Design and Stress Analysis of Extraterrestrial ... - The Black Vault

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Thermal stresses in a a, flat radiator At. panel
The-purpose of calculation'is to find a based on knoi~nE,
a) Pure -bend. We sha~ll, derive the eqdation for the foi'ces of'
elasticity in a rectangular plate.
We know that if we heat a free- quadratlic rectangular plate so
that the temperature through the *thickness will vary accor~ding to
'linear law, and -in the plane parallel to the: plail~es surface the
:temperature, ~wi-rl, -be--constant, i eformat-ion- -of--the- -layers- -re-at-i-ye- itothe~
middle surface will be A'- :ric and thmiddle surfac?- will
have the shape of a spher~e,. *
A similar character of plate deformation is obtained when
distributed bending moments are applied along, the of'a odees free
plate.
In those cases the bend of the plate iic two.mutuanly perpedicularle
directions will be a pure bend similar to the bend of a prismatic
rod in accordance with therhypothesis of the preservation of a twodimensional
shape for the- cross sec~tions and their rotation relative
to the neutral adxis and their normality to the elastic curve during
bend. This case is well known; thereforen, we shall begin- with it.
Let us examine the bend of a plate by distributed bending
moments applied along the contour.
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Let the xy plane be combined with the middle surface of the
plate until to its te &is deformation.
nutrl. nd heirnoraliy The x- and t y-axes, th will be-directed,
*s credrn
as shown in Fig. ch.5, along its edges. The upward dir6etion is I
bed
i hscs elkon teeoe esal bgnwthit
taken as th~e positive direction of the z-axis. Through ff W&
designate the bending moment per unit length acing along the edges
parallel to the y-axis. Moments will be positive if they are directed,
as shown in drawing, i.e., compression occurs on the upper surface
of the plate and extension on the lower. The thickness of the plate.
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