Spectral Methods Application in Problems of the Thin-walled Structures Deformation

The spectral method (p-FEM) is used to solve the problem of a thin-walled structure deformation, such as a stiffened panel. The problem of the continuous conjugation of the membrane function from H^1 and the deflection function from H^2 was solved by modifying the “boundary” functions. Basis systems were constructed that satisfy not only the essential but also the natural boundary conditions, which made it possible to increase the rate of convergence of the approximate solution. The veracity of the results is confirmed by comparing the obtained spectral solution with the solution obtained by the h-FEM. It has been shown that the exponential rate of convergence characteristic of spectral methods is preserved if the Gibbs phenomenon is avoided. The constructed basis systems can be effectively used for solving various problems of mechanics.