Deformation of laminated anisotropic bars in the three-dimensional statement 1. Transverse-longitudinal bending and edge compatibility condition

By using the methods of asymptotic splitting, the 3D problem on the transverse-longitudinal bending of elastic anisotropic laminated bars under the action of longitudinal and transverse loads is split into a number of plane boundary-value problems, whose solution allows one to construct asymptotic approximations for all components of the displacement vector and the strain tensor at each point in the bars. A system of ordinary differential equations of transverse-longitudinal bending is obtained for laminated bars with arbitrary anisotropy of its layers. A condition for the edge compatibility of materials in laminated orthotropic bars is deduced. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 379-410, May-June, 2009.