Classical Laminated Plate Theory Research Articles

Parametric stability of symmetrically laminated composite super-elliptical plates

Static and parametric stability of thin symmetrically laminated composite super-elliptical plates resting on Winkler-type foundation and subjected to uniform in-plane harmonic loads, under clamped, simply supported and free boundary conditions, are investigated based on the classical laminated plate theory. The governing equations are obtained from a variational approach and then the classical Ritz method is used to reduce the problem into a set of coupled Mathieu–Hill equations. Hsu’s technique is utilized to determine the dynamic instability regions of principal and combination resonance frequencies. Extensive numerical data are provided to examine the effects of plate aspect ratio, super-ellipticity power, foundation stiffness parameter, stacking sequence, and fiber orientation on the vibrational, static, and parametric stability characteristics of symmetrically laminated super-elliptical composite plates. Furthermore, three-dimensional buckling mode shapes are illustrated. The accuracy of formulation is checked by performing convergence studies and the validity of results is established by comparison with the existing results in the literature, exact results obtained from the analytical approach, and as well as from FEM results.

Modeling and experimental verification of the flow characteristics of an active controlled microfluidic valve with annular boundary

The principle and structural configuration of an active controlled microfluidic valve with annular boundary driven by a circular piezoelectric unimorph actuator is presented in this article. Its active controlled flowrate is modeled using the classical laminated plate theory and the extended Bernoulli equation in fluid mechanics. According to the established mathematical model, we simulate and analyze the influence of the voltage applied to the circular piezoelectric unimorph actuator and the structural parameters on the flow characteristics. The prototypes of the active controlled microfluidic valves with annular boundaries of three different combinations of the inner and outer radii are fabricated and tested. The experimental results show that the active controlled microfluidic valves with annular boundaries possess the on/off switching capability and the continuous control capability of the fluid with simple structure and easy fabrication processing; the maximum flowrate of the active controlled microfluidic valve with the annular boundary with the inner and outer radii of 1.5 and 3.5 mm, respectively, is 0.14 mL/s when the differential pressure of the inlet and outlet of the active controlled microfluidic valve is 1000 Pa and the voltage applied to circular piezoelectric unimorph actuator is 100 V; and the established flowrate model can accurately predict the controlled flowrate of the active controlled microfluidic valves with the maximum relative error of 6.7%.

Critical thrust force predictions during drilling: Analytical modeling and X-ray tomography quantification

In the past, several experimental and analytical studies have been conducted aimed towards predicting the critical thrust force responsible for delamination at the hole exit during drilling. Among these analytical models, few take into account the coupling between bending and stretching often observed in multi-directional (MD) laminates with an un-symmetrical stacking sequence considering the presence of an elliptical crack. In addition, in these analytical models, the tool/composite contact region is modeled without taking into account the chisel edge effect. In the present study, a unique analytical model for critical thrust force prediction has been proposed that explicitly accounts for the effect of the chisel and cutting edges. The interaction zone (composite/chisel edge and composite/principal cutting edge) has been modeled using classical lamination plate theory (CLPT) and linear elastic fracture mechanics (LEFM) principles. In addition, a comparison between the proposed analytical model predictions and experimental results from quasi-static punch tests accompanied with different X-ray tomography observations led to choosing the accurate loading profile developed during drilling.

Dynamic instability analysis of rotating delaminated tapered composite plates subjected to periodic in-plane loading

In this study, the dynamic instability analysis of rotating delaminated thickness tapered composite plates with different taper configurations subjected to periodic in-plane loads is performed. The governing differential equations of motion of the various configurations of a rotating thickness mid-plane delaminated tapered laminated composite plate are presented in the finite element formulation based on classical laminated plate theory including various rotational effects. The finite element formulation developed for the dynamic instability analysis of rotating delaminated tapered composite plate is validated by comparing the parametric exciting frequencies evaluated using the present finite element method (FEM) with those presented in available literature and comparing the natural frequencies of rotating delaminated tapered composite plate evaluated using the present FEM with experimentally measured results. Various parametric studies are also performed to study the effect of taper configurations, rotational speed, delamination length, delamination location and in-plane periodic loads on stability of the structure. It was seen that the influences of rotating speed on the principal DIR spectra among taper configurations and uniform plate are significant and the normalized width of principal and second instability regions of parametric resonance frequencies increase in the order of uniform, TC3, TC2 and TC1 for all the rotating speeds.

Thermomechanical buckling of hybrid cross-ply laminated rectangular plates

A thermomechanical buckling analysis is presented for simply supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and are subjected to the combined action of in-plane compressive edge loads, two types of thermal loads, and constant applied actuator voltage. The formulation of equations is based on the classical laminated plate theory and the von-Karman non-linear kinematic relations. The analysis uses an exact method to obtain closed-form solutions for the buckling load. The effects of applied actuator voltage, thermal and mechanical loads, plate geometry, and lay-up configuration of the laminated plates are investigated. The novelty of the present work is to obtain closed-form solutions for electro-thermomechanical buckling of hybrid composite plates, and to cover non-uniform temperature distribution loading. The results for various states are verified with known data in the literature.

