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1

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

Eshraghi I.

Archives of Mechanics

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2023

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Vol. 75, nr 4

469--492

EN

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.

2

Optimal reshaping and stress controlling of double-layer spherical structures under vertical loadings

Manguri Ahmed, Saeed Najmadeen, Mahmood Aram, Katebi Javad, Jankowski Robert

Archives of Civil Engineering

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2022

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Vol. 68, nr 4

591--606

EN

Architectural structures’ nodal coordinates are significant to shape appearance; vertical overloading causes displacement of the joints resulting in shape distortion. This research aims to reshape the distorted shape of a double-layer spherical numerical model under vertical loadings; meanwhile, the stress in members is kept within the elastic range. Furthermore, an algorithm is designed using the fmincon function to implement as few possible actuators as possible to alter the length of the most active bars. Fmincon function relies on four optimization algorithms: trust-region reflective, active set, Sequential quadratic progra mming (SQP), and interior-point. The fmincon function is subjected to the adjustment technique to search for the minimum number of actuators and optimum actuation. The algorithm excludes inactive actuators in several iterations. In this research, the 21st iteration gave optimum results, using 802 actuators and a total actuation of 1493 mm. MATLAB analyzes the structure before and after adjustment and finds the optimum actuator set. In addition, the optimal actuation found in MATLAB is applied to the modeled structure in MATLAB and SAP2000 to verify MATLAB results.

3

Shape control of the column with imperfections of loading heads by means of the stiffening rod

Sokół K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2010

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Vol. 9, nr 1

195-202

EN

This paper concerns an influence of the imprecise manufacturing or improper assembling processes of supporting and loading heads on transversal displacements, bending moments and axial force distribution of a column consisted of two rods, where one of rods is a stiffening element. The problem has been formulated by means of the principle of stationary total potential energy, the von Karman theory and linear constitutive equations for column material. The results of numerical calculation have shown how important it is to provide the axial load of the beams and columns.

4

The use of auxetic materials in smart structures

Hadjigeorgiou E. P., Stavroulakis G. E.

Computational Methods in Science and Technology

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2004

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Vol. 10, nr 2

147-160

EN

This paper presents a study of the implications of using auxetic materials in the design of smart structures. By using auxetic materials as core and piezoelectric actuators as face layers to provide control forces, the problem of the shape control of sandwich beams is analyzed under loading conditions. The mechanical model is based on the shear deformable theory for beams and the linear theory of piezoelectricity. The numerical solution of the model is based on superconvergent (locking-free) finite elements for the beam theory, using Hamilton's principle. The optimal voltages of the piezo-actuators for shape control of a cantilever beams with classical and auxetic material are determined by using a genetic optimization procedure. Related numerical solutions of static problems demonstrate the role of auxetic material in the deformation, shape control and stress distribution of the beam and related two-dimensional composite elastic structures.

5

Bridges with adaptive railway track

Flont P., Holnicki-Szulc J.

Journal of Theoretical and Applied Mechanics

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2002

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Vol. 40 nr 3

533-547

EN

The concept of an adaptive railway track, consisting of sleepers initially elevated (with the curvature tailored according to the detected, coming train) and then yielding in a controlled way under the moving vehicle is discussed. The problem formulated as a shape control requiring the minimum integral measure of the track deflection gives, as a side effect, a significant reduction of the corresponding integral measure of the dynamic contact forces between the track and wheels.

PL

Omówiona koncepcja samo-adaptującego się toru kolejowego opiera się na zastosowaniu inteligentnych podkładów. Podkłady, których wysokość może być zmieniana dzięki wyposażeniu ich w siłowniki, zastępują podkłady (mostownice) na moście. Idea adaptacyjnego toru polega na wstępnym uniesieniu toru, którego krzywizna dopasowana jest do zidentyfikowanego, nadjeżdżającego pociągu i następnie w kontrolowany sposób opuszczaniu pod przejeżdżającym pociągiem. Zdanie zstało sformułowane jako sterowanie kształtem toru przy założeniu minimalizacji całkowitej miary uogólnionego przemieszczenia toru. Jako efekt uboczny można spodziewać się znacznej redukcji skojarzonej całkowitej miary dynamicznego przyrostu obciążenia powstającego pomiędzy torem a kołami pociągu.