Computation of nuclear reactor shells by the factorization method under the conjugate conditions (Q2759405)

This paper deals with application of the factorization method under the conjugate conditions for computation of nuclear reactor shells. The cover of nuclear reactor shell is computed according to the theory of deformation of thick circular plate under the action of inner pressure, temperature and force factors. the walls of shell is replaced by the system of vertical beams and circular rings. Using the partition of vertical beam onto three parts, the authors obtain for the \(i\)-th part of the beam the differential equation \(W^{IV}_{i}+4k_{i}^4W_{i}=q/EI_{i},\;i=1,2,3\), where \(W\) is the deflection function, \(q\) is the stress generated by inner pressure. A general solution to this equation on the \(i\)-th part \((0<x<l_{i})\) is searched in the form \(W_{i}(x)=C_{i1}e^{-k_{i}x}\cos k_{i}x+C_{i2}e^{-k_{i}x}\sin k_{i}x+C_{i3}e^{-k_{i}(l_{i}-x)}\cos k_{i}x+C_{i4}e^{-k_{i}(l_{i}-x)}\sin k_{i}x+q/\alpha_{i}\), where \(\alpha_{i}\) is the coefficient of elastic repulsion of \(i\)-th ring; \(C_{ij}, i=1,2,3, j=1,2,3,4\) are constants. To determine constants \(C_{ij}\) the authors deduce a linear system of the 12-th order and solve this system by factorization method under the conjugate conditions.