Anisotropic Composite Beams Research Articles

Geometrically nonlinear shape sensing of anisotropic composite beam structure using iFEM algorithm and third-order shear deformation theory

The inverse finite element method (iFEM) has been used to achieve the shape sensing of small displacements based on linear elastic theory. However, with the development of smart structure technology, the formulation is not suitable for the anisotropic composite structures with large deformation in practical engineering. Therefore, a nonlinear iFEM algorithm is proposed to monitor the linear and nonlinear deformation of the anisotropic composite beams. The formulation not only involves the effect of orientation of composite fibers on strain distribution into the shape sensing model, but also accounts for the effect of shear deformation without any requirement of shear correction factor. Initially, the third-order shear deformation theory (TSDT) is reviewed along with deriving the nonlinear strain field based on von-Karman strain theory. Considering the problem that the couple term of the shear strain and bending strain is unmeasurable, the relationship between shear and bending displacements is established according to the derived constitutive equations. Then, the proposed nonlinear iFEM method reconstructs the deformed structural shape, where isogeometric analysis (IGA) approach is used to construct the displacement functions and the experimental section strains are calculated from the discretized surface strains. Finally, several examples are solved to verify the proposed methodology. Numerical results demonstrate that the nonlinear iFEM algorithm can improve the reconstruction accuracy by 4% with respect to the linear iFEM method for beam structures. Hence, the proposed approach can be used as a viable tool to predict nonlinear deformation of composite structure.

A new model for thermal buckling of an anisotropic elastic composite beam incorporating piezoelectric, flexoelectric and semiconducting effects

A new model for thermal buckling of an anisotropic elastic composite beam incorporating piezoelectric, flexoelectric and semiconducting effects

Experimental Investigation of Bubble Migration near Anisotropic Beams.

In order to resist bubble loading, anisotropic composite materials are the development direction of the future. The objective of this paper was to experimentally investigate the hydrodynamic performance of anisotropic laminate composite plates, with a focus on the effect of its anisotropic characteristics on single bubble migration. In these experiments, the bubble was generated in a transparent water tank filled with sufficiently degassed water by Joule heating at the connecting point of the electrodes through the discharge of a 6600 μF charge to 800 V, and a high-speed camera system with a recording speed of 40,000 frames per second was used to record the temporal evolution of bubble patterns and the dynamic responses of the laminated composite plates. The results are presented for two anisotropic cantilever composite beams with different ply angles, namely, 0° and 30°. Several variables, such as the shapes of the bubble, the curved trail of motion of the bubble center, bubble collapse time, and bubble initial standoff distances were extracted from the photographic images. The results showed that bubble migration near the 30° plate presents a curved bubble trail with an evident tilted angle during the collapse and rebound stages, which is very different from bubbles that all move vertically above the 0° plate. Furthermore, a characterization method for bubble migration was proposed to quantitatively describe the curved bubble trails and the deformation of the composite beams in temporal and spatial scales. This method shows that the curved bubble trails near the 30° plate are closely related to the dynamic response of composite beams, with a focus on the bending-twisting coupling effect.

Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method

New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problems.

Closed form solutions for an anisotropic composite beam on a two-parameter elastic foundation

Beams resting on elastic foundations are widely used in engineering design such as railroad tracks, pipelines, bridge decks, and automobile frames. Laminated composite beams can be tailored for specific design requirements and offer a desirable design framework for beams resting on elastic foundations. Therefore, the analysis of flexural behaviour of laminated composite beams on elastic foundations is of important consequence. Exact solutions for flexural deflection of composite beams with coupling terms between stretching, shearing, bending and twisting, resting on two-parameter elastic foundations for various types of loading and boundary conditions, are presented for the first time. The proposed new formulation is based on Euler–Bernoulli beam theory having four degrees of freedom, namely bending in two principal directions, axial elongation and twist. Governing equations and boundary conditions are derived from the principle of virtual work and expressed in a compact matrix–vector form. By decoupling bending in both principal directions from twist and axial elongation, the fourth-order differential equation for bending is derived and transformed into a system of first-order differential equations. An exact solution of this system of equations is obtained using a fundamental matrix approach. Fundamental matrices for different configurations of elastic foundation are provided. The ability of the presented mathematical model in predicting flexural behaviour of beams on elastic foundations is verified numerically by comparison with results available in the literature. In addition, the deflection of anisotropic beams is analysed for different types of stacking sequences, boundary and loading conditions. The effect of elastic foundation coefficients on the flexural behaviour is also investigated and discussed.

