A method of analytical decomposition in analyses of elastic structures of complex geometry
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hdl:2117/333987
Tipus de documentText en actes de congrés
Data publicació2015
EditorCIMNE
Condicions d'accésAccés obert
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Abstract
The paper addresses the new numerical-analytical method for analyzing two-dimensional linearly elastic heterogeneous structures composed of a number of contiguous rectangles. For each rectangle we can build a common solution in a form of series with indeterminate coefficients. These coefficients are evaluated meeting boundary conditions of the whole structure and conjugation conditions of the contiguous areas. The analytical method of superposition was used to build a general solution for the orthotropic/isotropic rectangle with arbitrary boundary conditions on its edges. This method was used in [1,2] to evaluate the stress fields in the two-dimensional elastic isotropic rectangle under symmetric loads on its opposite sides. The paper [3] reviewed the progress in the superposition method for the solution of boundary-value problems.In this paper in accordance with the superposition method the general solutions for the orthotropic and isotropic rectangles are composed of two solutions obtained by the method of initial functions [4,5] in the form of trigonometric series with undetermined coefficients. The process of satisfying the boundary conditions leads to an infinite system of linear algebraic equations to determine the unknown coefficients in the solution. A simple reduction to a finite system is used to obtain a solution. If a structure may be presented by a number of contiguous rectangles with finite dimensions then we can use general solutions constructed for each of the rectangles and get again an infinite linear algebraic system to determine unknown coefficients in all general solutions [6]. We name this approach a “method of analytical decomposition”. It can be used to analyze as homogeneous as heterogeneous structures. An application of this method is demonstrated on analyzing the stress and strain state of a rectangle (x [0,h], y [0,a]) loaded on the side x=0 and clamped on two opposite sides (y=0,a) with a number of cracks parallel to the axe Ox in in the neighborhood of the side x=h.
CitacióMatrosov, A.V. A method of analytical decomposition in analyses of elastic structures of complex geometry. A: ADMOS 2015. CIMNE, 2015, p. 72.
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Admos2015-51-A ... alytical Decomposition.pdf | 159,8Kb | Visualitza/Obre |