Experimental Investigation of the Stress Concentration in Axially Compressed Thick Cylindrical Shells with Rectangular Holes

The stress concentration in cylindrical shells of various thicknesses is studied experimentally. The shells are made of epoxy resin, have a hole, and are subjected to axial compression. The shell thickness and the opening angle are shown to affect the stresses near the corners of the hole. The experimental and theoretical values of the stress concentration factor are compared for a thin shell     

Stress Concentration in an Axially Compressed Cylindrical Shell of Medium Thickness with an Elliptic Opening

Stress concentrations at the periphery of elliptic and circular openings are determined experimentally by the photoelastic method for three compressed cylindrical shells of medium thickness made of epoxy resin. The experimental values are compared with numerical values obtained by the theory of thin shells     

Convergence of solutions for noncanonical bodies found by the boundary-shape perturbation method

The exact solution of the problem of the torsion of a solid cylindrical shaft with an ellipsoidal cavity is expanded into a series in powers of an eccentricity parameter. At the points of the cavity where the stress concentration is maximum (minimum), the expansion coefficients for the exact and approximate solutions coincide. The approximate solution is obtained by the first version of the boundary-shape perturbation method, which is used to solve three-dimensional problems of elasticity for bodies of revolution with nearly canonical shape. Successive approximations as an iteration process are shown to converge to the exact solutions     

Numerical solution of some three-dimensional problems of elasticity theory by Vekua's method

We consider the solution of the problem of elastic equilibrium of a three-dimensional orthotropic plate in the absence of displacements on the end surfaces under the action of forces applied to the lateral surfaces. The solution of the original problem by Vekua's method is reduced to the solution of a recursive sequence of two-dimensional problems. A numerical solution of these problems is obtained by computer using the finite-difference method. The effect of the number of Legendre polynomials on the accuracy with which the boundary conditions are satisfied is investigated.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 77–84, 1986.     

Determination of the stressed-strained state of nonthin transversally isotropic spherical shells with elastically stiffened curvilinear holes

An approximate analytical method has been developed for determining the stressed-strained state of nonthin transversally isotropic shallow spherical shells with noncircular elastic inclusions or stiffened holes, under both ideal and nonideal contact at the interface. The method is based on two tried and tested analytical methods—the method of Fourier expansion of the required functions using Legendre polynomials and the second version of the perturbation method for the boundary shape. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 18–28, August, 1999.