In this paper, the focus is on the developments towards a local discontinuous Galerkin (LDG) method for 3D elasticity and its application to contemporary practical engineering design. On the theoretical front, the definition of the numerical flux that guarantees stability of the method, based on the energy identity of elasticity, is presented. Among the practical advantages of the LDG method is its ability to handle non-congruent meshes which is a very useful feature for designing complex structures. We demostrate this advantage via results of the analysis of an armored vehicle's barrel-breech system. Optimal convergence rates of the method are shown via numerical experiments using a P1 approximation, for congruent as well as non-congruent meshes.