Anti-symmetric Lay-up Research Articles

Dynamic analysis of a laminated composite plate coupled with a piezoelectric energy harvester and traversed by a moving vehicle

The dynamic analysis is carried out of a laminated composite plate coupled with a piezoelectric energy harvester under the action of a moving vehicle. The finite element method along with Newmark’s method are applied to solve the discretized equations. Results are presented for two main cases: (i) free and forced vibrations of the laminated composite plate with no harvester and (ii) forced vibrations of the plate coupled with the energy harvester. Several parameters – such as the symmetric and anti-symmetric layups, length of the harvester, and piezoelectric material parameters – are considered to study their effects on the electrical output.

Analytical study of thermal buckling and post-buckling behavior of composite beams reinforced with SMA by Reddy Bickford theory

Shape memory alloys are used in composite structures due to their shape memory effect and phase transformation. The recovery force of the shape memory alloy improves the post-buckling behavior of the structure. In this study, the thermal buckling and post-buckling of Shape Memory Alloy (SMA) hybrid composite laminated beam subjected to uniform temperature distribution is investigated. To this purpose, considering Von-Karman non-linear strain terms for large deformation, the non-linear equations of SMA reinforced beam based on Reddy Bickford theory have been derived. Besides, the recovery stress of the restrained SMA wires during martensitic transformation was calculated based on the one-dimensional constitutive law of the Brinson’s model. A numerical solution using Galerkin’s method has been presented for solving the nonlinear partial differential equations to obtain the critical buckling temperature and transverse deformation of the beam in the post-buckling region in both symmetric and anti-symmetric layups. The effect of SMA volume fraction, pre-strain, the boundary condition of the beam, stacking sequence, and its geometric properties have been studied. The results show that even by adding a small amount of SMA to the composite, the critical buckling temperature increases significantly, and the beam deflection decreases. Besides, using this theory has an evident effect on the anti-symmetric layup, especially for the thick beams.

Free vibration analysis of rectangular sandwich plates with compressible core and various boundary conditions

Extended higher-order sandwich plate theory is used to analyze the free vibrations of rectangular sandwich plates with compressible core. Accordingly, first-order shear deformation theory is used to model the laminated face sheets. Besides, the in-plane and transverse displacements of the core are assumed to be cubic and quadratic functions of the thickness coordinate, respectively. To deduce the governing equations, Hamilton’s principle is used. Then, based on the Rayleigh-Ritz method, single series expansions with two-variable orthogonal polynomials – namely, the orthogonal plate functions – are considered to approximate the displacement components. Lastly, a generalized eigenvalue problem is solved to obtain the free vibrational characteristics of sandwich plates with both symmetric and anti-symmetric lay-ups subjected to various boundary conditions. The method is validated against the results obtained by different methods in the literature. Finally, the effects of the plate side-to-thickness ratio, in-plane aspect ratio, and core-to-face sheets thickness ratio on the natural frequencies are discussed.

The Effect of Non-Conservative Compressive Force on the Vibration of Rotating Composite Blades

This paper investigates the effectiveness of a resonance avoidance concept for composite rotor blades featuring extension–twist elastic coupling. The concept uses a tendon, attached to the tip of the blade, to apply a proper amount of compressive force to tune the vibration behavior of the blade actively. The tendon is simulated by applying a non-conservative axial compressive force applied to the blade tip. The main load carrying part of the structure is the composite spar box, which has an antisymmetric layup configuration. The nonlinear dynamic behavior of the composite blade is modelled by using the geometrically exact fully intrinsic beam equations. The resulting nonlinear differential equations are discretized using a time–space scheme, and the stationary and rotating frequencies of the blade are obtained. It is observed that the proposed resonance avoidance mechanism is effective for tuning the vibration behavior of composite blades. The applied compressive force can shift the frequencies and the location at which the frequency veering take place. Furthermore, the compressive force can also cause the composite blade to get unstable depending on the layup ply angle. Finally, the results, highlighting the importance of compressive force and ply angle on the dynamic behavior of composite blades, are presented and discussed.

