Exact solution of sandwich beams

Abstract

Seriously non-uniform warping cross-sections due to shear effects sharply expose the essential difference between solid and sandwich beams. Actually, the deflected configuration and stress distributions in sandwich beams are far beyond the scope that the elementary bending theory is applicable for their description. For analysis of sandwich beams, the most extensively employed classical theories are based on such assumption as the whole cross-section or each individual layer thereof remains plane for bent configuration. As a matter of fact, theories based on such assumptions appear particularly incapable of depicting the mechanical characteristic behavior of sandwich beams, with a weak core in particular. Not relying on any assumptions, the present work tends to have the sandwich beam considered as layered elastic continuum. Close solution thereupon obtained satisfies the governing equations, the boundary conditions, as well as the stress continuity and displacement compatibility requirements on interlayer interfaces. Experimental studies and numerical (finite element analysis) examinations favorably justify the validity of the present solution together with its superb capability of representing the displacement responses and stress distributions in sandwich beams.