Shape sensing of multilayered composite and sandwich beams based on Refined Zigzag Theory and inverse finite element method

Abstract An accurate and effective reconstruction method, which is commonly known as “shape sensing”, is presented for real-time reconstructing the deformation field of multilayered composite and sandwich laminated beam using the measured surface strains is presented. The proposed strategy uses the inverse finite element (iFEM) as a general framework and the Refine Zigzag Theory (RZT) as improved theory. Compared to the traditional iFEM, an additional kinematic variable is introduced to improve reconstruction accuracy of the axial displacement through the depth of the beam. Initially, the displacement fields, strain fields and equilibrium relations are presented. Then, the deformed displacement fields are described by the isogeometric analysis method, where the order of kinematic variables can be determined based on the equilibrium relations and the criteria for element interpolations. Next, transformation relationships are established between measured surface strains and section strains. And the number of strain sensor is further reduced through the boundary conditions. Finally, a least-square function is employed to establish the strain–displacement model. A cantilevered beam is used as a case to compare the reconstructed displacements with the theoretical displacement solutions. The numerical results demonstrate the superior accuracy capability and potential applicability of presented approach for performing accurate shape prediction of the RZT beam.