Classical Laminated Plate Theory Research Articles

Active vibration control of thin constrained composite damping plates with double piezoelectric layers

Vibrations and the damping behaviour of thin constrained composite plates with double piezoelectric layers are analytically explored by using Fourier transformation and classical laminated plate theory. Electric potential equations in the double piezoelectric layers are solved with respect to closed and open circuit boundary conditions, an exterior dielectric slab and active control. The natural frequencies and loss factors of the constrained smart composite plates with passive control methods are not notably changed in comparison with those of the constrained composite plates without piezoelectric effects since vibrational energy does not efficiently convert to electrical energy. The loss factors of the composite plates with active constrained damping increase and the natural frequencies have significant variations as the proportional derivative gains increase. Transverse displacement power spectra of the piezoelectric composite plates with active control are compared with those of the piezoelectric composite plates with passive control showing that active control has the best suppression performance of vibrations for the constrained laminated plates with double piezoelectric layers. Radial power spectral density, phase angles and cylindrical-wave power spectral density are calculated. Interesting patterns of wave propagation are explained when plane wave expansion is used to obtain Bessel cylindrical waves.

Modeling of the nonlinear dynamic degradation characteristics of fiber-reinforced composite thin plates in thermal environment

In this research, the nonlinear dynamic degradation characteristics of fiber-reinforced composite plates in thermal environment are investigated through a novel dynamic degradation model, which is established by introducing the thermal and time fitting coefficients simultaneously to express dynamic elastic moduli of such composite materials. Based on the classical laminated plate theory, the improved exponential function method, the complex modulus approach and the Ritz method, the dynamic equations are derived to solve the dynamic parameters. Besides, a particle swarm optimization algorithm is employed to iteratively calculate dynamic elastic moduli, and the nonlinear least squares technique in MATLAB software is utilized to draw the three-dimensional fitted surfaces of dynamic elastic moduli, degradation time and temperature data, so that the concerned fitting coefficients in the model developed can be identified. In order to validate the dynamic degradation model, experimental measurements of E120 carbon fiber/ FRD-YG-03 resin composite thin plates are undertaken. The first three natural frequencies, resonant responses and modal damping ratios obtained from the model are compared with experimental results at different degradation time and stabilized thermal environment, which are shown to be in good agreement. Also, the specific influences with and without consideration of the degradation behavior on the dynamic characteristics are investigated and evaluated.

Vibration Suppression of a Cantilevered Piezoelectric Laminated Composite Plate Subjected to Hygrothermal Loads

In this paper, the vibration suppression strategy for a cantilevered rectangular piezoelectric laminated composite plate is proposed by using the piezoelectric patches, which are attached to the upper and lower surfaces of the plate as the actuators and sensors, respectively. The main contributions of this study is as follows: Firstly, Based on classical laminated plate theory and considering the action of piezoelectric loadings, the dynamics equation of a piezoelectric laminated composite plate subjected to hygrothermal loads is derived by using Hamilton’s principle. The partial differential equations of the piezoelectric laminated composite plate are discretized to a two-degree-of-freedom control equation by using Galerkin method. Secondly, According to the discrete nominal model, a robust controller for the uncertain systems is proposed. Based on the state space equation, the output feedback controller for the system is designed. In the constructed full-dimensional state observer, the estimated state feedback is introduced to construct a closed-loop feedback system. Using the Lyapunov Matrix Inequality (LMI) method and Lyapunov Stability Theory, the feedback gain matrix and observation gain matrix for the system are designed to make the closed-loop system asymptotically stable. Finally, the accuracy and effectiveness of the controller are verified by numerical simulation.

Avoidance of Catastrophic Structural Failure as an Evolutionary Constraint: Biomechanics of the Acorn Weevil Rostrum

The acorn weevil (Curculio Linnaeus, 1758) rostrum (snout) exhibits remarkable flexibility and toughness derived from the microarchitecture of its exoskeleton. Modifications to the composite profile of the rostral cuticle that simultaneously enhance the flexibility and toughness of the distal portion of the snout are characterized. Using classical laminate plate theory, the effect of these modifications on the elastic behavior of the exoskeleton is estimated. It is shown that the tensile behavior of the rostrum across six Curculio species with high morphological variation correlates with changes in the relative layer thicknesses and orientation angles of layers in the exoskeleton. Accordingly, increased endocuticle thickness is strongly correlated with increased tensile strength. Rostrum stiffness is shown to be inversely correlated with work of fracture; thus allowing a highly curved rostrum to completely straighten without structural damage. Finally, exocuticle rich invaginations of the occipital sutures are identified both as a likely site of crack initiation in tensile failure and as a source of morphological constraint on the evolution of the rostrum in Curculio weevils. It is concluded that avoidance of catastrophic structural failure, as initiated in these sutures under tension, is the driving selective pressure in the evolution of the female Curculio rostrum.

