Inverse spectral Chebyshev method For full-field reconstruction under restricted surface access in composite plates

This paper presents an inverse spectral Chebyshev method (ISCM) with compressed sensing (CS) for full-field reconstruction of laminated composite plate responses governed by first-order shear deformation theory (FSDT) from sparse and noisy strain measurements. The approach exploits the intrinsic sparsity of FSDT kinematic fields in a Chebyshev spectral basis and enforces governing equilibrium constraints directly in spectral coefficient space through an equilibrium-informed enhanced iterative hard-thresholding (EIHT) algorithm. A theory-guided sparsity selection strategy based on Bernstein-type analyticity arguments is introduced, linking spectral coefficient decay rates to measurement noise levels and providing conservative, physics-informed bounds for selecting the sparsity level. Dedicated numerical studies using a forward spectral Chebyshev FSDT solver quantify effective sparsity levels for displacement, rotation, curvature, and transverse shear strain fields, demonstrating their compatibility with CS reconstruction despite the ill-conditioning associated with spatial differentiation. The framework is validated on laminated composite plates, demonstrating accurate recovery of displacements, rotations, curvatures, and shear strains from a sensor set much smaller than the number of degrees of freedom (DOFs), under additive Gaussian noise. These results indicate that ISCM provides a viable alternative to conventional inverse finite element methods (iFEM) for composite plate shape sensing and structural health monitoring under restricted surface access.