NUMERICAL SIMULATION OF THE BENDING OF A LAYERED BEAM WITH PRESTRESSED LAYER UNDER FINITE STRAINS USING THE SPECTRAL ELEMENT METHOD

The implementation of the spectral element method for the problems of nonlinear elasticity under finite strains is developed. The analysis is performed for structures made by junction of preliminarily strained parts. The bending of a layered beam with a prestressed layer is analyzed as a particular case. It is assumed that the beam consists of weakly compressible nonlinear-elastic material. The theory of superimposed finite strains is used for the problem statement. The discretization is performed using the Galerkin method. The proposed approach permits one to vary the order of spectral elements without the mesh refinement. The results of analysis are given. The comparison with a known analytical solution is performed. It is obtained that the results of spectral element analysis are close to the analytical solution. Substantial nonlinear effects are determined. The incomplete junction of layers is analyzed.