Geometrically nonlinear shape sensing of anisotropic composite beam structure using iFEM algorithm and third-order shear deformation theory

The inverse finite element method (iFEM) has been used to achieve the shape sensing of small displacements based on linear elastic theory. However, with the development of smart structure technology, the formulation is not suitable for the anisotropic composite structures with large deformation in practical engineering. Therefore, a nonlinear iFEM algorithm is proposed to monitor the linear and nonlinear deformation of the anisotropic composite beams. The formulation not only involves the effect of orientation of composite fibers on strain distribution into the shape sensing model, but also accounts for the effect of shear deformation without any requirement of shear correction factor. Initially, the third-order shear deformation theory (TSDT) is reviewed along with deriving the nonlinear strain field based on von-Karman strain theory. Considering the problem that the couple term of the shear strain and bending strain is unmeasurable, the relationship between shear and bending displacements is established according to the derived constitutive equations. Then, the proposed nonlinear iFEM method reconstructs the deformed structural shape, where isogeometric analysis (IGA) approach is used to construct the displacement functions and the experimental section strains are calculated from the discretized surface strains. Finally, several examples are solved to verify the proposed methodology. Numerical results demonstrate that the nonlinear iFEM algorithm can improve the reconstruction accuracy by 4% with respect to the linear iFEM method for beam structures. Hence, the proposed approach can be used as a viable tool to predict nonlinear deformation of composite structure.