Variational Statements and Computational Models for MultiField Problems and Multilayered Structures

Abstract

This work deals with classical and mixed variational statements for the analysis of layered structures under the effect of four different fields: mechanical, thermal, electrical and magnetic. Constitutive equations, in terms of coupled mechanical-thermal-electrical-magnetic filed variables, are obtained on the basis of a thermodynamics approach. The Principle of Virtual Displacements (PVD) and the Reissner's Mixed Variational Theorem (RMVT) are employed. The latter permits interlaminar variables, such as transverse stresses, transverse electrical displacements, etc. to be assumed “a priori.” A number of particular cases of the considered variational statements are proposed. A new condensed notation is introduced into the Unified Formulation (UF) framework, which leads to governing equations and finite element matrices in terms of a few fundamental nuclei. The Finite Element (FE) case for multilayerd plates has been addressed. Variable kinematics, as well as layer-wise and equivalent single layer descriptions have been implemented for the considered FEs according to UF. A few results show the effectiveness of the proposed approach.

Keywords:

• multifield problems
• multilayered plates
• classical and mixed methods
• unified formulation

Acknowledgments

This work has been carried out in the framework of STREP EU project CASSEM under contract NMP-CT-2005-013517. The partial support of European Space Agency (ESTEC-Contract No. 21082/06/NL/PA) is also acknowledged.

Notes

To be noticed that δ u ₁, δ u ₂, δ u ₃ come from the strain δ ε, δ φ from δ E and δ ϕ from δ H.