Series representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem of isotropic material is coincide with the existing solutions in the literature.
Two different sets of interpolating functions are used for the geometric and displacement representations respectively.
The sinusoidal-like pattern of movement was chosen since it reflects the acceleration, velocity and displacement representations of movement similarly, as they are all sine or cosine derivatives (Fig. 1A).
(Both involve the condensation and displacement of meanings, the representation of things by their opposites, the triumph of fallacy over logic — all to outwit the inner censor).
The generalization is based on a higher-order displacement field representation and on the definition of elasticity-based surface-averaged kinematic and static variables related through a local stiffness matrix.
Open image in new window Fig. 1 3D tetrahedral mesh used in validation of the developed elastic numerical model Open image in new window Fig. 2 Schematic representation of displacement (mm) (top) and y-stresses (Pa) (bottom) for a FEM tool box and b the developed numerical elastic model with σ y = 450 Pa.
Tractions and displacement components are given a spectral representation in the spatial coordinate along the interface.
Different models with a different representation of displacements and interlaminar stresses are shown to provide quite different results in terms of displacements, contact force and damage.
However, if nonlinearities are present, higher order harmonics may need to be included to ensure a proper representation of friction forces and displacements, with a detrimental effect on the computational time.
The TLS 3D model was merged with the GB-InSAR data obtaining a 3D GB-InSAR cumulative displacement map, which allowed to read detected LOS displacements directly on the observed scenario 3D representation, and therefore both to better localize the most critical areas, and compare the different techniques displacement data (Fig. 10).
