Photoelastic simulation of thermal stresses by mechanical prestraining

Several experiments are reported in which thermal stresses were simulated in photoelastic models by a mechanical-prestraining method. This method permitted the study of complex stress distributions arising from simple thermal-expansion conditions. The validity of the method is demonstrated by providing a comparison between theoretical and experimental results obtained for a fundamental disk problem. The usefulness of the method is illustrated by presenting some results of a tube-sheet experiment pertaining to a difficult engineering problem. Additional applications are described to indicate the variety of problems that may be studied by the prestraining method.Thomas Slot was formerly associated with Advanced Technology Laboratories, General Electric Co., Schenectady N.Y.; is now with Nuclear Materials and Propulsion Operation, General Electric Co., Cincinnati, Ohio.Paper was presented at 1965 SESA Spring Meeting held in Denver, Colo., on May 5–7.     

Multivariate stochastic delay differential equations and CAR representations of CARMA processes

In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a CAR($\infty$) representation. Furthermore, we show how the CAR($\infty$) representation gives rise to a prediction formula for CARMA processes. To be used in the above mentioned results we develop a general theory for multivariate stochastic delay differential equations, which will be of independent interest, and which will have particular focus on existence, uniqueness and representations.     

Tetraethylammonium chloride tetrahydrate,a ‘double channel’ host lattice constructed from (H2O)4Cl− tetrahedra linked between vertices

Crystals of (C₂H₅)₄NCl·4H₂O are orthorhombic, space groupCcca, witha=19.104(3),b=23.084(4),c=13.330(3) , andZ=16. The structure features an anionic host lattice constructed from the linkage of (H₂O)₄Cl^– tetrahedra by hydrogen bonds between vertices, generating two open linear channel systems which accommodate the ordered cations. FinalR _F =0.080 for 1516 observed MoK data measured at 22°C. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82035 (12 pages)Dedicated to Professor G. A. Jeffrey     

On the accuracy of two-dimensional photoelastic experiments in which uniform edge loading is obtained by the inflatable-tubing technique

Good agreement is reported between newly acquired numerical solutions and previously obtained photoelastic solutions for hollow hexagons under external pressure on three and six sides. A procedure is discussed for calibration of pressure by means of shear-stress measurements directly on the model being analyzed.     

Rheology of Polydisperse Star Polymer Melts: Extension of the Parameter‐Free Tube Model of Milner and McLeish to Arbitrary Arm‐Length Polydispersity

Summary: This paper considers the extension of the parameter‐free tube model of Milner and McLeish for stress relaxation in melts of monodisperse star polymers to star polymers whose arms have a continuous molecular weight distribution such as the Flory distribution in the case of star‐nylons and star‐polyesters. Exact expressions are derived for the relaxation spectrum and the relaxation modulus for star polymers having an arbitrary continuous arm‐length distribution. For a Flory distribution a comparison is made with results of dynamic measurements on a melt of 8‐arm poly(ε‐caprolactone) (PCL) stars. An excellent quantitative agreement over a large frequency range is found, however, only if one treats, in contrast with the original parameter‐free tube model approach, the entanglement molecular weight that determines the relaxation spectrum as a fitting parameter independent of the entanglement molecular weight of the linear PCL. This discrepancy is not in anyway related to the polydispersity in arm‐length, but a consequence of the thermorheological complexity of the PCL stars. A similar discrepancy has been observed for hydrogenated polybutadiene stars, as described by Levine and Milner.

Measured and calculated storage moduli G′ as a function of frequency ω.