O. I. Levchuk

On solution of three-dimensional physically nonlinear problems for symmetrically loaded elastic cylinders

Three-dimensional physically nonlinear boundary-value problems for elastic thick-walled circular cylinders are considered. Solutions are found in the form of series in powers of a specially selected small dimensionless physical parameter. The stressed state of the cylinder is investigated, which is affected by a high nonuniform external pressure. The effects of the physical nonlinearity of the material, the intensity of the external forces, and the geometrical characteristics of the cylinder on its elastic equilibrium are revealed.

The stress state of a laminated nonlinearly elastic thick-walled spherical shell

This paper deals with spatial axisymmetric boundary-value problems of the physically nonlinear theory of elasticity for piecewise-homogeneous spherical bodies. The passage to dimensionless characteristics of the stress-strain state allows us to extract a physical dimensionless small parameter in the nonlinear state equations. The solution of nonlinear equilibrium equations and boundary-value problems is searched for in the form of series in positive degrees of the small parameter. This approach allows reducing the stated physically nonlinear boundary-value problem to a sequence of corresponding linear nonhomogeneous problems. A specific analytical solution and numerical results are obtained for a two-layer nonlinearly elastic spherical shell under bilateral pressure.