Question: Explicitly develop the stress field Eq. (12.5.13) in Example 12.1 and determine the constants C 2 and C 3 for the case of stress-free edge

Explicitly develop the stress field Eq. (12.5.13) in Example 12.1 and determine the constants C2 and C3 for the case of stress-free edge conditions. Plot the value of σy through the thickness (vs. coordinate x) for both high-temperature (sin βy = 1) and low-temperature (sin βy =–1)
cases.

Equation 12.5.13

o = - [C cosh 3x + C3x sinh 6x] sin y - ExT, sin By y = 6 C cosh 8x + C3 (x sinh .x+cosh Bx) sin By -0 C2 C

Data from example 12.1

Consider the thermoelastic problem in a rectangular domain as shown in Fig. 12.1. We assume that the vertical

Now since the temperature field was symmetric in x, we expect the stresses to also exhibit the same symmetry.

a a X

o = - [C cosh 3x + C3x sinh 6x] sin y - EaT, sin By y = 6 C cosh 8x + C3 (x sinh .x+cosh Bx) sin By -0 C2 C sinh 6x + C3x cosh 6x+-sinh 6x cos By h 8x)] cos Txy =

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