Twist morphing of a composite rotor blade using a novel metamaterial

A novel meta-material has been designed and implemented into a rotor blade to enhance aerodynamic efficiency by achieving a passive twist during rotation. The twist is induced by bend-twist coupling exhibited in the meta-material, which is created to possess anisotropic elastic properties at the bulk level. A concept design of a rectangular blade spar is proposed where the metamaterial is used as the core material to induce twist. Using finite element analysis(FEA) we demonstrate how the bend-twist property of the blade spar is governed by cell geometries of the core material. The twist is activated by a lagwise bending moment generated from a movable mass at the blade tip due to off-centre centrifugal forces. The relationship between the twist, mass location and rotational speed has been explored. Moreover, it was found that the bend-twist property achieved by the proposed blade spar is more effective compared to that of an anisotropic thin-walled composite beam.

Geometrically nonlinear vibration of anisotropic composite beams using isogeometric third-order shear deformation theory

Due to broad usage of anisotropic composite beams in modern engineering structures, the main goal of the present work is to examine their geometrically nonlinear vibration. To this end, a third-order shear deformation theory with a nonlinear von-Kármán strain field is used for anisotropic beams and combined with the advantages of the isogeometric framework. The layup properties are assumed to be anisotropic in the depth direction and a transient tip follower force is considered. The governing nonlinear equations of vibration are integrated by means of the Newmark approach and solved with the Newton–Raphson method. Flutter loads as well as natural frequencies are obtained by eigenvalue analysis. The effects of various important factors such as non-prismatic shape, orientation of the composite fibers, critical follower force and bifurcation point are studied, using both h- and p-refinements. The results show that the nonlinear vibration and flutter characteristics of the anisotropic composite beams are completely different from those for orthotropic and isotropic ones. Thick beams with anisotropic layups are more sensitive to the shear parameter than conventional ones and deform primarily in shear mode rather than in bending. Anisotropic beams reveal a higher flutter instability force than other cases for a given shear parameter value. Another important phenomenon is that the stress distribution in anisotropic layups shows irregular patterns both in depth and time. Anisotropic layups with ply angles between 15° and 45° seem to present enhanced nonlinear performance with respect to other layup choices. A coarse mesh of quartic C3 B-splines is observed to provide high accuracy for nonlinear deflections in anisotropic cases even for rather low shear parameters.

Free Vibration of Composite Thin-Walled Beams with Chordwise Asymmetric Closed Cross-Sections

In this paper, some analytical results via extended Galerkin method on free vibration characteristics of an anisotropic composite beam, which is modeled as a nonuniform thin-walled structure with a chordwise asymmetric closed cross-section and corrected the warping functions, are newly presented. For this study, nonclassical parameters such as warping restraint, transverse shear flexibility, and structural couplings induced by two special configurations, such as circumferentially uniform stiffness (CUS) and circumferentially asymmetric stiffness (CAS), are incorporated. And also, design parameters of the beam associated with preset angles, pretwist angles, taper ratios, and section ratios are additionally investigated. The results of this study could play an important role in more efficient designs of composite thin-walled beams.

A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

Natural damped vibrations of anisotropic composite box beams. 1. Statement of the problem

Natural damped vibrations of anisotropic composite box beams. 1. Statement of the problem

Effect of the Transverse Shear Deformation on the Free Vibration of Rotating Blades Modeled as Thin-Walled Composite Beams

In this paper, vibration analysis of a blade modeled as an anisotropic composite thin-walled beam is carried out. The analytical formulation of the beam is derived for the flapwise bending, chordwise bending and transverse shear deformations. The equations of motion are solved by applying the extended Galerkin method (EGM) for anti-symmetric lay-up configuration that is also referred as Circumferentially Uniform Stiffness (CUS). Consequently, the natural frequencies are validated by making comparisons with the results in literature and it is observed that there is a good agreement between the results. Combined effects of transverse shear, fiber orientation, and rotational speed on the natural frequencies are further investigated.

