Fundamental sequences of functions in the approximation of solutions to exterior problems in the bending of thin micropolar plates

Abstract

In this paper we show how to construct fundamental sequences for approximate solutions to exterior Dirichlet and Neumann-type problems in the bending of micropolar plates. The sequences are based on singular solutions of the governing equilibrium equations. These singular solutions are, however, unbounded at infinity. This leads to difficulties when applying the usual methods for proving linear independence and completeness. By decomposing the sequences into divergent and convergent parts we show that they can be accommodated in a more general framework developed in previous work. This allows us to overcome the difficulties mentioned above. Kupradze's method of generalised Fourier series is then modified and used to construct approximations which converge uniformly to the corresponding exact solutions

Keywords:

• Generalised Fourier series
• bending of micropolar plates
• Cauchy singular integral equations