Boundary conditions for elastic beam bending

Abstract

For beam bending problem, the reciprocal theorem and P–N solution are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. Through generalizing the method proposed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. When stress and mixed conditions are imposed on the beam edge, these decaying state conditions are derived explicitly, and they are used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of beam theories. More importantly, the appropriate boundary conditions with two different sets of mixed edge-data are obtained for the first time. To cite this article: Y. Gao et al., C. R. Mecanique 335 (2007).