  We present some new analytical tools for the error analysis of hybridizable
discontinuous Galerkin (HDG) method for linear elasticity. These tools allow us
to analyze more variants of HDG method using the projection-based approach,
which renders the error analysis simple and concise. The key result is a
tailored projection for the Lehrenfeld-Sch\"{o}berl type HDG (HDG+ for
simplicity) methods. By using the projection we recover the error estimates of
HDG+ for steady-state and time-harmonic elasticity in a simpler analysis. We
also present a semi-discrete (in space) HDG+ method for transient elastic waves
and prove it is uniformly-in-time optimal convergent by using the
projection-based error analysis. Numerical experiments supporting our analysis
are presented at the end.
