Douglas Coffin

Elastica solution for the hygrothermal buckling of a beam

An elliptic integral solution for the post-buckling response of a linear-elastic and hygrothermal beam fully restrained against axial expansion is presented. Whereas in the classical solutions the extension of the beam can be neglected, a well-posed formulation of the title problem must include the extension. The solution for the limiting case of a string is presented. The present solution shows that the magnitude of the compressive axial load is a maximum at the onset of buckling and decreases as the potential for free expansion is increased; this is in contrast to the approximate solutions found in the literature.

IN-PLANE MOISTURE TRANSPORT IN PAPER DETECTED BY MAGNETIC RESONANCE IMAGING

Magnetic resonance imaging was used to visualize in-plane moisture transport in laboratory-made handsheets, heavy paperboard, and polyethylene-coated paperboard. Beginning with wet samples sealed on both surfaces, the moisture content was reduced through evaporation from the outside edges. The diffusion of moisture to the outside edges, i.e., in the plane of the sheets, was found to be isotropic with respect to the sample machine and cross directions. Isotropic in-plane moisture diffusion was observed for samples exhibiting a relatively high degree of fiber orientation, and under conditions of forced convection with air flow rates up to 10 L/min past the outside edges.

Beams on a two-dimensional pasternak base subjected to loads that cause lift-off

Abstract First, two closely related problems, shown in Fig. 1, published by Chernigovskaya (1961. In Issledovaniya po Dinamike Sooruzhenii i Raschetu Konstruktsii na Uprugoni Osnovanii (Edited by B. G. Korenev. pp. 113–141. Gosstroiizdat, Moscow) and Ting (1973, J. Franklin Inst. 296 (2), 77–89) are discussed. It is shown that neither of their formulations is correct. The aim of this paper is to show how to correctly formulate and solve problems of this type. Utilizing the variational approach for variable matching points derived by Kerr (1976. Int. J. Solids Structures 12 , 1–11), a formulation lor the problem analyzed by Ting is presented, that is mechanically reasonable and mathematically well posed. The analytical solution obtained is evaluated numerically and then compared with related test results by Durelli et al . (1969. J. Struct. Div. ASCE 95 , 1713–1725). This paper concludes with a discussion of the results obtained.

Anatomical basis for biophysical differences between Pinus nigra and P. resinosa (Pinaceae) leaves

Differences in the flexibility of Pinus nigra and P. resinosa leaves can be used to discriminate these two similarly looking pine species from one another. When bent along the longitudinal axis, P. resinosa leaves snap, while P. nigra leaves appear flexible. This useful field test has had no known biophysical or anatomical explanation until now. Analysis of the first order mechanics of bending and buckling of the pine needles was used to elucidate any important anatomical differences between these two species that can account for their different biophysical behaviors when bent. Neither the cross section of the total leaf area nor the inner core area between the two species differed significantly. Differences in the pattern of cell wall thickening and lignification of the endodermal layer of the inner core of the leaves best explain the differences in bending behavior. Thus, subtle variation in anatomy can influence the biophysical properties of naturally occurring structures, which in turn could have important implications for the engineering of manufactured objects.

First-Order Approximations for the Effective Shearing Viscosities of Continuous-Fiber Suspensions

The effective shearing viscosities required to model aligned-continuous-fiber suspensions as a transversely isotropic fluid are investigated. Relations for the longitudinal shearing viscosity and the transverse shearing viscosity are developed by considering the kinematics of adjacent rigid fibers interacting with the viscous fluid matrix in states of shear deformation. This simple micromechanical analysis revealed that the longitudinal and transverse shearing viscosities of the medium may be considered to be equal. The present prediction for the in-plane shearing viscosity accounts for the constraint of fiber inextensibility and differs from previous relations [4-6]. In addition, the relationships presented herein were used in Reference [11], but development and discussion of these relationships, as given in the following, are lacking in the literature. Predictions for both Newtonian and shear thinning Carreau matrix fluids are presented and compared to results of a finite-element analysis as well as the earlier work of Christensen [10]. Finally, these simple relations are compared to experimental observations in order to evaluate their validity.

On membrane and plate problems for which the linear theories are not admissible

A horizontal clamped plate is subjected to the weight of a liquid above it. When the free surface of the liquid coalesces with the plane of the undeformed upper surface of the plate, according to the classical theory of plates (which results in an eigen-value problem), nonzero deflections will exist only for discrete values of the ratio γ/D ; where γ is the specific weight of the liquid and D is the flexural stiffness of the plate. The purpose of this paper is to clarify this apparently unreasonble result. It is shown, using a nonlinear analysis, that problems of this type exhibit a bifurcation point from the undeformed state and that the eigenvalues of the linear analysis determine merely the bifurcation points. Thus, for problems of this type, a linear formulation is not suitable. Because of its analytical simplicity, at first, the membrane strip is analyzed in detail. This is followed by the analysis of the plate.

Electrospinning of TiO 2 for dye sensitized solar cells

Dye adsorption on TiO2 and electron transport in TiO2 film are the two critical elements in determining the dye sensitized solar cell (DSSC) efficiency. Increasing dye adsorption which in turn increases the light harvesting is usually achieved by using nanoporous or nanoparticle TiO2 films. Electron transport is determined by the inter-particle resistance of TiO2 film. Electrospinning is a viable method for forming porous structure materials with high surface area. In this study, it was found that electrospinning alone is not able to achieve good solar cell performance due to the low electron transport caused by the pores in the TiO2 film. To increase dye adsorption without sacrificing the electron transport, a hybrid bilayer TiO2 structure with each layer prepared by different methods, blade coating and electrospinning was explored. This hybrid structure was compared with the single doctor bladed structure. A significant increase of Jsc was observed for the bilayer structure which resulted in an improvement of solar cell efficiency of 30% (from 1.6% to 2.11%).

Flange Wrinkling In The Forming Of Thermoplastic Composite Sheets

In sheet forming, the creation of wrinkles in the flange area of the blank commonly occurs. When diaphragm forming aligned‐fiber‐reinforced thermoplastic composites, observations reveal that the wrinkles tend to occur at angles oriented at forty‐five degrees to the axis of the fibers. Intuition suggests that this is related to shear, but this may be misleading. The results of a stress‐analysis and buckling analysis of this flange wrinkling problem are discussed. The forming of the thermoplastic sheets occurs at elevated temperatures and the sheet is essentially inextensible in the fiber direction. This leads to high anisotropy ratios of in‐plane stiffness properties. The out‐of‐plane bending of the sheet will be strongly influenced by the presence of polymeric diaphragms. To investigate the buckling problem for this forming situation, a finite‐difference formulation was developed. The solution revealed that only when one considers the combined effect of the thermoplastic composite and the polymeric diaphr...