A survey of several methods under the heading of strong formulation finite element method (SFEM) is presented. These approaches are distinguished from classical one, termed weak formulation finite element method (WFEM). The main advantage of the SFEM is that it uses differential quadrature method (DQM) for the discretization of the equations and the mapping technique for the coordinate transformation from the Cartesian to the computational domain. Moreover, the element connectivity is performed by using kinematic and static conditions, so that displacements and stresses are continuous across the element boundaries. Numerical investigations integrate this survey by giving details on the subject.

In this paper the Semi-Analytical Finite Element (SAFE) method for modeling guided wave propagation is extended to account for linear viscoelastic material damping. Linear viscoelasticity is introduced by allowing for complex stiffness constitutive matrices for the material. Dispersive characteristics of viscoelastic waveguides, such as phase velocity, attenuation, energy velocity and cross-sectional wavestructures are extracted. Knowledge of the above-mentioned dispersive properties is important in any structural health monitoring attempt that uses ultrasonic guided waves for long range inspection. The proposed damped formulation is applied to several waveguides with different mechanical and geometric properties. In particular, a viscoelastic isotropic plate, a railroad track and a pipe are studied.

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