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Finite element modelling and static shape control of a functionally graded piezoelectric beam

Eshraghi I.

Archives of Mechanics

2023

Vol. 75, nr 4

469--492

A finite element model is developed for discretization and analysis of the functionally graded piezoelectric material (FGPM) beam based on the Timoshenko beam theory and assuming linear constitutive relation for the corresponding piezoelectric material behavior. Results obtained using the developed finite element code are compared with the available experimental and numerical results for smart structures with and without graded properties. Static shape control of the beam is conducted using the Buildup Voltage Distribution (BVD) algorithm by implementing this method in the finite element routine. Numerical simulations have been performed to study the performance of the shape control algorithm by optimizing the distribution of the applied voltages. Furthermore, the effect of the number of iterations on the result accuracy as well as the variation of the control voltage distribution with the number of discretized regions and the volume fractions of the constituent material is studied. A fast numerical convergence with good accuracy is observed for the shape control of FGPM beams using the developed method. The proposed technique is a good candidate for the modeling, analysis, and control of smart structures with graded properties.

Transient dynamic analysis of functionally graded micro-beams considering small-scale effects

Eshraghi I., Dag S.

Archives of Mechanics

2021

Vol. 73, nr 4

303--337

A domain-boundary element method, based on modified couple stress theory, is developed for transient dynamic analysis of functionally graded micro-beams. Incorporating static fundamental solutions as weight functions in weighted residual expressions, governing partial differential equations of motion are converted to a set of coupled integral equations. A system of ordinary differential equations in time is obtained by domain discretization and solved using the Houbolt time marching scheme. Developed procedures are verified through comparisons to the results available in the literature for micro- and macro-scale beams. Numerical results illustrate elastodynamic responses of graded micro-beams subjected to various loading types. It is shown that metal-rich micro-beams and those with a smaller length scale parameter ratio undergo higher displacements and are subjected to larger normal stresses.