| Abstrakt: |
This article is intended to derive the first-order structural functions method solution to a three-dimensional problem of bending a heterogeneous, linear elastic plate with material properties, depending on the third coordinate. Structural functions method is a technique, which allows computing an approximate solution to the linear elasticity problem, stated for a heterogeneous body with coordinate-dependant material properties (original body), by using a solution to the similar elasticity problem, stated for a homogeneous body with constant material properties (concomitant body). The displacements in the original body are approximated with a weighted sum of concomitant problem solution derivatives, and the weighting coefficients are named structural functions of a corresponding order. We pass through all the steps of the first-order structural functions method for the three-dimensional statement of a rectangular, simply supported at the contour, linear elastic multilayered plate bending problem, and use a classical three-dimensional solution procedure to build the concomitant problem solution. Obtained formulas for structural functions are also expressed in the terms of Young's modulus and Poisson's ratio for orthotropic and isotropic materials. The obtained solution for the original plate allows modelling the zig-zag effect for the in-plane displacements; satisfy the interlaminar continuity conditions. In the numerical tests for plates with low number of layers, the structural functions' approximation shows a nice coincidence with a known three-dimensional solution. [ABSTRACT FROM AUTHOR] |
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