Strain‐based displacement field reconstruction method for thin rectangular plate through orthogonal deflection curves bridging

Abstract

In the existing studies of strain-based displacement field detection for thin rectangular plate, either the boundary conditions are too difficult to handle or the sensors layout and algorithm computing process are too complex to satisfy the requirement of rapid reconstruction of nonlinear vibration shape. In this paper, a strain-displacement conversion method for reconstructing the deformed shape of rectangular plate with typical boundary conditions is presented. This method overcomes the above shortcomings for small deflection nonlinear vibration in linear elastic range. Strains measuring points are uniformly and regularly distributed in the middle area of the plate. Unmeasurable boundary strains will be estimated using the new derived formula according to quadratic interpolation of strains and boundary conditions. The principle of the proposed method is to bridge the orthogonal deflection curves by translating and rotating them. In this way, framework of displacement field can be formed. First, curvature integral method is employed to shape the orthogonal deflection curves of deformed plate. Then, the rotating angles and translating displacements are deduced according to boundary conditions. For some special boundary plates, it even needs to solve nonlinear optimization problem to get the rotating angles. The displacement field reconstructed by the proposed method shows great agreement with the finite element analyses results, which verifies the effectiveness of the methodology.