Design and finite element assessment of fully uncoupled multi-directional layups for delamination tests

In this paper, a procedure to obtain fully uncoupled multi-directional stacking sequences for delamination specimens is outlined. For such sequences, in-plane, membrane-bending and torsion–bending coupling terms are null (in closed-form solution in the framework of classical laminated plate theory) for the entire stack and for both its halves, which form two arms in the pre-cracked region of a typical delamination specimen. This is achieved exploiting the superposition of quasi-trivial quasi-homogeneous stacking sequences, according to appropriate rules. Any pair of orientations of the plies embedding the delamination plane can be obtained. To assess the effectiveness of the proposed approach, a fully uncoupled multi-directional sequence is designed and compared to other relevant sequences proposed in the literature. Finite element simulations of double cantilever beam test are performed using classic virtual crack closure technique and a revised state-of-the-art virtual crack closure technique formulation too. Some interesting conclusions regarding proper design of multidirectional stacks for delamination tests are drawn. Moreover, the results confirm the suitability of fully uncoupled multi-directional sequences for delamination tests. Thanks to their properties, these sequences might lay the foundations for the development of standard test procedures for delamination in angle-ply interfaces.

Buckling Analysis of Laminated Composite Plate with Different Boundary Conditions using modified Fourier series

Buckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained gives good agreement with those published by other researchers.

Correlation of CLPT and FSDT Responses in CNT/Polymer Composite Beams Under Deflection and Buckling

The principal intention of this research paper is to compare the Classical Laminate Plate Theory (CLPT) and First-order Shear Deformation Theory (FSDT) based on the buckling and deflection performance of Carbon Nanotube (CNT) Reinforced Polymer Composite beams. A symmetric, eight layered, and simply supported nanocomposite beam is taken for the comparison of CLPT and FSDT. The Mori-Tanaka micro-mechanical approach is used for the computation of elastic constants as a function of volume fraction of CNT reinforcement for the CNT/Polymer composite material. The elastic constants obtained are extensively utilized to discover the critical buckling loads and deflections by using CLPT and FSDT. The variations are presented in graphical form for the buckling and deflection of beams for various stacking sequences and CNT volume fractions. The effect of shear deformation is studied in both deflection and buckling of nanocomposite beams. The effect of beam thickness on the bending loads and buckling loads in both the theories is also studied from the results.

A parametric study for static deflections of symmetrically laminated rectangular thin plates

This study focuses on static deflection analysis of uniformly lateral loaded composite thin rectangular plate with uniformly lateral loads. Stacking sequence of symmetrically laminated quasi-isotropic plates has the sequence of the orientation angles -45°, 0°, +45°, 90°. Boundary conditions were selected as clamped and simply supported hinges at the edges of the plates. The Finite Difference Method (FDM) was used to determine the maximum deflection of the plates based on the governing differential equations of Classical Laminated Plate Theory (CLPT). Effect of the lamination type, boundary condition and aspect ratio (a/b, b/a) on maximum deflections was investigated parametrically, which are of importance in preliminary design phase of composite plates. Results obtained were compared with those of the Finite Element Method (FEM) received from literature. It was found out that the both groups of the results agree on.

Optical Properties and Mechanical Modeling of Acetylated Transparent Wood Composite Laminates.

Transparent wood composites (TWCs) are a new class of light-transmitting wood-based materials composed of a delignified wood template that is infiltrated with a refractive- index-matched polymer resin. Recent research has focused primarily on the fabrication and characterization of single-ply TWCs. However, multi-ply composite laminates are of interest due to the mechanical advantages they impart compared to the single ply. In this work, 1- and 2-ply [0°/90°] TWC laminates were fabricated using a delignified wood template (C) and an acetylated delignified wood template (AC). The optical and mechanical properties of resultant C and AC TWC laminates were determined using ultraviolet-visible spectroscopy (UV-Vis) and tensile testing (5× replicates), respectively. In addition, the ability of classical lamination plate theory and simple rule of mixtures to predict multi-ply tensile modulus and strength, respectively, from ply-level mechanical properties were investigated and are reported herein. Experimental results highlight tradeoffs that exist between the mechanical and optical responses of both unmodified and chemically modified TWCs. Template acetylation reduced the stiffness and strength in the 0° fiber direction by 2.4 GPa and 58.9 MPa, respectively, compared to the unmodified samples. At high wavelengths of light (>515 nm), AC samples exhibited higher transmittance than the C samples. Above 687 nm, the 2-ply AC sample exhibited a higher transmittance than the 1-ply C sample, indicating that thickness-dependent optical constraints can be overcome with improved interfacial interactions. Finally, both predictive models were successful in predicting the elastic modulus and tensile strength response for the 2-ply C and AC samples.

