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Non-axisymmetric buckling of shallow spherical shells. (English. Russian original) Zbl 0737.73050

J. Appl. Math. Mech. 54, No. 3, 375-388 (1990); translation from Prikl. Mat. Mekh. 54, No. 3, 454-468 (1990).
Summary: The buckling of elastic shallow orthotropic spherical shells subjected to a transverse load is investiated on the basis of geometrically nonlinear equilibrium equations in a non-axisymmetric formulation. By using the method of finite differences and a continuation procedure in the parameters in combination with a Newton operator method an algorithm is constructed to determine the state of shell stress and strain in the pre- and post-critical stages.
The upper critical loads (CL) of spherical shells are determined for different external pressure distribution laws taking perturbing factors such as initial harmonic and azimuthal imperfection directions in the shape of the shell middle surface and analogous load deviations from a uniformly distributed load into account. Under the imperfections mentioned, good agreement is obtained with the results for the upper CL found by the theory of buckling and the initial post-critical behaviour [e.g.: the second author, ibid. 47, 662-672 (1983; Zbl 0546.73038)]. Special attention is paid to an investigtion of the non-axisymmetrical buckling of an isotropic spherical shell closed at the apex. It is shown that the presence of small initial imperfections is the reason for a substantial reduction in the upper critical load and, moreover, its value can be determined by the formula for unimodal buckling not at the least bifurcation point but at the one following if the initial damage component proportional to the harmonic natural mode of this second bifurcation point is predominant.

MSC:

74G60 Bifurcation and buckling
74K15 Membranes
74S20 Finite difference methods applied to problems in solid mechanics

Citations:

Zbl 0546.73038
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References:

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