Abstract: The principle of virtual displacements (PVDs) extended to elasto-thermo-electric problems includes virtual internal elastic, thermal and electric works. The governing equations have displacement vector, temperature and electric potential as primary variables of the problem, and the elasto-thermal, elasto-electric and pure elastic problems are obtained as particular cases by deleting the appropriate contributions in the general elasto-thermo-electric variational statement. The most sensitive issue is given by thermal coupling because the thermo-elastic and thermo-electric effects change depending on the type of load and analysis considered (mechanical load, temperature or electric potential imposed and free vibration analysis). This feature means that the form of the virtual internal thermal work in such variational statements changes depending on the analysis performed and the load applied. Results about multilayered plates and shells suggest the appropriate extension of the variational statement for each analysis, and they give an exhaustive explanation for several forms of the PVD proposed.

Key words: Principle of virtual displacements (PVDs), Variational statements, Elasto-thermo-electric problems, Multilayered structures, Virtual internal elastic work, Virtual internal thermal work, Virtual internal electric work

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