Mechanics |
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1998, No. 2
V.E. Naumov, T.B. Lavrova, Yu.N. Radayev, L.V. Stepanova
TO THE MEMORY OF G.I. BYKOVTSEV
Y.N. Radayev
TENSOR MEASURES AND HARMONIC ANALYSIS OF THREE-DIMENSIONAL DAMAGE STATE
The paper is concerned with the algorithm of the derivation of damage tensors and local averaged measures of the three-dimensional anisotropic damage from the classical Finger strain measure. The algorithm affords the damage tensor of any even rank can be obtained.
Emphasis is given to the exact deàønitions of the high rank tensor measures of the damage and the mechanical interpretation of their eigenelements. The proposed algorithm is illustrated by the derivation of the second, fourth, sixth and eighth order damage tensor. For every case the typical profiles of the directional damage distributions, which show the increasing accuracy in the description of the anisotropic damage, are given.
Averaged local damage characteristics are defined and then determined in terms of the damage tensor eigenvalues.
A harmonic analysis of the three dimensional directional damage distribution is discussed. By using the harmonic analysis technique, the sequence of damage tensors is shown can be determined as a result of the averaging over the sphere of the unit directions. The harmonic developments afford the damage tensor and its spectrum to be directly computed from the experimental histograms.
Y.E. Senitskii
This paper in the limits of corrected shell theory taking into account shear deformations and inertia of cross-section turning an exact solution of nonaxialsymmetric dynamic problem for a non-homogeneous thickness shallow spherical shell is shown. Most general cases of elastic fixing on the countor and arbitrary non-stationary loading are discussed. The solution is obtained by means of the method of finite biorthogonal transform.
N.N. Stolyarov, N.I. Dedov, A.N. Simakov
OPTIMISATION OF CYLINDER SHELLS UNDER THERMOFORCE LOADING
It had got a differential equation, describing the deforming of the strengthing cylinder shell and equations for the radial displacement and the angle turn of the cross-area of the ring under elastic-plastic thermoforce loading. It had offered equations of joint deformation for the multybinding thin shell construction in joints of shells between themselves and with the ring. It had worked out algorithms and programmes of calculation of strain-stress state of cylinder shell with the changing cross-area and the optimisation its geometrical parameters.