Vibration-based delamination detection in composite beams through frequency changes

Delamination is a common damage in fibre reinforced composite laminates, usually hidden from external view, that can substantially reduce the structural stiffness which changes the dynamic response of the structures such as natural frequencies. Natural frequencies are the most reliable parameters for detecting damage while they do not directly provide information regarding its location and severity. To determine the location and severity of damage, it is necessary to solve the inverse problem using frequency shifts in multiple modes. In this paper, the graphical approach, which was previously employed for estimating two variables of crack (location and size) in isotropic beams, is extended in the current work to estimate the three variables of delamination (interface, span-wise location and size) in anisotropic composite beams from measured frequency shifts. Compared to the use of optimisation or neural network for detection, graphical technique is computationally inexpensive and quick since it solves the inverse problem without iterations or network training. The present approach has been validated using numerical simulation as well as experimental data from modal testing conducted on quasi-isotropic simply supported and cantilever beams. Results show that the proposed graphical technique can be used to assess the location and severity of delamination in composite beams with a high degree of accuracy.

Aeroelastic Stability and Response of Composite Swept Wings in Subsonic Flow Using Indicial Aerodynamics

In this study, the aeroelastic stability and response of an aircraft swept composite wing in subsonic compressible flow are investigated. The composite wing was modeled as an anisotropic thin-walled composite beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. Also, the structural model consists of a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsional model, and rotary inertia. The finite state form of the unsteady aerodynamic loads have been modeled based on the indicial aerodynamic theory and strip theory in the subsonic compressible flow. Novel Mach dependent exponential approximations of the indicial aerodynamic functions have been developed. The extended Galerkin’s method was used to construct the mass, stiffness, and damping matrices of the nonconservative aeroelastic system. Eigen analysis of the system was performed to obtain the aeroelastic instability (divergence and flutter) boundaries. Also, solving the equations of motion in the time domain leads to the aeroelastic response of wing in different flight speeds. The obtained results are compared with the available results in the literature, which reveals an excellent agreement. The numerical results obtained in this article seek to clarify the effects of geometrical and material couplings and flight Mach number on the aeroelastic instability and response of composite wings in subsonic compressible flow.

Exact Analysis of Postbuckling Behavior of Anisotropic Composite Slender Beams Subjected to Axial Compression

Buckling and postbuckling behavior of laminated composite slender beams is presented. The nonlinear model is introduced by using the exact expression of the curvature. The material of each layer of the beam is assumed to be linearly elastic. The formulations are based on Timoshenko’s stability theory including nonlinearity. A numerical solution of elliptical integral form is employed to determine buckling loads and postbuckling equilibrium paths of composite beams. Results from the proposed method are theoretically exact from small to very large curvatures and transverse and longitudinal displacements for slender beams under axial compressive loads. The numerical illustrations concern the postbuckling response of laminated beams with different types of boundary conditions, geometric parameters, and stacking sequences. The results reveal that the geometric parameters, boundary conditions, and stack sequences have a significant effect on the postbuckling behavior of laminated composite beams.

2-D analytical model for characterizing flexural damping responses of composite laminates

Abstract The flexural damping behaviors of composite laminates were characterized analytically in this study. A 2-D analytical model was developed based on the extension of Ni–Adams model [Ni RG, Adams RD. The damping and dynamic moduli of symmetric laminated composite beams—theoretical and experimental results. J Compos Mater 1984;18(2):104–21] accounting for the energy dissipation contributed by the laminar stresses of σxy and σyy. The specific damping capacity (SDC) of the composite was determined in accordance with the energy dissipation concept, which was defined as the ratio of the dissipated energy to the stored energy for per circle of vibration. The 2-D analytical model was validated by comparing the SDC of [0/−60/60]s and [0/90/45/−45]s laminates with the experimental data and the finite element (FEM) results. In addition, the effects of interlaminar stress on the flexural damping responses of laminated plates were also characterized in the 3-D FEM analysis. Results indicated that the interlaminar stress effect may not be so significant that the current 2-D model is adequate for the evaluation of the damping responses of the composite laminates. Furthermore, the present predictions, as compared to the Ni–Adams [Ni RG, Adams RD. The damping and dynamic moduli of symmetric laminated composite beams—theoretical and experimental results. J Compos Mater 1984;18(2):104–21] and Adams–Maheri [Adams RD, Maheri MR. Dynamic flexural properties of anisotropic fibrous composite beams. Compos Sci Technol 1994;50(4):497–514] models, generally demonstrate good agreements with the experimental data and the FEM results.

