NON-UNIFORM SHRINKAGE IN CASE-BONDED VISCO-ELASTIC HOLLOW CYLINDER OF INFINITE LENGTH,
COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
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The effect of non-uniform shrinkage or swelling on stresses and displacements in a thick-walled cylinder of visco-elastic material is discussed. The cylinder is assumed to be of infinite length, reducing the problem to one of plane strain. The cylinder is contained in a rigid case, resulting in zero circumferential and radial displacement components at the outer face, while the inner face is free of tractions. Use is made of the analogy between shrinkage swelling and temperature distribution in the body. While assuming the space distribution to be arbitrary, the time distribution is exponential, with the cooling heating rate as a parameter. The purpose of the analysis is to establish, in first approximation, the intensity of the circumferential and radial stresses in the cylinder and on the interface between cylinder and case for a specific realistic assumption concerning the visco-elastic response and various assumptions concerning the space distribution of shrinkage and several values of the cooling rate.