Question

8.25 A [0/90], laminate is clamped on all sides to a rigid frame and undergoes a temperature change ΔΤ (Fig. P8.25) Obtain an expression for the force N, developed in terms of ΔΤ, the engineering properties of the lamina (E, E2, V12. G12) and its coefficients of thermal expansion, α, and α2. Fig. P8.25

Answer 1

As it constrained at all the sides therefore no mechanical strains. Only stress/force will be due to coefficient of thermal expansion and temperature change.

Assuming 0/90 degree layer having equal thickness of h.

$N_x = -(C_{11}*h*\Delta T \alpha _1+C_{12}*h*\Delta T \alpha _2 +C_{22}*h*\Delta T \alpha _1+C_{12}*h*\Delta T \alpha _2)$

where,

$C_{11} = \frac{E_1}{1-v_{12}^2}$

1- V V12

V12E2 -12ー 12