Elastic Wave Propagation in Laminated Composites Using the Space-Time Least-Squares Formulation inh,p,kFramework

Abstract

In this paper, numerical simulation of one-dimensional elastic wave propagation in periodically laminated composites using space-time least-squares finite element processes in h, p, k mathematical framework in [ 1 Surana, K. S. , Ahmadi, A. R. and Reddy, J. N. 2002. “k-version of finite element method for self-adjoint operators in BVP,”. Int. J. Comp. Meth. Engng. Sci. Mech. (formerly, Int. Journal of Comp. Eng. Sci., 3(2): 155–218. [Crossref] , [Google Scholar] , 2 Surana, K. S. , Ahmadi, A. R. and Reddy, J. N. 2004. “k-version of finite element method for non-self-adjoint operators in BVP,”. Int. J. Comp. Meth. Engng. Sci. Mech. (formerly, Int. Journal of Comp. Eng. Sci., 4(4): 737–812. [Google Scholar] , 3 Surana, K. S. , Ahmadi, A. R. and Reddy, J. N. 2004. “k-version of finite element method for non-linear differential operators in BVP,”. Int. J. Comp. Meth. Engng. Sci. Mech. (formerly, Int. Journal of Comp. Eng. Sci., 5(1): 133–207. [Crossref] , [Google Scholar] , 4 Surana, K. S. , Allu, S. and Reddy, J. N. 2005. The “k-version of finite element method for initial value problems: Mathematical and computational framework,”. Int. Journal of Num. Meth. Eng., in review [Google Scholar] ] is presented. It is demonstrated that in space-time coupled processes, if one uses time marching procedure to simulate the evolution in which the solution is computed for a space-time strip for one increment of time, then time marched, the space-time local approximations of class C⁰ and degree p in time yield global differentiability of order p in time for the space-time strip. However, the inter-strip global differentiability in time remains limited by the global differentiability of the local approximations in time. Four different space-time least-squares finite element formulations are presented here and their merits and drawbacks, convergence rates, and their ability to incorporate single material physics as well as bi-material interface macro physics of wave propagation, transmission, reflection and interaction in laminated composites are discussed. Numerical results are presented to illustrate mathematical features of each formulation for wave propagation in a single medium as well as in domains containing bi-material interfaces. Numerical results are also computed for an impact experiment and compared with experimental data.