scholarly journals On an approximate solution for the bending of a beam of rectangular cross-section under any system of load.—additional note

1904 ◽  
Vol 72 (477-486) ◽  
pp. 391-393
Keyword(s):  
Approximate Solution ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Additional Note

My attention has lately been called by M. Flamant to certain discrepancies in some formulæ given by me in a paper recently published under the above title. On investigation I have found that a set of formulæ of the paper in question, namely, those of 41, contained several inaccuracies.

scholarly journals On an approximate solution for the bending of a beam of rectangular cross-section under any system of load, with special reference to points of concentrated or discontinuous loading

1902 ◽  
Vol 70 (459-466) ◽  
pp. 491-496
Keyword(s):  
Approximate Solution ◽  
Special Reference ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Elastic Equilibrium ◽  
Elastic Solid ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Applied Stresses

The paper investigates the elastic equilibrium of a long bar of rectangular cross-section in those cases where the problem may be treated as one of two dimensions, namely:— ( a .) When the strain being in the plane of xy , the elastic solid extends indefinitely in the direction of the applied stresses over the bounding planes y = ± b , x = ± a being the same for any two sections parallel to the plane of xy . We then have a strictly two-dimensional strain.

An Experimental and Analytical Study of Close-Contact Melting

1986 ◽  
Vol 108 (4) ◽  
pp. 894-899 ◽  
Author(s):  
M. K. Moallemi ◽  
B. W. Webb ◽  
R. Viskanta
Keyword(s):  
Approximate Solution ◽  
Surface Temperature ◽  
Cross Section ◽  
Analytical Study ◽  
Close Contact ◽  
Rectangular Cross Section ◽  
Melting Rate ◽  
Contact Melting ◽  
Series Of Experiments ◽  
Convection Dominated

Close-contact melting was investigated by performing a series of experiments in which blocks of solid n-octadecane (with circular or rectangular cross section) were melted by a horizontal planar heat source at constant surface temperature. Close contact between the source and the solid prevailed throughout the experiments by permitting the uncontained solid to descend under its own weight while squeezing the melt out of the gap separating it from the source. The velocity of the solid was measured and is reported as a function of the instantaneous weight of the solid. Effects of the surface temperature of the source and radius of the solid on its temporal velocity are also reported. A closed-form approximate solution is developed for the motion of solid and predictions are compared with the experimental data. The results for the solid velocity are correlated in terms of the governing parameters of the problem as revealed by the approximate solution. Compared with natural convection-dominated melting from below (solid confined and contained in a rectangular cavity) close contact gives rise to approximately a sevenfold increase in the melting rate of the solid.

scholarly journals WAVE TRANSMISSION THROUGH PERMEABLE BREAKWATERS

1972 ◽  
Vol 1 (13) ◽  
pp. 99 ◽  
Author(s):  
Charles K. Sollitt ◽  
Ralph H. Cross
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Cross Section ◽  
Wave Breaking ◽  
Wave Reflection ◽  
Rectangular Cross Section ◽  
Wave Component ◽  
Additional Consideration ◽  
Reflection And Transmission ◽  
Theoretical Results

A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.

scholarly journals IV. On an approximate solution for the bending of a beam of rectangular cross-section under any system of Lond, with special reference to points of concentrated or discontinuous loading

1903 ◽  
Vol 201 (331-345) ◽  
pp. 63-155 ◽  
Keyword(s):  
Approximate Solution ◽  
Special Reference ◽  
Cross Section ◽  
Elastic Material ◽  
Rectangular Cross Section ◽  
Theory Of Elasticity ◽  
Surface Forces ◽  
Complete Form ◽  
Rectangular Parallelopiped

The consideration of the stresses and strains which occur in a rectangular parallelopiped of elastic material subjected to given surface forces over its six faces leads to one of the most general, as it is one of the oldest, problems in the Theory of Elasticity. Lame, in his ‘Lemons sur l’Elastieite des Corps solides,’ published in 1852, describes it as “le plus difficile peut-etre de la theorie mathematique de ’elasticity.” In spite of repeated attempts, however, the problem remains still unsolved. In its complete form it may he stated as follows:—

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