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“The problem of nonlinear deformation, buckling, and postbuckling behavior of inhomogeneous shells is solved by a combined algorithm that employs the parameter continuation method, a modified Newton–Kantorovich method, and a procedure for automatic correction of algorithm parameters [97]. Each step increments (or decrements) the external load parameter P, which is related to the parameters of the mechanical (Q) and temperature (T) fields. The solution of the nonlinear problem is the relationship between the parameter P and the displacement field U of the FESM [Finite Element Shell Model], which is determined at each step of loading DP. This relationship is usually represented by a load-deflection (P-U) curve at characteristic points of the shell.” [97] N. A. Solovei and O. P. Krivenko, “Influence of heating on the stability of smooth shallow spherical shells with linearly varying thickness,” Opir. Mater. Teor. Sporud, 74, 60–73 (2004)
The image shown here is Fig. 5 from:
V. A. Bazhenov and N. A. Solovei (Kyiv National University of Construction and Architecture, 31 Vozdukhoflotskii Av., Kyiv, Ukraine, 03037), “Nonlinear deformation and buckling of elastic inhomogeneous shells under thermomechanical loads”, International Applied Mechanics, Vol. 45, No. 9, 2009, pp. 923-953,
doi: 10.1007/s10778-010-0236-1
ABSTRACT: The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finite-element scheme. The method is justified numerically. Results of practical importance are obtained in analyzing poorely studied classes of inhomogeneous shells. These results provide an insight into the nonlinear deformation and buckling of shells under various combinations of thermomechanical loads.
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