Experimental study of multi-stable morphing structures actuated by pneumatic actuation

In this paper, we proposed a new pneumatic actuation method inspired from a soft robot, which could drive the multi-stable carbon fiber-reinforced polymer (CFRP) structure transition among five stable configurations under air pressure. Multi-stable structure was manufactured by the carbon fiber prepreg laid in asymmetrical and anti-symmetric layup methods and stacked at the joint during the preparation process according to the designed scheme. In experiments, multi-stable structures with two different fibers layups were prepared to study the snap-through behaviors. The snap-through process of two kinds of multi-stable structures was investigated by experiment. The parameters used to characterize efficiency of the pneumatic actuator actuating the multi-stable structures, including air pressure and snap time, were measured. The influence of the pneumatic actuator on the curvature of multi-stable structures was discussed by comparing the shape characteristic of multi-stable structures with or without pneumatic actuation, and it showed pneumatic actuator has little effect to the structure. The results demonstrated that the proposed pneumatic actuation could be used to drive multi-stable morphing structure flexibly. The combination of multi-stable laminates develops the function of multiple point bending and shape retention of pneumatic actuation.

A thermo-mechanical stress prediction improvement of using the classical lamination theory via Saint-Venant’s principle for laminated composite plates

Saint-Venant’s principle was introduced as the principle of the stress resultant equivalence for one dimensional structures, such as beams, cylindrical and prismatic structures. According to the principle, the stress distributions may be different around the area where forces are applied, but their resultants are invariant. In this paper, we apply the Saint-Venant’s principle to improve the thermomechanical stresses calculated by the Classical lamination theory (CLT). First we solve the CLT for laminated composite plates, calculate the transverse shear stresses using three-dimensional stress equilibrium equations, and obtain the improved displacement field with perturbation terms via transverse shear constitutive equations. At this point, these perturbation terms are unknown, which can be determined by applying the stress resultant equivalence (or the Saint-Venant’s principle). Once the terms are calculated, the improved displacements and stresses are obtained. To verify the accuracy of the proposed approach, simply-supported plates under mechanical and/or thermal loadings are taken as a test-bed, in which symmetric and anti-symmetric cross-ply layups are considered. The results obtained are compared to those of three-dimensional elasticity as well as first-order shear deformation theory. Finally the errors induced by the present approach are systematically analyzed in terms of the stress resultants.

Study on bi-stable behaviors of un-stressed thin cylindrical shells based on the extremal principle

Bi-stable structure can be stable in both its extended and coiled forms. For the un-stressed thin cylindrical shell, the strain energy expressions are deduced by using a theoretical model in terms of only two parameters. Based on the principle of minimum potential energy, the bi-stable behaviors of the cylindrical shells are investigated. The results indicate that the isotropic cylindrical shell does not have the second stable configuration and laminated cylindrical shells with symmetric or antisymmetric layup of fibers have the second stable state under some confined conditions. In the case of antisymmetric laminated cylindrical shell, the analytical expressions of the stability are derived based on the extremal principle, and the shell can achieve a compact coiled configuration without twist deformation in its second stable state. In the case of symmetric laminated cylindrical shell, the explicit solutions for the stability conditions cannot be deduced. Numerical results show that stable configuration of symmetric shell is difficult to achieve and symmetric shell has twist deformation in its second stable form. In addition, the roll-up radii of the antisymmetric laminated cylindrical shells are calculated using the finite element package ABAQUS. The results show that the value of the roll-up radii is larger from FE simulation than from theoretical analysis. By and large, the predicted roll-up radii of the cylindrical shells using ABAQUS agree well with the theoretical results.

Exact solution of thermal buckling and post buckling of composite and SMA hybrid composite beam by layerwise theory

The thermal buckling and post-buckling behavior of laminated composite beam reinforced with Shape Memory Alloy (SMA) wires is explored. The thermo-mechanical behavior of embedded SMA wires is formulated based on one-dimensional Brinson SMA model. Using a variational approach, the Layer-Wise Theory (LWT) of beams is employed to develop the governing equations. The von Karman strain–displacement relations are used to account for the large deflection effects. A closed-form solution of the resulting systems of nonlinear equations is represented. Exemplary case studies are assessed by comparing with available literature. Considering symmetric and antisymmetric layups, the influence of thickness/span ratio, degree of anisotropy, SMA pre-strain and volume fraction upon the buckling and post-buckling of thick composite and hybrid composite beams are examined and discussed in detail.

Elastic-damage deformation response of fiber-reinforced polymer composite laminates with lamina interfaces

The single-layer and multi-layer finite element models are developed and examined for adequacy in predicting the elastic-damage response of fiber-reinforced polymer composite laminates. A new experimental-computational approach featuring a two-tier mesh convergence analysis of the finite element models is developed. A 12-ply carbon fiber-reinforced polymer composite laminate beam specimen with anti-symmetric layups is designed and loaded to induce matrix damage under significant deflection without catastrophic fracture. A constitutive model incorporating Hashin’s equations for damage initiation criteria, along with an energy-based damage propagation law is employed in the finite element simulation. The results shows that the multi-layer finite element model predicts well the load–deflection curve of the carbon fiber-reinforced polymer composite laminate, while the single-layer model overestimates the elastic flexural stiffness of the specimen by 47 %. During the flexural deformation, matrix damage initiates in the central and edge regions of the critical laminas under compressive and tensile stresses, respectively. The multi-layer finite element model also predicted the matrix-induced interface delamination along the edges of the critical laminas under tension, as observed experimentally. The model demonstrates the adequacy in representing the role of lamina interface in dictating the elastic-damage response of carbon fiber-reinforced polymer composite laminates manufactured by prepreg layups method.

