Abstract
In this study, we propose a method to estimate structural deformation and failure by using displacement-strain transformation matrices, i.e., strain-to-displacement transformation (SDT) and displacement-to-strain transformation (DST). The proposed SDT method can be used to estimate the complete structural deformation where it is not possible to apply deformation measurement sensors, and the DST method can be used for to estimate structural failures where strain and stress sensors cannot be applied. We applied the SDT matrix to a 1D beam, a 2D plate, rotating structures and real wind turbine blades, and successfully estimated the deformation in the structures. However, certain difficulties were encountered while estimating the displacement of brittle material such as an alumina beam. The study aims at estimating the displacement and stress to predict the failure of the structure. We also explored applying the method to multi-material structures such as a two-beam bonded structure. In the study, we used alumina–aluminum bonded structures because alumina is bonded to the substrate to protect the structure from heat in many cases. Finally, we present the results of the displacement and failure estimation for the alumina–aluminum structure.
Highlights
It is necessary to consider maximum deformation, strain, stress and failure of the structure to ensure safe operations
Displacement Estimation Results Using strain-to-displacement transformation (SDT) Method where δmax denotes the maximum deflection of the beam, P denotes the force at the endpoint of the
To validate the estimation accuracy of the SDT and displacement-to-strain transformation (DST) methods, experiment results were beam, l denotes the length of the beam, E denotes the elastic modulus of the beam, I denotes the compared with the results of the SDT and DST methods, finite elements method (FEM) and the moment of inertia in the rectangular cross-section of the beam, b denotes the width of the crossanalytical method
Summary
It is necessary to consider maximum deformation, strain, stress and failure of the structure to ensure safe operations. Deformation and strain can be measured using displacement sensors, such as linear variable differential transformers (LVDTs) [1], potentiometers [2], laser displacement sensors [3], strain sensors, such as strain gages [4] and fiber optic sensors [5]. In some cases, it is not possible to measure the deformation by using displacement sensors. It is not possible to measure strain by using strain sensors. The displacement and strain are expressed as the product of the mode matrix, and the modal coordinates are expressed as follows:. O denotes the displacement, {s} denotes the strain, ηN denotes the modal coordinate vector, φN denotes the displacement mode matrix, and ψN denotes the strain mode matrix. If we rearrange {d} and {s} with the modal coordinate matrix, we obtain Equations (4) and (5): −1
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