A general formulation for the reduction of the three-dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented The dimensional reduction is based on a variationalasymptotic formulation, using the slenderness ratio as small parameter In the proposed scheme, the coupled linear electroelastic equations are solved at the cross-sectional level using the finite element method Furthermore, modal components of the displacement field are added to introduce arbitrary deformation shapes into the onedimensional analysis, and arbitrary electric modes are used to define applied electric fields at the cross section This results in a general definition of a coupled electroelastic stiffness, which can be used in virtually all composite and active beam formulations, as well as in the development of new low-order high-accuracy reduced models for active structures Finally, the formulation also yields recovery relations for the elastic and electric fields in the original three-dimensional solid, once the one-dimensional problem is solved The method has been implemented in a computer program (UM/VABS) and numerical results are presented for active anisotropic beam cross sections of simple geometries, which are shown to compare very well with three-dimensional finite element analysis

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/76969/AIAA-12451-957.pdf;sequence=1

Cross-sectional analysis of nonhomogeneous anisotropic active slender structures

In this article, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has bee...

Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate:

Improved shell finite element for piezothermoelastic analysis of smart fiber reinforced composite structures

Coupled electro-thermo-elastic equations applicable for the analysis of smart structures with piezoelectric patches/layers have been derived from the fundamental principles of mass, linear momentum, angular momentum, energy and charge conservation. The relevant constitutive equations have been obtained by using the second law of thermodynamics. The interaction of the electric field and polarization introduces distributed non-linear body force in the piezo material, and in addition renders the stress tensor non-symmetric due to distributed couple. Using the linear equations, and applying a layer-by-layer finite element model, the induced electric potential and mechanical deformations in the piezo and non-piezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical, electrical and thermal loadings. The mathematical formulation and the solution technique have been validated by comparing the results of the present study with those available in the literature. It is also shown that piezo patches can be effectively used for shape control.

https://iopscience.iop.org/article/10.1088/0964-1726/15/2/021/pdf

Electro-thermo-elastic formulation for the analysis of smart structures

In this paper some variational principles are revisited for the fundamental equations of a regular region of piezoelectric, thermopiezoelectric, and hygrothermopiezoelectric (but non-stochastic, non-local, and non-relativistic) materials in the elastic range. Certain oversights, and especially, those involving the so-called Hu-Washizu variational principle of piezoelectricity that was first formulated in a paper (“Variational Principles in Piezoelectricity,” Lettere Al Nuovo Cimento, vol. 7, 449–454, 1973) are clarified within the “ISI-Web of Science” publications in the open literature. Similar variational principles of piezoelectricity are cited.

Variational Principles for Piezoelectric, Thermopiezoelectric, and Hygrothermopiezoelectric Continua Revisited

Coupled electrothermoelastic equations applicable to the analysis of smart structures have been derived from first principles. Using the equations and applying a layer-by-layer finite element model, the induced potential and mechanical deformations in the piezo and nonpiezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical load and actuation potential. The present study clearly brings out the essential difference between sensing and actuation. It is also brought out that the interaction between polarization and electric field in the piezo continuum leads to nonlinear distributed body force and nonsymmetric stress tensor. These nonlinear effects are found to have significant influence on the deformation of a smart beam under actuation. Shape control studies of multipatch smart beams have also been investigated.

Linear and Nonlinear Analysis of a Smart Beam Using General Electrothermoelastic Formulation

Using laws of conservation, a general electrothermoelastic formulation has been developed for the analysis of smart structures Based on this formulation a layer-by-layer finite element model has been developed using variational principle It is shown that the layer-by-layer finite element modeling effectively captures the continuity of shear stress across the interface between piezolayers and the metallic host material Several studies of actuation and sensing of single and multipatch smart beams have been carried out The key difference between actuation and sensing has been brought out with regard to the variation of shear stress along the span at interfaces between piezopatch and the core In addition, the influence of electric field along the span of a piezo cantilever beam has been studied, and it is shown that this electric field produces a large transverse shear stress resulting in a steplike deformation of the piezobeam It is envisaged that this concept can be used to develop a switch in a microelectromechanical-system device

Electroelastic analysis and layer-by-layer modeling of a smart beam

Mechanical and tribological behavior of TiB2/ Al2O3 coating on high-speed steel using electron beam deposition

Abstract In this study, Zn–Ni–Cu and Zn–Ni–Cu–TiB2 coatings were deposited using high-velocity oxy-fuel (HVOF) thermal spray technique on a mild steel substrate. Corrosion tests like neutral salt spray (NSS) following (ASTM B-117) standard and immersion cycle test following ASTM G-31, ASTM G1-03, standards were carried out for Zn–Ni–Cu and Zn–Ni–Cu–TiB2 coated mild steel along with uncoated mild steel acting as a control. Both Zn–Ni–Cu and Zn–Ni–Cu–TiB2 coated mild steel were corrosion resistant as compared to uncoated mild steel. Raman analysis following the immersion cycle test inferred that uncoated mild steel had all forms of rust. While Zn–Ni–Cu and Zn–Ni–Cu–TiB2 coated mild steel developed very little rust. The characterization helped to understand the changes in the surface before and after tests. It was observed that both Zn–Ni–Cu and Zn–Ni–Cu–TiB2 coated mild steel had little corrosion degradation of surface as compared to uncoated mild steel. Suggesting that both coatings performed significantly better compared to uncoated mild steel in corrosive environments. Polarization and EIS tests of both coated and uncoated mild steel in a 3.5% NaCl medium helped to understand the behaviour of coatings over a range of frequencies. Both coated samples had high polarization potential Ecorr values and lower polarization current Icorr values as compared to uncoated mild steel. Inferring better performance of coatings in corrosive environments as compared to uncoated mild steel.

Sheikh N. Ahmad

Papers

Electro-thermo-elastic formulation for the analysis of smart structures

Linear and Nonlinear Analysis of a Smart Beam Using General Electrothermoelastic Formulation

Electroelastic analysis and layer-by-layer modeling of a smart beam

Mechanical and tribological behavior of TiB2/ Al2O3 coating on high-speed steel using electron beam deposition

Corrosion behaviour OF HVOF deposited Zn–Ni–Cu and Zn–Ni–Cu–TiB2 coatings on mild steel