads may relate to reductions due to a specific imperfection effect on elastic buckling collapses.



Mutoh, I., Kato, S. and Chiba, Y. (1996), "Alternative lower bounds analysis of elastic thin shells of revolution", Engineering Computations, Vol. 13 No. 2/3/4, pp. 41-75.




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