Computing orthotropic constructions using the variation method based on three-dimensional functions with final carriers

At the moment the finite element method (FEM) is often used to compute complex orthotropic thin-walled constructions including thin-walled orthotropic shells. As a rule, one of two approaches is used to make computations using this method. In the first approach the simplifying hypothesis (for example Tymoshenko's hypothesis) is used in which the distribution of stress along the thickness of a thin-walled construction is neglected which reduces the dimension of a task. The second approach uses the ratio of the three-dimensional theory of elasticity without the use of the simplifying hypotheses. In this presented method which is very similar to the FEM, the ratio of the three-dimensional elasticity theory without the simplifying hypotheses is also used for the computations. The paper presents the variation method aiming to determine the stress-strain state of three-dimensional elastic constructions based on the use of the approximating functions with final carriers having an arbitrary degree of approximation [1]. The three-dimensional approximating functions mentioned before are used to compute the orthotropic constructions in this paper. The same approximating functions are used in the papers [2, 3] for the computation of shells in which the resolving equations are obtained on the basis of the simplifying hypothesis. In a general view, the method is based on the use of the curvilinear system of coordinates that does it quite universal. It is shown that the same approximations can be used to compute the three-dimensional autotrophic constructions and orthotropic shells. It is noted that the computation can be efficiently made not only by thickening the lattice but by increasing the order of the approximating functions. The reliability of the suggested method is confirmed by the presented numerical results which fit well with the known solutions.