Dynamics of Composite Aircraft Wings Carrying External Stores

This paper focuses on the free vibration and dynamic response to external time-dependent loads of aircraft wings modeled as thin-walled anisotropic composite beams carrying eccentrically located heavy stores. In this context, bending-twisting coupling induced by both the eccentric heavy stores arbitrarily located along the wing span and chord and by the anisotropy of the constituent material that is essential when dealing with aircraft wing problems was included in the approach of the problem. In addition to the anisotropy of constituent materials, transverse shear and warping restraint effects were also incorporated. The governing equations of the wing-store system and the related boundary conditions are derived via Hamilton's principle. To solve the eigenvalue/boundary problems, the extended Galerkin method is applied. Numerical simulations highlighting the implications of external stores coupled with the implementation of the structural tailoring on eigenfrequency and dynamic response to external time-dependent loads are supplied and pertinent conclusions are outlined.

Aeroelastic instability of aircraft composite wings in an incompressible flow

Abstract The aeroelastic stability of an aircraft wing modeled as an anisotropic composite thin-walled beam in an incompressible flow is investigated. The wing is built-up as a single-cell box beam whose central point is noncoincident with the mid-chord of the profile. The effects of material anisotropy, transverse shear, warping inhibition, nonuniform torsional model and rotary inertia are considered in the structural model. The unsteady incompressible aerodynamics based on Wagner’s function is used to determine the aerodynamic loads. The effects of the offset between reference axis and the mid-chord (“ a ” parameter), fiber orientation and sweep angle on stability boundary are considered, their effects on the stability boundary are discussed and a number of important conclusions are drawn.

Local buckling of wide-flange thin-walled anisotropic composite beams

The present contribution deals with the onset of local buckling of compressively loaded thin-walled beams with open I, C, Z, T and L-cross-sections made of laminated composite materials. The method employs a discrete plate analysis approach in the course of which each structural subelement of interest—which presently is the flange—of the thin-walled cross-section is considered as a separate composite plate with elastic rotational restraints at those edges where an adjacent substructural element is located. While in many investigations the lamination schemes of webs and flanges are considered to be purely orthotropic, in the present paper the laminate layups are allowed to be of an arbitrary non-orthotropic nature, which also allows for the analysis of laminates with inherent bending–torsion coupling. The analysis of the buckling loads of the flanges of thin-walled composite beams is performed using the Ritz-method for which some especially adjusted displacement shape functions are employed. For the case of pure orthotropy, a novel closed-form solution is described. The accuracy of the employed approaches is established by comparison with accompanying finite element simulations of thin-walled composite beams. It is revealed that the presented methodology is highly efficient in terms of computational effort and yet performs with satisfying accuracy, which makes it very attractive for actual practical applications whenever the local stability behaviour of wide-flange thin-walled composite beams is to be considered.

Implications of warping restraint on statics and dynamics of elastically tailored thin-walled composite beams

Static response and free vibration of elastically tailored thin-walled beams accounting for the warping restraint effect are investigated via an exact solution methodology within the context of a refined beam model. Analytical results obtained from the restrained warping model are compared with those based on its Saint–Venant model counterpart. It is revealed that the beam slenderness and thickness ratio, as well as the elastic anisotropy, considered in conjunction with the warping restraint have profound effects on the static and dynamic response characteristics. It is also shown that even for anisotropic composite thin-walled beams with high slenderness ratios, warping restraint can still be significant, implying the inadequacy of merely considering the geometric aspects in the modeling of anisotropic composite thin-walled beams.

Aeroelastic instability of aircraft wings modelled as anisotropic composite thin-walled beams in incompressible flow

An encompassing aeroelastic model developed toward investigating the influence of directionality property of advanced composite materials and non-classical effects such as transverse shear and warping restraint on the aeroelastic instability of composite aircraft wings is presented. Within the model developed herein, both divergence and flutter instabilities are simultaneously addressed. The aircraft wing is modelled as an anisotropic composite thin-walled beam featuring circumferentially asymmetric stiffness lay-up that generates, for the problem at hand, elastic coupling among plunging, pitching and transverse shear motions. The unsteady incompressible aerodynamics used here is based on the concept of indicial functions. Issues related to aeroelastic instability are discussed, the influence of warping restraint and transverse shear on the critical speed are evaluated, and pertinent conclusions are outlined.