KOITER ESTIMATE REVISITED

We prove a general adimensional energy estimate between the solution of the three-dimensional Lamé system on a thin clamped shell and a displacement reconstructed from the solution of the classical two-dimensional Koiter model. This estimate only involves the thickness parameter ε, constants attached to the mid-surface S, the two-dimensional energy of the solution of the Koiter model and "wavelengths" associated with this latter solution. This bound is in the same spirit as Koiter's heuristic estimate in Ref. 26 and can be viewed as an a posteriori estimation of the modeling error by means of the two-dimensional solution. It is general with respect to the geometry of the mid-surface S which is an arbitrary smooth manifold with boundary. Taking boundary layer terms into account, we prove that our estimates are sharp in the cases of plates and elliptic shells.

A Proposed Method for Anticipated-Allowable Piping, Mechanical and Seismic Nozzle Load Design

Nozzle loads impose an important constraint in the design of pressure containing equipment. Pressure vessels are connected to external piping by a nozzle welded to the vessel wall and a flange connection. The nozzle loads are due to the piping expansion or contraction caused by the difference between the installation and operating temperatures. Pressure vessel designers need to know, early in the design process, the piping loads that a nozzle may be subjected to. It is important that such loads do not overstress the vessel-nozzle intersection. However the actual piping loads many times are only determined long after the pressure vessel materials are ordered and even procured. The intention of this paper is to provide an empirical but also realistic load set as a function of nozzle external radius, r, vessel external radius, R, vessel thickness, t, and allowable stress, S. The basis of this work is practical experience and also existing theoretical work. This will be a valuable tool in the hands of the pressure vessel mechanical designer. It will allow him to prescribe an early-heuristic estimate of the allowable nozzle loads that will cover external piping loads. These “anticipated” or design loads will allow a pressure vessel mechanical designer to reinforce his design early into the manufacturing of a pressure vessel. Finally, piping engineers will know the terminal allowable loads and thus determine the best piping routing and support arrangements if space constraints allow it.