Variational method of homogeneous solutions in axisymmetric elasticity problem for piecewise homogeneous cylinder

Abstract

Variational method of homogeneous solutions is implemented to axisymmetric elasticity problems
for piecewise homogeneous elastic cylinder with a free lateral surface. The strain-stressed state is
caused by jumps of stress and displacement components prescribed on the interfacial surface
between two homogeneous cylinders. The method is based on representation of the Love strain
function, which satisfy biharmonic equation, as series decomposition by complete system of
functions being eigen-functions of elasticity problem for semi-infinite homogeneous cylinder with
traction-free lateral surface. The implementation reduces the problem to the infinite system of
algebraic equations, which is solved by reduction. Obtained solution is used to study stress
concentration in vicinity of joint of two dissimilar materials.