Axisymmetric stresses and displacement in two finite circular cylinders in contact



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A boundary value problem of two elastic bodies in contact is considered. The bodies are finite circular cylinders of different dimensions and material constants and are isotropic and homogeneous. They are forced into contact across the plane faces such that the resulting stresses and displacements are axisymmetric. The solution utilizes Love's stress function to generate a family of biorthogonal eigenfunctions for each cylinder. The interrelated Fourier coefficients are expressed implicitly by an infinite system of linear algebraic equations. By truncation, an explicit solution of the Fourier coefficients is obtained. Two example problems are solved: first, the two cylinders are placed in frictionless contact; second, the two cylinders are placed in bonded contact. In each problem, the other face of each cylinder undergoes a constant displacement with zero shear tractions. Selected numerical results are presented in graphical form.