An efficient method for solving the structural dynamics of finite elastic structures containing discontinuities using analytical/numerical matching with finite element analysis

Analytical/Numerical Matching (ANM) is a method designed to efficiently solve many types of problems containing discontinuities. The method separates local and global effects, and solves separate sub-problems using high resolution around the discontinuity and low resolution away from the discontinuity. This work demonstrates the methodology for applying ANM to 2D and 3D finite dynamic structures using finite element analysis (FEA) and hybrid modal/FEA methods for the solution of the high-resolution (local) and low-resolution (global) subproblems. The ANM method is illustrated on a thick 2D beam having several displacement constraints attached to the lower surface of the beam and a 3D cylindrical shell excited by various forcing functions and displacement constraints. Ordinarily (and here, for verification purposes) these problems would be solved using high-resolution finite element analysis due to the local discontinuities around the applied forcing and displacement constraints. Using ANM, these discontinuities and through-the-thickness effects are modeled separately in the geometrically compact local sub-problem using a high-resolution mesh of 2D plane or 3D solid finite elements. The much larger global sub-problem contains no discontinuities and is reduced to a low-resolution finite element problem or one that rapidly converges when using a modal approach. The third sub-problem (matching) is solved analytically and therefore carries no computational burden. The agreement between the ANM solutions and the traditional FEA (or modal/FEA) solutions is excellent. Furthermore, the computational savings are significant. Finally, a method for efficiently implementing fluid-loading effects into the in-vacuo ANM methodology is demonstrated for the 2D thick beam and 3D cylindrical shell problems.