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Analytical solution of the electro-mechanical flexural coupling between piezoelectric actuators and flexible-spring boundary structure in smart composite plates

Gohari Soheil, Mozafari F., Moslemi N., Mouloodi Saeed, Sharifi S., Rahmanpanah Hadi, Burvill Colin

Archives of Civil and Mechanical Engineering

2021

Vol. 21, no. 1

546--570

An analytical solution has been developed developed in this research for electro-mechanical flexural response of smart laminated piezoelectric composite rectangular plates encompassing flexible-spring boundary conditions at two opposite edges. Flexible-spring boundary structure is introduced to the system by inclusion of rotational springs of adjustable stiffness which can vary depending on changes in the rotational fixity factor of the springs. To add to the case study complexity, the two other edges are kept free. Three advantages of employing the proposed analytical method include: (1) the electro-mechanical flexural coupling between the piezoelectric actuators and the plate’s rotational springs of adjustable stiffness is addressed; (2) there is no need for trial deformation and characteristic function—therefore, it has higher accuracy than conventional semi-inverse methods; (3) there is no restriction imposed to the position, type, and number of applied loads. The Linear Theory of Piezoelectricity and Classical Plate Theory are adopted to derive the exact elasticity equation. The higher-order Fourier integral and higher-order unit step function differential equations are combined to derive the analytical equations. The analytical results are validated against those obtained from Abaqus Finite Element (FE) package. The results comparison showed good agreement. The proposed smart plates can potentially be applied to real-life structural systems such as smart floors and bridges and the proposed analytical solution can be used to analyze the flexural deformation response.

Prediction of displacement in the equine third metacarpal bone using a neural network prediction algorithm

Mouloodi Saeed, Rahmanpanah Hadi, Burvill Colin, Davies Helen M. S.

Biocybernetics and Biomedical Engineering

2020

Vol. 40, no. 2

849--863

Bone is a nonlinear, inhomogeneous and anisotropic material. To predict the behavior of bones expert systems are employed to reduce the computational cost and to enhance the accuracy of simulations. In this study, an artificial neural network (ANN) was used for the prediction of displacement in long bones followed by ex-vivo experiments. Three hydrated third metacarpal bones (MC3) from 3 thoroughbred horses were used in the experiments. A set of strain gauges were distributed around the midshaft of the bones. These bones were then loaded in compression in an MTS machine. The recordings of strains, load, load exposure time, and displacement were used as ANN input parameters. The ANN which was trained using 3,250 experimental data points from two bones predicted the displace-ment of the third bone (R2 ≥ 0.98). It was suggested that the ANN should be trained using noisy data points. The proposed modification in the training algorithm makes the ANN very robust against noisy inputs measurements. The performance of the ANN was evaluated in response to changes in the number of input data points and then by assuming a lack of strain data. A finite element analysis (FEA) was conducted to replicate one cycle of force-displace-ment experimental data (to gain the same accuracy produced by the ANN). The comparison of FEA and ANN displacement predictions indicates that the ANN produced a satisfactory outcome within a couple of seconds, while FEA required more than 160 times as long to solve the same model (CPU time: 5 h and 30 min).