Abstract
UDC 539.3 A second variant of the boundary perturbation method was developed in the monograph [4] to solve three-dimensional boundary-value problems of the mechanics of deformable bodies bounded by nonorthogonal (in particular, noncircular cylindrical) surfaces (surfaces for which conditions of orthogonality are not satisfied at arbitrary points between the unit normal and the unit coordinate vectors). The method describes nonorthogonal surfaces by linear equations in a small parameter characterizing the amplitude of the deviation of the given surface from circular cylindrical shape. Numerous problems solved by the method and the corresponding numerical results were systematized and analyzed in [2, 4]. Although the assumptions made regarding the linearity of the equation of the interface relative to a small parameter simplified the mathematical calculations, it limited the generality of the approach, the range of problems that can be solved, and their practical value. Some of these deficiencies are corrected in the present study. Here, we generalize the second variant of the boundary-perturbation method to the case when the noncircular cylindrical interfaces of a laminated body are described by nonlinear parametric equations.
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