Refinement of the asymptotic expansions when solving the spatial problem of the bending and twisting of composite bars

A linear elastic problem of the static deformation of laminated composite bars of constant cross- section is formulated in dimensionless form in three dimensions without taking account of thermal effects and mass loads. An asymptotic representation of the solution of the problem, that is more complete than the previous representation and enables the spatial stress-strain state of composite bars to be determined beyond the limits of boundary layer zones, is constructed within the framework of the method of rigidity functions proposed by Gorynin and Nemirovskii. The relative thickness of the bar is used as a small geometric parameter. The two-dimensional and one-dimensional boundary value problems arising after decomposing the initial three-dimensional equations for the bending and twisting of composite bars are analysed. Analytical solutions are obtained for several two-dimensional boundary value problems determining the characteristic displacement functions when Poissons ratios of all the layers are identical. Certain effective rigidities of a composite bar under different forms of loading and deformation are calculated for this case in explicit form.