  We study the behaviour of Smectic-A (SmA) liquid crystals with a modified
Landau-de Gennes (mLdG) model. The director and orientational order of SmA are
described by a tensor-order parameter $\mathbf{Q}$, and the positional order is
described by a real scalar $u$, which represents the deviation from the average
concentration of liquid crystal molecules. Firstly, we prove the existence and
regularity of the global minimiser of the mLdG free energy. Then, we
analytically prove that the mLdG model can exhibit Isotropic-Nematic-Smectic
phase transition in terms of the critical temperatures and stabilities of
phases. Furthermore, we explore smectic configurations confined within a square
domain with edge length $\lambda$. We analytically study the positional order
far from and near the defects and the limiting cases with $\lambda\to 0$ and
$\lambda\to\infty$, to potentially guide the behavior of SmA in finite domain
size.With finite $\lambda$, we numerically recover BD-like and D-like states
observed in experiments. The stability of a BD-like state is enhanced by the
layer structure of positional order. The analogous $\mathbf{Q}$ profile of
D-like states in nematics and smectics indicates the memory of the director in
the N-S phase transition. We also study the frustrated smectic energy landscape
and the strategy to alleviate the frustration.
