Exact solution of a thick beam on Pasternak subsoil in finite element calculations

摘要

Advanced numerical analysis of structures forces the massive implementation of numerical algorithms, relying on certain convergence of sequences of discrete finite element and similar approximations in spaces of integrable functions, conceding non-physical discontinuities and imperfectness to all numerical results. This is demonstrated on a model example of a thick elastic beam on the 2-parametric Pasternak subsoil. A potential remedy, discussed in this paper, comes from the implementation of available knowledge of analytical solutions in standard variational formulations. The resulting sparse system of linear algebraic equations can be derived without any numerical differentiation; the numerical quadrature is limited to some integrals of explicitly known (MAPLE-generated) functions. Potential generalizations, including selected nonlinear problems, are sketched.