A geometric buckling expression for regular polygons: II. Analyses based on the multiple reciprocity boundary element method

Journal Article · Wed Sep 01 00:00:00 EDT 1993 · Nuclear Technology; (United States)

OSTI ID:6109327

Itagaki, Masafumi; Miyoshi, Yoshinori; Hirose, Hideyuki ^[1]

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1. Japan Atomic Energy Research Inst., Ibaraki (Japan)

A procedure is presented for the determination of geometric buckling for regular polygons. A new computation technique, the multiple reciprocity boundary element method (MRBEM), has been applied to solve the one-group neutron diffusion equation. The main difficulty in applying the ordinary boundary element method (BEM) to neutron diffusion problems has been the need to compute a domain integral, resulting from the fission source. The MRBEM has been developed for transforming this type of domain integral into an equivalent boundary integral. The basic idea of the MRBEM is to apply repeatedly the reciprocity theorem (Green's second formula) using a sequence of higher order fundamental solutions. The MRBEM requires discretization of the boundary only rather than of the domain. This advantage is useful for extensive survey analyses of buckling for complex geometries. The results of survey analyses have indicated that the general form of geometric buckling is B[sub g][sup 2] = (a[sub n]/R[sub c])[sup 2], where R[sub c] represents the radius of the circumscribed circle of the regular polygon under consideration. The geometric constant A[sub n] depends on the type of regular polygon and takes the value of [pi] for a square and 2.405 for a circle, an extreme case that has an infinite number of sides. Values of a[sub n] for a triangle, pentagon, hexagon, and octagon have been calculated as 4.190, 2.281, 2.675, and 2.547, respectively.

• OSTI ID: 6109327
• Journal Information: Nuclear Technology; (United States), Journal Name: Nuclear Technology; (United States) Vol. 103:3; ISSN 0029-5450; ISSN NUTYBB
• Country of Publication: United States
• Language: English

Related Subjects

663610* -- Neutron Physics-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUNDARY CONDITIONS
BOUNDARY ELEMENT METHOD
BUCKLING
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
FISSILE MATERIALS
FISSIONABLE MATERIALS
GEOMETRIC BUCKLING
INTEGRALS
MATERIALS
NEUTRON DIFFUSION EQUATION
NEUTRON TRANSPORT THEORY
NUMERICAL SOLUTION
SHAPE
TRANSPORT THEORY