Numerical modeling for elastodynamic problems in laminated composite cylinders
Propagation and scattering of elastic waves in laminated composite cylinders are studied in this thesis. Axisymmetric steady-state elastodynamic Green's functions for laminated composite cylinders are constructed by the superposition of numerically generated modal solutions from an eigensystem, which is based on a semi-analytical finite element formulation. Boundary element method is employed to investigate scattering of waves due to circumferential flaws in laminated composite cylinders. Also, a hybrid method, which combines axisymmetric finite element modeling in an interior bounded region containing arbitrary inclusions with a spectral representation in exterior regions, is formulated to analyze more varied wave scattering problems. These methods are demonstrated through solving wave scattering problems with circumferential joints, surface breaking cracks, and V-shaped weldments with interface cracks. Three-dimensional wave propagation problem in laminated composite cylinders is decomposed into a series of two-dimensional problems, which are associated with the circumferential wave numbers. Two methods are proposed to construct explicit expressions of three-dimensional steady-state elastodynamic Green's functions. One is based on an integral transform. The other is by means of imposing symmetric/antisymmetric conditions on the cross-section containing the source load for a cylinder with cylindrically monotropic properties. The second method, being more restrictive with respect to material properties, is intended primarily as a cross-check of the integral transform version of Green's functions. Numerical implementation details are discussed in terms of two example thickness profiles to exploit the essential keys for the convergence and accuracy of Green's functions.