LIT - Refined Beam Models Based on the Boley Method - RBMBM

In this proposal we want to enhance an approximate solution procedure for anisotropic and for functionally-graded rectangular strips, where we will also take into account thermoelastic and piezoelectric relations. The iterative solution method is based on a procedure dating back to Prof. Bruno A. Boley, who passed away beginning of this year. The goal of the present project is develop more advanced beam solutions, which consider e.g. the thickness-to-length ratio, the elasticity constants, and the distribution of the external load as an important parameter. The practical importance of these higher order analytical solutions is the basis for the development of advanced control algorithms in the field of displacement tracking (shape control) and stress tracking (stress control). The obtained beam solutions can be considered as more accurate than the elementary Bernoulli-Euler beam solution. We only focus for solution in the linear regime (no geometric nonlinearity). Finally, we treat the end-stress problem for thermoelastic and piezoelectric materials. For the latter material we extend St. Venant’s principle to these materials, e.g. we investigate the difference of a perfectly non-electroded edge (when the electric displacement component strictly vanishes locally) to a distribution of the electric displacement vector, which vanishes in average only.