V. A. Maksimyuk

Numerical stress-strain analysis of shells including the nonlinear and shear properties of composites

A presentation is made of the numerical results obtained in a stress–strain analysis of thin and nonthin orthotropic shells with due regard for the physical nonlinearity and small and nonsmall shear stiffness of composites. A spherical shell with a circular hole is used as an example to analyze how the above-mentioned factors affect the distribution of stresses and strains depending on the shell thickness for adopted deformation models (the Kirchhoff–Love and Timoshenko hypotheses). Generalized conclusions are drawn from which it is possible to decide which of the composite properties and shell models should be given more priority.

Solution of physically nonlinear problems of the theory of orthotropic shells using mixed functionals

Variants of the theory of nonlinearly elastic orthotropic shells are outlined depending on the relations between the parameters of their composite materials. The corresponding mixed linearized functionals are constructed. A system of resolvent equations that is adjusted to a specific variant of the theory with the help of special matrices is derived. The results of a strain analysis of a cylindrical shell with an opening for four variants of the theory are compared with experimental data

Numerical Nonlinear Elastic Analysis of Orthotropic Spherical Shells with an Elliptic Cutout

Study is made of how the nonlinear properties of orthotropic composites and the ellipticity of an opening affect the stress–strain state of thin spherical shells subjected to internal pressure. An analysis of numerical results reveals compression on the inside surface of the shell near the broad of the elliptical opening. It is pointed out that as the ellipticity increases, the deformation process near the opening transforms from uniform tension and bending, typical of a shell with a circular opening, to dominated tension near the narrow of the opening and to dominated bending near the broad.

Study of the nonlinearly elastic state of an orthotropic cylindrical shell with a hole, using mixed functionals

An analogy is established between some terms of the functionals under consideration and the formulas of the theory of random processes. On this basis, the efficiency of mixed functionals is attributed to a deeper minimum they help to reach by taking the energy of so-called false strains into consideration. We perform a numerical stress—strain analysis of an organoplastic cylindrical shell with a side circular hole and study how the orthotropy and nonlinear properties of the composite affect the stress distribution near the hole. The case is discovered where the orientation of the composite about the cylindrical shell changes so that a larger nonlinear effect corresponds to a smaller initial stress