Full sets of equations

Finally, the full set of constitutive equation written with stiffness matrices looks like:

\begin{matrix} [\begin{matrix} {[A]}_{lam} & {[B]}_{lam} \\ {[B]}_{lam} & {[D]}_{lam} \end{matrix}] \cdot {\begin{matrix} {ϵ^{0}}_{lam} \\ {κ}_{lam} \end{matrix}} = {\begin{matrix} {N}_{lam} \\ {M}_{lam} \end{matrix}} \\ + {\begin{matrix} {α E h}_{lam} \\ {α E h^{2}}_{lam} \end{matrix}} (T_{0} - T_{ref}) + {\begin{matrix} {α E h^{2}}_{lam} \\ {α E h^{3}}_{lam} \end{matrix}} T_{, z} \\ + {\begin{matrix} {β E h}_{lam} \\ {β E h^{2}}_{lam} \end{matrix}} (H_{0} - H_{ref}) + {\begin{matrix} {β E h^{2}}_{lam} \\ {β E h^{3}}_{lam} \end{matrix}} H_{, z}, & (II.1.84) \end{matrix}

\begin{matrix} {[G]}_{lam} \cdot {Γ}_{lam} = {Q}_{lam} + {α_{s} G h}_{lam} (T_{0} - T_{ref}) + {α_{s} G h^{2}}_{lam} T_{, z} \\ + {β_{s} G h}_{lam} (H_{0} - H_{ref}) + {β_{s} G h^{2}}_{lam} H_{, z} . & (II.1.85) \end{matrix}

The two previous expressions are inverted as follows:

\begin{matrix} [\begin{matrix} {[a]}_{lam} & {[b]}_{lam} \\ [b] T_{lam} & {[d]}_{lam} \end{matrix}] \cdot {\begin{matrix} {N}_{lam} \\ {M}_{lam} \end{matrix}} \\ = {\begin{matrix} {ϵ^{0}}_{lam} \\ {κ}_{lam} \end{matrix}} + {\begin{matrix} {α_{0}^{ϵ}}_{lam} \\ {α_{0}^{κ}}_{lam} \end{matrix}} (T_{0} - T_{ref}) + {\begin{matrix} {α_{1}^{ϵ}}_{lam} \\ {α_{1}^{κ}}_{lam} \end{matrix}} T_{, z} \\ + {\begin{matrix} {β_{0}^{ϵ}}_{lam} \\ {β_{0}^{κ}}_{lam} \end{matrix}} (H_{0} - H_{ref}) + {\begin{matrix} {β_{1}^{ϵ}}_{lam} \\ {β_{1}^{κ}}_{lam} \end{matrix}} H_{, z}, & (II.1.86) \end{matrix}

\begin{matrix} {[G]}_{lam}^{- 1} \cdot {Q}_{lam} = {[Γ]}_{lam} - {α_{0}^{s}}_{lam} (T_{0} - T_{ref}) - {α_{1}^{s}}_{lam} T_{, z} \\ - {β_{0}^{s}}_{lam} (H_{0} - H_{ref}) - {β_{1}^{s}}_{lam} H_{, z} . & (II.1.87) \end{matrix}