Experimental study on the effect of interface fiber orientation and utilized delamination initiation techniques on fracture toughness of glass/epoxy composite laminates

Critical energy release rate for delamination initiation in composites as a material property, supposed to be independent from non-material variables. However, a thorough literature review presented in this study shows that in many cases it may vary with the variation of layup configuration or geometrical and dimensions. This study is aimed to investigate the effect of interface layers orientation on fracture toughness by eliminating the other influential parameters such as stacking sequence, by selecting the anti-symmetric layup configuration of Double Cantilever Beam, [Formula: see text], in which θ will be 0°, 30°, 45° and 60°. The energy release rates data have been calculated using different criteria and techniques to obtain the load and displacement at initial crack growth and the results were compared with the standard methods. The damage zone near the crack tip is also illustrated before and after the crack propagation by microscopic images of delamination front, and discussed for all investigated interface fiber angles. Experimental results show that the effect of interface layers orientation on fracture toughness of the investigated layup configurations based on the nonlinear technique as a standard procedure is negligible while other techniques show a considerable changes in the calculated energy release rate with the increase of interface layers angle from zero to 60 degrees.

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.

BISTABLE CHARACTERISTICS OF IRREGULAR ANTI-SYMMETRIC LAY-UP COMPOSITE CYLINDRICAL SHELLS

The bistable characteristics of the irregular anti-symmetric cylindrical shell (IACS), such as [+α1/ -α2/ +α2/ -α1] lay-up, are presented using theoretical methodology and finite element (FE) analysis. A novel approach named two points loading method is used to induce a snap-through of the shell in FE analysis. Unlike regular [+α/ -α/ +α/ -α] lay-up anti-symmetric cylindrical shells, two or more different ply angles are included in the irregular anti-symmetric lay-up. Besides ply angles, the bistable characteristics of composite cylindrical shells with irregular anti-symmetric lay-ups are also affected by the sequence of lay-ups. Both analytical and FE results show that IACS with different bistable behaviors can be obtained by changing the ply angles or sequence of the lay-ups. It is very useful for the design and manufacture of the bistable structure. There is a reasonable agreement between analytical and FE predictions; possible reasons of differences between analytical and FE results are given.

The bistable behaviors of carbon-fiber/epoxy anti-symmetric composite shells

Bistability of cross-ply [0n°/90n°] laminates has already been examined in detail by researchers. Another kind of bistable composite shell manufactured from carbon-fiber/epoxy prepreg with anti-symmetric layup, such as [30°/−30°/0°/30°/−30°], is investigated in this paper using analytical, experimental and numerical methods. A new experimental method named two points loading method is presented to capture the bistable behavior of the manufactured specimens. The coiled-up radius and the snap loads, including snap-through and snap-back load used to induce the bistable composite shell to snap between two stable shapes are measured. The factors affecting the bistable performance of the anti-symmetric composite shell, including structure sizes and layup conditions, are discussed by comparing experimental test results and analytical solutions. Good agreement was found between analytical predictions and measured results. The finite element results are approximately in accord with experimental results. Possible reasons of differences between numerical simulation and experimental results are given.

BI-STABLE ANALYSES OF LAMINATED FGM SHELLS

Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.

Bistable characteristic of laminated shells with graded fibers

Based on an inextensional two-parameter analytical model for cylindrical shells, the relationships between the bistable properties of laminated shells with graded fibers and the distribution patterns of the fibers are studied in this article. The fibers are distributed through-thickness in power law from the middle surface to top or bottom surface. Two types of layup, i.e., antisymmetric and symmetric layups, are considered for obtaining the second stable configuration of laminated shells. The distribution regulation of the constituent volume fraction has been obtained for the availability of the second stable equilibrium configurations for both the symmetric and antisymmetric layups. It is showed that the laminated shells with symmetric layups are more difficult to form the second stable configurations than the shells with antisymmetric layups. The effects of the distribution patterns and Young’s modulus of fibers on the bistable configuration of laminated shells are examined. It is revealed that distributing fibers nearly to the top and bottom surfaces and higher Young’s modulus of the fibers are favorable to form second stable configuration and make it coil tighter.

