Solution of the Problem of Linear Viscoelasticity for Multiply Connected Anisotropic Plates
S. A. Kaloerov, A. I. Zanko
Donetsk National University, Donetsk, 83001, Ukraine
Keywords: вязкоупругость, многосвязная плита, комплексные потенциалы теории изгиба плит, метод малого параметра, обобщенный метод наименьших квадратов, viscoelasticity, multiply connected plate, complex potentials of the plate bending theory, small parameter method, generalized least squares method
Abstract
This paper describes the method of solving the problems of linear viscoelasticity for thin plates under the influence of bending moments and transverse forces. The small parameter method was used to reduce the original problem to a sequence of boundary-value problems solved via complex potentials of the bending theory of multiply connected anisotropic plates. The general representations of complex potentials and boundary conditions for their determination are obtained. The method for determining the stress state of the plate at any time with respect to complex approximation potentials is developed by replacing the powers of the small parameter with Rabotnov operators. The problem of a plate with elliptical holes is solved. The numerical calculation results in the case of a plate with one or two holes are given. The changes of bending moments in time until stationary condition is reached and the influence of geometric characteristics of the plate on these variable are studied.
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