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This document describes the development of an innovative and computationally efficient modeling approach for the prediction of the transient response in elastic rods and strips. The introduced beam element exploits the advantages of wavelets for the spatial discretization of the displacement field. Results are validated against with confirmed models and are found to be in agreement. The model appears to be very accurate and computationally more efficient than other popular numerical methods.

A new time domain spectral finite element is developed for improving the efficiency of numerical simulations of guided waves in laminated composite strips. The finite element relies on a new generalized laminate mechanics model formulated to represent symmetric and anti-symmetric Lamb waves. The laminate mechanics incorporate third-order polynomial terms for the approximation of axial and transverse displacement fields through the thickness, and consider the displacements of the upper and lower surfaces as degrees of freedom. Based on the resultant governing equations of the laminate section, a new finite element with 8 nodal degrees of freedom is formulated, with its nodes collocated with Gauss-Lobatto-Legendre integration points. Stiffness and mass matrices are assembled and the transient response is predicted with explicit central differences time integration. The transient response of an orthotropic composite strip exited by a 5-count Gaussian pulse is investigated. Results are validated against a semi-analytical solution Numerical results exhibit substantial improvement in the convergence and accuracy of the introduced element regarding the prediction of symmetric and anti-symmetric wave propagation.