Thermal strain
Temperature strain is determined by the coefficients of thermal expansion and difference of temperatures between strained and strainless states. Components of the thermal strain for plane stress and isotropic material are defined by the following equation: \[ \{ε_0\} = \begin{Bmatrix} α\\ α \\ 0 \end{Bmatrix} Δ T ; \]
plane stress, orthotropic material: \[ \{ε_0\} = \begin{Bmatrix} α_x\\ α_y \\ 0 \end{Bmatrix} Δ T ; \]
plane strain, isotropic material: \[ \{ε_0\} = (1+ν) \begin{Bmatrix} α\\ α \\ 0 \end{Bmatrix} Δ T ; \]
plane strain, orthotropic material: \[ \{ε_0\} = \begin{Bmatrix} α_x + ν_{xz}α_z\\ α_y + ν_{yz}α_z\\ 0 \end{Bmatrix} Δ T ; \]
axisymmetric problem, isotropic material: \[ \{ε_0\} = \begin{Bmatrix} α\\ α \\ α \\ 0 \end{Bmatrix} Δ T ; \]
axisymmetric problem, orthotropic material:
\[ \{ε_0\} =
\begin{Bmatrix}
α_z\\
α_r \\
α_θ \\
0
\end{Bmatrix} Δ T ;
\]
where α is a coefficient of thermal expansion for isotropic material; αx,
αy, αz, αr, αθ
are the coefficients of thermal expansion along the corresponding axes for orthotropic material;
ΔT is the temperature difference between strained and strainless states.