A variational method of homogeneous solutions for axisymmetric elasticity problems for cylinder

Abstract

A variational method of homogeneous solutions for axisymmetric elasticity problems for semiinfinite and finite cylinders with loaded end faces and free lateral surface has been developed. As examples of application of the proposed approach the problem of bending of the thick disk by concentrated forces applied to its end faces have been considered.

Residual stresses in a finite cylinder. Direct and inverse problems and their solving using the variational method of homogeneous solutions

“…Here µ = E/2(1 + ν) is the shear modulus. The solution of the problem (19), (14), obtained with the use of variational method of homogeneous solutions, is presented in the paper [8]. For the considered here case of symmetry, with respect to the plan z = 0, strain-stressed state, the solution of equation (19) can be presented in the form:…”

“…As B k are complex constants, it makes possible to satisfy both conditions (14), prescribed on the bases of the cylinder. We use for that the variational approach [8,11].…”

“…The convergence of the solution, obtaining with the use of reduction method, can be evaluated by investigation of how the value of the functional is changing with increasing of the number N . Results of such studies, conducted earlier, are presented in the paper [8,11].…”

“…The equations (8) and the boundary conditions (9) form a mathematical model for axisymmetric residual stresses in the cylinder in the case, when eigenstrain components are depending only on a radial coordinate.…”

“…The components of eigenstrain tensor are considered as given functions in this problem. It is solved with the use of the variational method of homogeneous solutions [8,9]. On this basis features of residual stresses are studied for some distributions of eigenstrain tensor components prescribed in the body volume.…”