Stress constraint topology optimization using layerwise theory for composite laminates

An improved stress-based topology optimization method for laminated composites is proposed by applying the layerwise theory in this research. The layerwise theory is an analysis technique for laminated composites or fiber-reinforced composites that has been developed to overcome the disadvantages of the classical laminated plate theory (CLPT). Because transverse shear deformation is ignored in the CLPT, it cannot be used for thick plates or multiple-layered composites. Therefore, new methods have been developed for analyzing them, and one of them is the layerwise theory. Using the layerwise theory, it is possible to accurately analyze a thick plate and predict the behavior of multiple layers of composites. In the layerwise theory, because a new displacement field and a modified finite element (FE) model are used, the FE model of the stress-based topology optimization method (STOM) is reconstructed to apply the layerwise theory. To apply the STOM for composite materials, the specific failure criterion developed for anisotropic materials must be selected. Therefore, the Tsai–Hill criterion and Tsai–Wu criterion are adapted to the STOM formula to consider the failure of composite materials. Further, the orientation of each layer in a composite significantly affects the optimization result as well as stiffness. Therefore, in this study, we optimize the density and orientation simultaneously by setting the orientation as a design variable. Finally, several types of p-norm approaches are proposed, and one of them can be chosen depending on the location of the maximum value of the constraint.

Sound radiation of cross-laminated timber panels based on a higher order plate theory

In this contribution, the problem of sound radiation by a rectangular baffled cross-laminated timber (CLT) plate excited by a point force is addressed. Due to the inherent properties of CLT, a higher order shear deformable plate theory is needed to capture its deformation field. To this end, a recently proposed equivalent single layer plate theory is extended to incorporate dynamic effects. The derived plate model is applied to flexural wave propagation in infinitely extended plates, revealing coincidence frequency bands of the considered CLT elements. For a simply supported rectangular plate, natural frequencies and total acoustic power output to the far-field are computed. Throughout all simulations, results obtained by the proposed higher order plate theory are set in contrast with those applying first order shear deformation theory and classical laminated plate theory, because those models are typically used for vibro-acoustic simulations of cross-laminated timber panels. Comparison of the natural frequencies shows that these quantities of the higher order theory are in excellent agreement with the outcomes of finite element simulations based on continuum elements. In contrast, the outcomes of the lower order models deviate with increasing frequency. Consequently, both lower order models fail at assessing acoustic power output in the low to mid frequency range when comparing results with the proposed plate theory.

Agglomeration and aspect ratio effects on the long-term creep of carbon nanotubes/fiber/polymer composite cylindrical shells

The present study is an attempt to trace the influences of agglomeration, uniform dispersion, and aspect ratio of carbon nanotubes on long-term creep strain and stress in carbon nanotubes/fiber/polymer composite cylindrical shells. The thin-walled cylindrical vessel is subjected to an internal pressure. For this purpose, the effect of the carbon nanotubes agglomeration and aspect ratio on the elastic properties of carbon nanotube-reinforced composites were investigated, by means of the Halpin–Tsai and Eshelby–Mori–Tanaka approaches. Classical-laminated plate theory and stress–strain relations were used to derive the governing equations for radial and circumferential creep strain. The Schapery single integral nonlinear viscoelasticity model was used for modeling the behavior of materials reliably. The present results indicated that the higher aspect ratio and uniform dispersion decreased creep strain, but agglomeration increased creep strain.

Transverse inhomogeneity of laminated cylindrical panel influence on post-buckling behaviour

The present paper concerns the influence of transverse heterogeneity caused by layer stacking sequence in laminated cylindrical panels under compression on their stability and post-buckling behaviour. According to the classical laminated plate theory (CLPT) this inhomogeneity causes not trivial coupling matrix B terms. A method of the modal solution to the nonlinear buckling problem within Koiter’s asymptotic theory, using the semi-analytical method (SAM) and the transition matrix method, was applied in the analysis. Post-buckling behaviour of laminated shallow cylindrical panel within the first- and second-order non-linear approximation were determined when the coupling matrix B was included or neglected. Additionally for model 1D the dimensionless stiffness reduction coefficient values were estimated which already in the phase of composite structure design process makes it easier to assess the influence of coupling matrix on stability. Just like in the case of plate elements, when the value of these coefficients is close to 1, the effect of couplings on stability is negligible. If the value of these coefficients is significantly less than 1, then the effect of the coupling matrix terms on stability increases.

