Fibre Bragg grating (FBG) strain sensors are not only a very well-established research field, but they are also acquiring a bigger market share due to their sensitivity and low costs In this paper we review FBG strain sensors with high focus on the underlying physical principles, the interrogation, and the read-out techniques Particular emphasis is given to recent advances in highly-performing, single head FBG, a category FBG strain sensors belong to Different sensing schemes are described, including FBG strain sensors based on mode splitting Their operation principle and performance are reported and compared with the conventional architectures In conclusion, some advanced applications and key sectors the global fibre-optic strain sensors market are envisaged, as well as the main market players acting in this field

Fibre Bragg Grating Based Strain Sensors: Review of Technology and Applications.

for the force on a dielectric in an electrical field E and bounded by a surface S with unit normal n. He used an operational \"definition\" of stress and concluded that the compensating mechanical forces which must be introduced operationally are not derivable from a tensor. It is suggested here that Slepian's analysis is essentially correct and that the difficulty arises because of the choice of an operationally \"defined\" stress. This choice is inconsistent with the existence of an electrical surface stress-which is familiar, in the magnetic analogue, in studies of the form effect-and it is argued here that the Euler-Cauchy definition of stress is the appropriate one. The Definition of Stress.-In authoritative works on continuum mechanics stress is introduced by means of the stress hypothesis of Euler and Cauchy,2 that is, by asserting that, acting upon any imagined closed geometrical surface a within the body, there exists a field of stress vectors t which has an equivalent effect to the (interparticle) forces exerted by the material outside aupon the material within. For a dielectric material the interaprticle (i.e., intermolecular) forces are partly long-range in character and they may therefore contribute not only to t but also to f, the body force per unit volume. For the present purpose, however, the important point to note is that ais an imagined geometrical surface and not a physical surface of separation within the material. An alternative procedure is to use the operational definition of stress in which it is imagined that a physical cut is made in the material along an internal element of surface dd = nda. If means are then introduced for keeping the strains in the material on both sides of the cut the same as they were before the cut was made, then the force introduced by these means is t'do-, where t' is the operationally defined stress vector. In adopting this operational definition, Slepian commented: \"It is not assumed that the cut and the introduced means do not disturb the microstructure and micromechanics of the material. For example, in the case of a fluid the cut and means would cause molecules to be reflected which would otherwise pass through the geometric element of surface dS. It is assumed, however, that in spite of the change in the micromechanics, there is no change in the observable macromechanics.\"' It may also be noted there is a further element of idealization involved in that the cut is imagined to be of finite extent: in practice, as discussed later in this paper, it is only possible to measure the force on an element of volume when the element is completely separated from the rest of the body. For an ordinary elastic material the stress acting at a physical surface of separa-

The elastic dielectric.

The static bending and buckling behaviors of bi-directional functionally graded (BFG) plates with porosity are investigated in this paper. An improved first-order shear deformation theory with an assuming parabolic distribution shear stresses is developed to describe the displacement, strain, and stress fields of the plates. The significant novelty of the proposed theory is that the transverse shear stresses equal to zero at two free surfaces of the BFG plates. Therefore, no shear correction factor is required as in other first-order shear deformation theory. A four-node quadrilateral plate element (IMQ4) is developed based on the improved first-order shear deformation theory, mixed finite element method (FEM) and Hamilton's principle for analysis of BFG plates. Several comparison studies are provided to demonstrate the precision and robustness of the proposed plate element IMQ4. Then the proposed plate element, IMQ4, is employed to analyze the bending and buckling responses of the BFG plates. Some new numerical results on the flexural and buckling behaviors of BFG plates are achieved via a deep parametric study. 

Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM

Modified couple stress-based geometrically nonlinear oscillations of porous functionally graded microplates using NURBS-based isogeometric approach

This paper is concerned with a geometrically non-linear solid shell element to analyse piezoelectric structures. The finite element formulation is based on a variational principle of the Hu-Washizu type and includes six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has eight nodes with four nodal degrees of freedoms, three displacements and the electric potential. A bilinear distribution through the thickness of the independent electric field is assumed to fulfill the electric charge conservation law in bending dominated situations exactly. The presented finite shell element is able to model arbitrary curved shell structures and incorporates a 3D-material law. A geometrically non-linear theory allows large deformations and includes stability problems. Linear and non-linear numerical examples demonstrate the ability of the proposed model to analyse piezoelectric devices.

/pdf/a-geometrically-non-linear-piezoelectric-solid-shell-element-3htwix0y4c.pdf

A geometrically non‐linear piezoelectric solid shell element based on a mixed multi‐field variational formulation

Taking the von Karman geometrically nonlinearity into account, this paper presents a nonlinear finite element formulation of axially functionally graded(AFG) tapered microbeams, which is based on the modified couple stress and Euler–Bernoulli beam theory. The profiles of physical parameters such as elasticity modulus and mass density of the microbeam are assumed to be a simple power-law form along the length direction, while either width or height of the beam changes linearly in axial direction. The size-dependent nonlinear free vibration of AFG non-uniform microbeams is analyzed by using finite element simulation. The correctness of the present analysis is validated by comparing computed results with those available for AFG tapered beams. The effects of vibration amplitude, variation of the taper ratio in cross section and gradient index of material along the length and material length scale parameter as well as boundary conditions on nonlinear fundamental frequency are discussed.