Bi-Stable Character of Laminated Cylindrical Shells

The bistable properties of laminated shells with graded fibers and the distribution patterns are studied based on an inextensional two-parameter analytical model for cylindrical shells. The fibers are distributed through-thickness in power law from the middle surface to top or bottom surface. The antisymmetric layup is considered for obtaining the second stable configuration of laminated shells. The distribution regulation of the constituent volume fraction has been obtained for the availability of the second stable equilibrium configurations for the antisymmetric layup. The effects of the distribution patterns of the fibers on the bistable configuration of laminated shells are examined.

Free vibration analysis of composite plates via refined theories accounting for uncertainties

The free vibration analysis of composite thin and relatively thick plates accounting for uncertainty is addressed in this work. Classical and refined two-dimensional models derived via Carrera's Unified Formulation (CUF) are considered. Material properties and geometrical parameters are supposed to be random. The fundamental frequency related to the first bending eigenmode is stochastically described in terms of the mean value, the standard deviation, the related confidence intervals and the cumulative distribution function. The Monte Carlo Method is employed to account for uncertainty. Cross-ply, simply supported, orthotropic plates are accounted for. Symmetric and anti-symmetric lay-ups are investigated. Displacements based and mixed two-dimensional theories are adopted. Equivalent single layer and layer wise approaches are considered. A Navier type solution is assumed. The conducted analyses have shown that for the considered cases, the fundamental natural frequency is not very sensitive to the uncertainty in the material parameters, while uncertainty in the geometrical parameters should be accounted for. In the case of thin plates, all the considered models yield statistically matching results. For relatively thick plates, the difference in the mean value of the natural frequency is due to the different number of degrees of freedom in the model.

Free Vibration Analysis of Composite Plates via Refined Theories Accounting for Uncertainties

The free vibration analysis of composite thin and relatively thick plates accounting for uncertainty is addressed in this work. Classical and refined two-dimensional models derived via Carrera's Unified Formulation (CUF) are considered. Material properties and geometrical parameters are supposed to be random. The fundamental frequency related to the first bending eigenmode is stochastically described in terms of the mean value, the standard deviation, the related confidence intervals and the cumulative distribution function. The Monte Carlo Method is employed to account for uncertainty. Cross-ply, simply supported, orthotropic plates are accounted for. Symmetric and anti-symmetric lay-ups are investigated. Displacements based and mixed two-dimensional theories are adopted. Equivalent single layer and layer wise approaches are considered. A Navier type solution is assumed. The conducted analyses have shown that for the considered cases, the fundamental natural frequency is not very sensitive to the uncertainty in the material parameters, while uncertainty in the geometrical parameters should be accounted for. In the case of thin plates, all the considered models yield statistically matching results. For relatively thick plates, the difference in the mean value of the natural frequency is due to the different number of degrees of freedom in the model.

Analysis of critical buckling load of laminated composites plate with different boundary conditions using FEM and analytical methods

Abstract In this study, the critical buckling load of fiber reinforced composite plate was calculated by analytical and finite element methods. The critical buckling loads and composite deformations were obtained on the basis of plate dimensions ratio ( L x / L y ). The deformation behaviour of the plate is shown for modes i = 1,2 and different values of orientation angles [0/ θ ] 2 . As a result of the analysis, for the composite plates with symmetric and antisymmetric layup the critical buckling loads were obtained for different support conditions. It was observed that difference between results increased depending on θ angle, although critical buckling load values obtained by using numerical and finite element methods were nearly same in [0/ θ ] 2 orientation angles.

Thermal buckling load optimization of laminated skew plates

In this study thermal buckling load optimization of laminated skew plates subjected to uniformly distributed temperature load is investigated. All of the laminates considered are assumed to have fully clamped boundary conditions, though the general boundary conditions may also be studied without any difficulty. The objective function is to maximize the critical temperature capacity of the laminated skew plates and the fibre orientation is considered as design variable. The first-order shear deformation theory is used in the mathematical formulation. Nine-node Lagrangian rectangular plate element is used for the finite element solution of the skew laminates. The temperature field is assumed to be uniform over the plate surface and varies in the thickness direction only. Modified feasible direction method (MFD) is used for the optimization routine. A program based on FORTRAN is used for the optimization problem. Finally, the effect of number of layers, skew angles, aspect ratios, width-to-thickness ratios and antisymmetric lay-up on the optimal designs is investigated and the results are compared.