SummaryA transient contact problem with frictional heating for two sliding halfplanes is considered. One of the half-planes is slightly rounded to give a hertzian initial pressure distribution; the other is a rigid non-conductor. It is shown that if the ratio of initial width of contact to the width in the steady state is less than some critical value, the contact area shrinks smoothly until the steady state is reached. Otherwise the pressure dis~ibution develops a wavy perturbation and eventually bifurcates. Results are compared with previous approximate solutions.

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We study the influence of the eccentricity of the load and the ratio R/t on the stress state of the cylinder using the theory of thin shells in bending. The elastic displacements are presented in the form of a Fourier expansion, the coefficients of which are found by the variational formulation of the problem combined with the penalty approach for a numerical implementation of contact conditions. Results are applied to certain problems of buckling of a circular bar and compared with previous approximate solutions.

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