Exact Analytical Solution of the Problem of Elastic Bending of a Multilayer Beam with a Normal Trapezoidal Load

An exact analytical solution to the problem of plane transverse bending of a section of a narrow multilayer beam under the action of a normal load on the longitudinal faces, distributed according to the law of the trapezoid, is presented. The solution is constructed using the principle of superposition on the basis of the authors’ general solutions to the problems of bending multilayer consoles under the action of loads at the free end, uniformly and linearly distributed load on longitudinal faces. On its basis, separate interchanges for multilayer beams with different methods of fixing the ends were obtained: hinged, rigid and combined. The obtained relations make it possible to determine the stress-strain state of multilayer beams with an arbitrary number of homogeneous (orthotropic, isotropic) and functional-gradient layers, taking into account transverse shear and compression deformations.