By Difillippo, F.C.; USDOE Office of Fissile Materials Disposition (MD) (US); Oak Ridge National Laboratory.; United States. Dept. of Energy. Office of Scientific and Technical Information
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Extra resources for Analysis of Rod Removal Transient Experiments in VVER Reactors at Zero Power
And ~ are assumed to be zero. 'Oa "f. p = e3 a = 0 -VG"f. "f. 5 can be applied to the above expression. The following relationship defining the stress-strain properties of an isotropic material may be developed. Ga p = ~[ea + _V_e"f. Sa] (l+v) P (l-v)"f. 1 Shell Geometry A shell structure may be defined as a body consisting of an inner surface, called the middle surface, and two outer surfaces which are parallel to each other. The normal distances from the middle to the outer surfaces are assumed to be the same although they need not be constant.
10) The factors dx i and dxj cannot simply be cancelled on both sides since these expressions represent the sums of products containing the factors 'Yll , 'Y12, ... etc. 10 holds for the components of any line element vector ds. l. l. + u I. u I. 11) This process may then be repeated for i, j = 2, 3. 11 is valid for all iJ. The strain - displacement equation dermed above is nonlinear as a result of the quadratic term ukl. u I.. It is based solely on the assumption that the body 1 kJ undergoing deformation is continuous.
34 define the Christoffel symbols of the frrst and second kind respectively. 32 shows that the Christoffel symbols are symmetric with respect to the fIrst two subscripts. r"I)k = r jik ~. 38) = ~. 39) )1 In detennining the tensorial quantities associated with a coordinate system it is usually possible to obtain explicit expressions for the covariant components of the metric tensor. 41 yields v,. ) == i V,. ) g. 32 to form 20 k . (vi,. ) g. J 1 V,. J viI. Defining J J = (vi,. 44) The quantity viI.