The construction of a spatial model for calculating the thermally stressed state of shallow shells on a rigid basis

Abstract

Modern calculations of layered plates and shells in a three-dimensional formulation are based on a technique where the distribution of the desired functions over the thickness of a structure is sought by the method of discrete orthogonalization. In this article, based on the approaches developed by the authors, the thermally stressed state of layered composite shallow shells with a rigidly fixed lower surface is analyzed. The distribution of the desired functions over the thickness of the structure is found based on the exact analytical solution of the system of differential equations. An approach to studying the thermally stressed state of layered composite shells is also considered, and a spatial model for calculating the thermally stressed state of shallow shells on a rigid basis is constructed. Currently, this is a very urgent task when calculating the pavement of bridges. A feature of this approach is the assignment of the desired functions to the outer surfaces of the layers, which allows one to break the layer into sublayers, reducing the approximation error to almost zero. To build a spatial model, a load option is selected with temperature loads (according to the sine law) and boundary conditions (Navier), which lead to the distribution of the desired functions in terms of a plate with trigonometric harmonics of the Fourier series. A polynomial approximation of the desired functions by thickness is involved. Using the model under consideration, an analysis of flat layered composite shells on a rigid basis under the influence of temperature load was carried out. The considered example showed that the proposed model provides sufficient accuracy in the calculations of layered shallow shells when considering each layer within one sublayer. When dividing each layer into 32, 64, 128 sublayers, almost the same result was obtained. The proposed approach can be used as a reference method for testing applied approaches in calculating the stress states of layered shallow composite shells.