This article presents a finite element formulation for the calculation of the spectral response of a fiber Bragg grating sensor embedded in a host material system. The formulation is based on a 3D element for which the propagation constant is calculated from the optical and geometric properties in the plane perpendicular to light propagation, after which the optical transfer matrix is calculated. The effects of axial strain, transverse strain, fiber curvature and shear loading are implemented into the formulation. This novel approach permits the prediction of the sensor response when the sensor is embedded in a complicated material system for which analytical or approximative solutions do not accurately predict the strain state in the sensor. A numerical example of a relatively simple sensor geometry is presented to verify the formulation. The integration of the proposed sensor finite element formulation into a classical structural mechanics finite element program to perform the complete analysis is also discussed.

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