Size dependent nonlinear free vibration of axially functionally graded tapered microbeams using finite element method

In the present paper, a novel refined hybrid piezoelectric element formulation is developed for mechanical analysis and active vibration control of laminated structures bonded to piezoelectric sensors and actuators. By invoking the electrical field potential equation, a 'quasi-decoupling' method for treating the coupling electromechanical effects is presented and a modified generalized variational principle with a weaker interelement continuity condition is proposed. On the basis of this functional, a general formulation for a refined hybrid piezoelectric element method is established by incorporating an orthogonal interpolation approach and enhanced assumed strain (EAS) modes. A linearly distributed transverse EAS in the thickness direction is adopted to overcome the thickness locking of solid shell elements. Compared with the conventional incompatible brick element approach, the present formulation is very reliable, more accurate, computationally efficient and can be used to model the response of thin plates and shell structures.

https://iopscience.iop.org/article/10.1088/0964-1726/13/4/N02/pdf

The formulation of a refined hybrid enhanced assumed strain solid shell element and its application to model smart structures containing distributed piezoelectric sensors/actuators

Based on the Timoshenko beam theory, von Karman geometric nonlinearity assumption and the modified couple stress theory, this paper presents linear and nonlinear free vibration analysis of rotating two-dimensional functionally graded micro-beam with even and uneven porous distributions. The material properties vary along the axial and thickness directions. The NURBS function is employed as the basic one to overcome the inherent difficulty of constructing higher order continuous displacement function for modified couple stress theory based finite element formulation. The validity of the present simulation is validated by comparing numerical results with those available literatures for rotating functionally graded micro-beams. Finally, the effects of several parameters such as porosity, power law index, material length scale parameter, rotational speed and hub radius on dimensionless frequencies and nonlinear frequency ratios are discussed.

Nonlinear free vibration analysis of a rotating two-dimensional functionally graded porous micro-beam using isogeometric analysis

Based on the first-order shear deformation theory (FSDT) as well as isogeometric analysis (IGA), the static bending, free vibration and buckling analysis of porous bi-directional functionally graded (BDFG) plates are investigated in this paper. The bi-directional gradients vary along the thickness (z-) and x-axis directions according to the power law, and porosity distributions are divided into even and uneven types. With the help of Hamilton principle, the governing equations of porous BDFG plates are derived. Compared with other reported literatures, several examples reveal that the accuracy and convergence of the present IGA model utilizing cubic non-uniform rational B-splines (NURBS). The effects of aspect ratios, boundary conditions, porosity distributions and coefficients on static bending, free vibration and buckling analysis of porous BDFG plates are studied in detail. These results show that increasing the volume fraction of porosity makes considerable effects on the mechanical behaviors of porous BDFG plates. Moreover, the deflections, frequencies and buckling loads of BDFG plates with even porosity are quite sensitive to the variation of porosity coefficients.

Porosity-dependent isogeometric analysis of bi-directional functionally graded plates

In this paper, based on the strain gradient theory, a size-dependent porous axially functional gradient (AFG) flexoelectric Euler-Bernoulli nanobeam model is developed. A modified power-law formula incorporating porosity volume fraction is presented to describe material properties of porous AFG nanobeam, and two typical porosity distributions patterns are considered. The generalized differential quadrature method is employed to discretize governing equations into a series of linear algebraic equations, so that the static bending deflections and free vibration frequencies are calculated conveniently for various boundary conditions. The credibility of the present mathematical formulation and the associated numerical solution are validated by comparing the results in previous literatures. Parametric studies are performed to illustrate the effects of the flexoelectricity, material length scale parameters, functionally graded index, porosity volume fraction, porosity distribution patterns on the static bending and free vibration behaviors of porous AFG flexoelectric nanobeam. The numerical results may provide support for the application of porous AFG flexoelectric nanobeam in Nano-electro-mechanical system.

Shijie Zheng

Papers

Size dependent nonlinear free vibration of axially functionally graded tapered microbeams using finite element method

The formulation of a refined hybrid enhanced assumed strain solid shell element and its application to model smart structures containing distributed piezoelectric sensors/actuators

Nonlinear free vibration analysis of a rotating two-dimensional functionally graded porous micro-beam using isogeometric analysis

Porosity-dependent isogeometric analysis of bi-directional functionally graded plates

Effects of porosity and flexoelectricity on static bending and free vibration of AFG piezoelectric nanobeams