Three-dimensional bending stress-strain state of rectangular variable-thickness orthotropic plates (Q1921727)

We consider a three-dimensional boundary value problem of the bending of a variable-thickness orthotropic plate, with nonplanar faces perpendicular to the load, which admits representation by a double trigonometric series. The method of perturbation of the shape of the boundary for surfaces close to the coordinate planes is used to solve the problem. On the basis of the solution built, we examine the laws governing the stress-strain state of orthotropic plates with surfaces that periodically curve in one direction as they are bent by localized loads, depending on the amplitude and frequency of the undulation of the curvatures and the degree of load localization.