Ritz method analysis of rectilinear orthotropic composite circular plates undergoing in-plane bending and torsional moments

In this article, the elastic problem of composite circular plates with rectilinear orthotropic characteristics, in case of in-plane bending and torsional moments applied, is resolved. According to classical lamination plate theory, the analysis makes use of the Ritz method along with the principle of virtual displacements, originally combined in order to obtain displacements components. The procedure represents an important step for the setting-up of a spot joint element able to simulate in FE analyses the structural behavior of point junctions applied to composite components. The accuracy of the procedure has been demonstrated comparing analytical results to FE reference analyses.

Composites and Effects of Discontinuities on Its Performance: A Review

This paper presents a brief study about the composites, governing equations for analysis, manufacturing methods, and performance analysis of composites with and without discontinuities. Study is done about the utility of plate theories like Classical Laminated Plate Theory, First-Order Shear Deformation Theory, and Higher-Order Shear Deformation Theory in analysis of composite plates with and without holes. Analytical methods like Rayleigh–Ritz are also studied. Some experimental aspects for analysing the various methods in use have been highlighted. The outcomes corresponding to deviations of parameters like aspect ratio, boundary conditions, hole size on composite are discussed. This study will helpful for researchers in this domain to choose carefully among the various theories and analyses techniques available for their further research.

A modified first order shear deformation theory for Reissner-Mindlin composite panels with internal delamination

In this paper, an extended first order shear deformation theory is proposed for Reissner-Mindlin laminated composite panels with internal delamination. The distinctive feature of the present theory is that a contact mechanism is involved in the governing equations based on FSDT by introducing a constitutive relation between the contact force and the transverse deflection and are expressed in terms of the displacements and the rotation functions. The proposed theory is applied to investigate the structural failure of a delaminated Reissner-Mindlin composite panel subjected to in-plane compression. Numerical solutions are computed by developing MATLAB program for different values of thickness-to-width ratio, material properties, aspect ratio and delamination conditions and are compared with those obtained from the modified classic laminated plate theory established in previous works and with ABAQUS results. Both theories and ABAQUS analysis predict a consistent global buckling mode without opening in between the delamination. The comparisons of the two solutions not only validate the efficiency and accuracy of the proposed M-FSDT but also evidence that neglecting the transverse shear strain may lead to the overestimation of the load capacity of the panel up to more than 35% when the thickness-to-width ratio is greater than 0.15.

A new Fourier transform-based fundamental solution for laminated composite plates with coupled bending and extension

We present in this note a new derivation for a Fourier transform-based fundamental solution for the coupled bending-stretching problem of laminated composite plates. The classical laminated plate theory is used for the description of the kinematics of the plate.

Buckling and Pre Stressed Dynamics Analysis of Laminated Composite Plate with Different Boundary Conditions

Critical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge conditions, aspect ratio, lamination angle, thickness ratio, orthotropic ratio, the results obtained gives good agreement with those published by other researchers.

Nonlinear vibration study of fiber-reinforced composite thin plate with strain-dependent property based on strain energy density function method

The strain energy density function method is proposed to study the nonlinear vibration behavior of the fiber-reinforced composite thin plate with strain dependence. First, the material nonlinearity of the fiber-reinforced composite is extended to the vibration field. On the basis of Jones-Nelson nonlinear model, a theoretical model with the consideration of the strain-dependent nonlinearity is established to illustrate the theoretical principle of the strain energy density function method. In the model, the nonlinear elastic moduli in different fiber directions are expressed as a function of the strain energy density. The nonlinear natural frequencies are solved by Ritz method in conjunction with the classical laminated plate theory and Hamilton’s principle, and the nonlinear vibration responses are calculated by Newton–Raphson iteration method. Moreover, a TC300 carbon/epoxy composite plate is taken as a research object. In order to determine the corresponding parameters in the theoretical model, the composite beam specimens are cut off to conduct the stress-strain measurement. The nonlinear natural frequencies and vibration responses of the composite plate under different excitation levels are obtained. The comparisons between the theoretical calculation and experimental test show that the maximum calculation error of the first six natural frequencies with considering the strain-dependent nonlinearity is less than 4.3%, and the maximum calculation error of the resonant responses is less than 12.0% for the third mode and the sixth mode, thus the practicability and reliability of the proposed method have been verified.

Effect of backup plate in drilling of composite laminates, analytical and experimental approaches

Delamination is the most severe damage in drilling of composite laminates. Using the backup plate is an appropriate method to control drilling induced delamination. In this paper, an analytical model is applied to determine the critical thrust force and the feed rate for drilling of composite laminates with backup plate. To achieve this aim, the classical laminate plate theory (CLPT), the linear elastic fracture mechanic (LEFM) and the oblique cutting model are used. In analytical models, two separate distributed loads have been exerted by cutting and chisel edges. Based on the model results, the effect of the drill diameter, the chisel edge size, and the backup plate size, on the critical thrust force and the feed rate are investigated. Experimental tests are carried out to prove the analytical model.