Examples Of Laminates Research Articles

Coupling four-parameters bond-based peridynamic and finite elements for damage analysis of composite structures

The difficulty in inferring the failure region is the main obstacle for applying coupling algorithms for progressive damage analysis of composite structures. This paper presents a new finite element and peridynamic (PD) coupling framework, in which an adaptive transformation technique is implemented for failure analysis of laminated structures. Since the mechanical properties of a multi-layer laminate can be characterized by single-layer finite elements, this coupling model (CM) exhibits great potential in balancing numerical accuracy and computational efficiency. During the damage evolution process, the single-layer finite element is adaptively transformated into multi-layer PD material points according to the transformation criterion as the load increases, and then the damage begins to nucleate and evolve in the PD subregions. Compared with other coupling models, the PD subregions adaptively appear in the potential failure sites, and its area is much smaller than other finite element subregions. Thus, the theoretical advantages of coupling algorithms in modeling multi-layer structures can be fully utilized, and the computational efficiency of numerical models will be greatly improved. The accuracy of the developed coupling model is demonstrated by the stretching example of composite laminates, and the damage examples of laminates with a cutout further demonstrates the strong capability of the proposed coupling model in capturing the failure characteristics.

Detecting laminate damage using embedded electrically active plies – An analytical approach

Assessment of damage initiation and progression in composite laminates with embedded electrically active plies is modeled. Utilizing electrically active layers embedded in composite laminates as damage sensors is proposed by several researchers and is mainly assessed experimentally. Sensing damage using embedded electrically active plies is generally preferred over the use of surface mounted PZT wafers since the range of the latter is limited to a very narrow area underneath the surface, while multiple damage mechanisms can generally be found in several plies of the laminate.The solution presented invokes two levels of analysis. Firstly, on the laminate level, applied membrane loads and/or bending moments induce stresses in the plies according to some distribution factors, which depend on the elastic properties and thickness fractions of the plies. To obtain these factors, the conventional lamination theory is implemented. Secondly, on the ply level, each unidirectional composite ply, whether electrically active or inactive, is modeled using the Mori-Tanaka averaging model. Both the fiber and matrix stresses are computed and a response in the form of electrical displacement is found in the electrically active plies. Upon damage in certain plies, some eignstresses are applied such that the stress components, which invoke the damage criteria vanish. These eignstresses affect not only the failed plies but also other plies and subsequently the overall behavior of the laminate. Deviations in the electric response of electrically active plies from that found in the undamaged state serves as a damage detector.This paper outlines a transformation field methodology which implements the above formulation and shows examples for laminates subjected to bending moments. Variation of the electric displacement with the progression of damage is examined in terms of the location of the electroactive ply within the laminate thickness.

Exact Solution of the Elastica with Transverse Shear Effects

A new derivation of Euler's Elastica with transverse shear effects included is presented. The elastic potential energy of bending and transverse shear is set up. The work of the axial compression force is determined. The equation of equilibrium is derived using the variation of the total potential. Using substitution of variables an exact solution is derived. The equation is transcendental and does not have a closed form solution. It is evaluated in a dimensionless form by using a numerical procedure. Finally, numerical examples of laminates made of composite material (fiber reinforced) and sandwich panels are provided.

Reliability and Sensitivity Analysis of Laminate Using Different Methods

Reliability of laminate structure is deeply influenced by uncertainties such as fiber properties, loads and design sizes. It is very difficult to evaluate the reliability and sensitivity of laminate structure because that laminate structure is anisotropic and the limit state function (LSF) is a high nonlinear function. In this paper, reliability and sensitivity are evaluated by using first order reliability method (FORM), response surface method (RSM) and Monte Carlo simulation (MCS). The study aims to find a numerical method to evaluate the reliability and sensitivity of laminate structures efficiently and accurately. An example of laminate with a large number of variables is analyzed. The results obtained by using different methods are compared in terms of efficiency and accuracy. It is shown that FORM is not accuracy, and RSM has a very good accuracy and efficient in terms of reliability, but the accuracy of sensitivity obtained by using RSM is not good enough.

Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions

The thickness vibrations of a finitely deformed infinite periodic laminate made out of two layers of dielectric elastomers is studied. The laminate is pre-stretched by inducing a bias electric field perpendicular to the layers. Incremental time-harmonic fields superimposed on the initial finite deformation are considered next. Utilizing the Bloch-Floquet theorem along with the transfer matrix method we determine the dispersion relation which relates the incremental fields frequency and the phase velocity.Ranges of frequencies at which waves cannot propagate are identified whenever the Bloch-parameter is complex. These band-gaps depend on the phases properties, their volume fraction, and most importantly on the electric bias field. Our analysis reveals how these band-gaps can be shifted and their width can be modified by changing the bias electric field. This implies that by controlling the electrostatic bias field desired frequencies can be filtered out. Representative examples of laminates with different combinations of commercially available dielectric elastomers are examined.

Designing quasi-isotropic laminates with respect to bending

A calculation method for laminated composites with quasi-isotropic bending stiffnesses is presented. In contrast to existing treatises concerning quasi-isotropic laminate configurations this method includes the utilisation of different ply materials and thicknesses in the laminate design process. A diagram is derived, which facilitates, in a simple manner, the design of quasi-isotropic laminates with respect to their bending stiffnesses. Examples of laminates with quasi-isotropic bending stiffnesses are presented, which do have less than half the number of plies of isotropic laminates (16 plies or 12 plies, respectively). Based on the same method the corresponding diagram for quasi-isotropic laminates with respect to extensional stiffnesses is presented and some examples of these laminates are given.

Just How Good are Knitted Fabrics

Knitted fabrics have been available in the FRP market for over a decade. Although the market share of these fabrics has been steadily increasing, incomplete understanding often leads to inefficient or improper use of the materials. Examples of lam inates for several different applications comparing the use of traditional reinforcement fabrics with equivalent laminates using knitted fabrics are presented to illustrate the proper use of knitted fabrics and the trade-offs of cost, weight, stiffness and strength.

Boundary beam characteristics orthonormal polynomials in energy approach for vibration of symmetric laminates — I: Classical boundary conditions

An investigation on the effects of boundary constraints on the vibratory characteristics of symmetrically laminated rectangular plates is carried out. The research findings are reported in a two-part paper. Vibration frequency parameters and mode shapes for symmetric laminates with classical boundary conditions are reported in Part I and elastically restrained boundaries in Part II. The analysis is performed based on the use of admissible beam characteristics orthonormal polynomial functions in the Rayleigh-Ritz method to derive the governing eigenvalue equation. In this paper, several examples for laminates with different combinations of free, simply supported and clamped edges are solved to demonstrate the accuracy and flexibility of the present method. Discussion on the effects of boundary conditions, fiber orientations and stacking sequences on the vibrational response is included.