Abstract
We consider cylindrical rods whose elastic properties smoothly vary along the axis, i.e., the fast change of mechanic characteristics is admitted only in cross directions. In the general case, asymptotically exact estimates for the difference of a solution to the three-dimensional problem of elasticity theory in a narrow cylinder and an approximate solution constructed within the framework of a one-dimensional model of a rod age given. As was shown, under wakened smoothness requirements on the right-hand sides of the problem, the accuracy of approximation becomes lower. Bibliography: 21 titles.
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