Erratum: “Physical apparatus parameters and model for vibrating tube densimeters at pressures to 140 MPa and temperatures to 473 K” [Rev. Sci. Instrum. 85, 095111 (2014)]

Although the discussion today is intended to be technical, it may be useful to start with a few words about the nature of the problem. What is parity and what is its violation ? Basically, this means going back to the principle that the laws of physics are indistinguishable if one changes from a right-handed to a left-handed co-ordinate system, or in other words, that any physical apparatus observed in a mirror will appear to obey the same laws of physics as the original. We are well aware of the fact that this symmetry holds wherever we have checked it throughout classical physics; it holds throughout atomic physics, and it seems to hold to a very good degree of accuracy in nuclear physics as well. In physics we always proceed by attempting generalizations, being prepared to give these up when evidence is in contradiction with them; and therefore in general when we see a symmetry hold good to a very high degree of accuracy, we are inclined to assume that it will hold absolutely.

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Membrane analogy for multi-material bars under torsion

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0124 ◽

2019 ◽

Vol 475 (2225) ◽

pp. 20190124 ◽

Cited By ~ 2

Author(s):

Laura Galuppi ◽

Gianni Royer-Carfagni

Keyword(s):

Finite Element ◽

Cross Section ◽

Cross Sections ◽

Three Dimensional ◽

Element Model ◽

Elastic Problem ◽

Two Dimensional ◽

Torsion Problem ◽

Linear Elastic ◽

Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

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