Application of the finite element method in combination with the contact layer method to determine the stress-strain state of multilayer beams

The purpose of this article is to develop a method for calculating multilayer beams using the finite element method in combination with the contact layer method. The contact layer is an elastic anisotropic medium, consisting of rigid short bars, working only in tension-compression in the vertical direction and shear. The contact layers model the connections through which the layers of multilayer beams interact. To determine the stress-strain state of the beam, it is represented as a set of beam finite elements (FE) of each layer connected by finite elements of contact layers. As beam elements, modified FEs are used, in which horizontal displacements along the upper and lower edges, as well as deflection, act as degrees of freedom in the node. An example of the calculation of a three-layer beam hinged at the ends under the action of a uniformly distributed load is presented. The outer layers of the beam are made of carbon fiber, and the middle layer is made of the syntactic one based on glass spheres. The calculation is performed with and without taking into account the deformations of the transverse shear of the layers. The meshing of the beam along the length into finite elements is assumed to be non-uniform with a thickening in the near-support zone in order to be able to catch the edge effects. The solution is implemented in the MATLAB environment. As a result of the calculation, it was found that there is a range of change in which the stiffness of the contact layers does not have a noticeable effect on the deflections of the structure. For the considered example, a significant difference was revealed in the values of maximum displacements, as well as in the character of the diagrams of bending moments and shear forces in the outer layers when calculating with and without taking into account transverse shear deformations. At the same time, transverse shear deformations do not have a noticeable effect on the stresses in the contact layers.