Seismic Stress Fields for Nuclear Elbows Using Toroidal Elasticity Theory,
LANG-RESEARCH WEST SANTA MONICA CA
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Toroidal elasticity, first introduced at London, England 1980 is a new tool of stress analysis. It merges a toroidal geometry with the fully three dimensional theory fo elasticity. For isotropic materials, it includes both stress and strain compatibility relations in order to ensure that the deformations are properly determined and topologically correct. Since the theory is complete, all three components of displacement, all six components of strain, and all six components of stress may be determined. The compatibility equations, though rigorously correct, are lengthy. To apply the theory to a large number of boundary value problems, the method of successive approximation has been adopted. All equations are expanded in powers of 1R where R is the toroidal radius. This leads to a set of working equations appropriate for the solution of problems. In the present paper the methods of toroidal elasticity are extended to the problem of determining the stress fields in a hollow circular elbow or pipe bend under the action of seismic accelerations. The seismic accelerations are represented by equivalent body forces X, Y, Z acting in arbitrary directions. The seismic forces may also be viewed as upper bounds obtained from seismic response curves.