Initial imperfection effects on postbuckling response of laminated plates under end-shortening strain using Chebyshev techniques

The effects of initial imperfection on postbuckling behaviour of laminated plates subject to end shortening stain are investigated in this paper. Different boundary conditions and lay-up configurations are considered and classical laminated plate theory is used for developing the equilibrium equations. The equilibrium equations are solved directly by substituting the displacement fields with equivalent finite double Chebyshev polynomials. This technique allows imposing different combinations of boundary conditions on all edges of composite laminated plates. The final nonlinear system of equations is obtained by discretizing both equilibrium equations and boundary conditions with finite Chebyshev polynomials. Nonlinear terms caused by the product of variables are linearized by using quadratic extrapolation technique to solve the system of equations. Since number of equations is always more than the number of unknown parameters, the least squares technique is used to solve the system of equations. Some results for angle-ply and cross-ply composite plates with different boundary conditions are computed and compared with those available in the literature, wherever possible.

Dynamic characterization of tapered laminated composite sandwich plates partially treated with magnetorheological elastomer

This study investigates the dynamic performance of the partially treated magnetorheological elastomer tapered composite sandwich plates. Various partially treated tapered magnetorheological elastomer laminated composite sandwich plate models are formulated by dropping-off the plies longitudinally in top and bottom composite face layers to yield tapered plates as the face layers. The uniform rubber and magnetorheological elastomer materials are considered as the core layer. The governing differential equations of motion of the various partially treated magnetorheological elastomer tapered composite sandwich plate configurations are derived using classical laminated plate theory and solved numerically. Further, silicon-based magnetorheological elastomer and natural rubber are being fabricated and tested to identify the various mechanical properties. The effectiveness of the developed finite element formulation is demonstrated by comparing the results obtained with experimental tests and available literature. Also, various partially treated magnetorheological elastomer tapered laminated composite sandwich plates are considered to the study the effect of location and size of magnetorheological elastomer segment on various dynamic properties under various boundary conditions. The effects of magnetic field on the variation of natural frequencies and loss factors of the various partially treated magnetorheological elastomer tapered laminated composite sandwich plate configurations are analysed at different boundary conditions. Also, the effect of taper angle of top and bottom layers, aspect ratio, ply orientations on the natural frequencies of different configurations are analysed. Further, the transverse vibration responses of three different partially treated magnetorheological elastomer tapered laminated composite sandwich plate configurations under harmonic excitation are analysed at various magnetic fields. This analysis suggests that the location and size of the magnetorheological elastomer segments strongly influence the natural frequency, loss factor and transverse displacements of the partially treated magnetorheological elastomer tapered laminated composite sandwich plates apart from the intensities of the applied magnetic field. This shows the applicability of partial treatment to critical components of a large structure to achieve a more efficient and compact vibration control mechanism with variable damping.

Asymptotic analysis for composite laminated plate with periodically fillers in viscoelastic damping material core

A novel functional structure which can generate large structural loss factor (LF) in low frequency is designed in this research. The free flexural dynamic characteristics of composite laminated plate (CLP) cored with viscoelastic damping material (VDM) are studied by considering its frequency- and temperature-dependent properties. The heavy-density-material-rods (HDMRs) are periodically embedded into CLP. CLP's in-plane variables are obtained by classic laminated plate theory (CLPT) first, and then substituted it into the equilibrium equations which are derived from the Hamilton's principle, the flexural and shearing deformation compatible equations according to the mechanism of a primitive cell. The analytical deformation equation of the CLP is solved by the second order “rapid” asymptotic method, and LF is obtained, subsequently. The parameters that affect the LF are thoroughly analyzed. The validity of the research is verified by FEM. The research show the advantages of the presented CLP which could be applied in engineering under low frequency zone, especially in 1–200 Hz.

A Closed-Form Solution for Thermal Buckling of Cross-Ply Piezolaminated Plates

A thermal buckling analysis is presented for simply-supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and subjected to the combined action of thermal load and constant applied actuator voltage. The material properties of the composite and piezoelectric layers are assumed to be functions of temperature. Derivations of the equations are based on the classical laminated plate theory, using the von-Karman nonlinear kinematic relations. The Ritz method is adopted to obtain closed-form solutions for the critical buckling temperature. Numerical examples are presented to verify the proposed method. The effects of the applied actuator voltage, plate geometry and stacking sequence of laminates are investigated.

Nonlinear forced vibration of carbon fiber/epoxy prepreg composite beams: Theory and experiment

Abstract In the present work, a nonlinear forced vibration model for fiber reinforced composites was developed with varying fiber orientations and laminate sequences. A nonlinear viscoelastic beam model was developed using nonlinear von Karman strains and Kelvin–Voigt stress–strain relationship to model viscoelasticity. The effect of fiber orientation and laminate sequence was included in the model using classic laminated plate theory. Method of multiple time scales was used to solve the resulting nonlinear equation and an inverse problem approach was used to extract the model parameters from experimental data. Theoretical model parameters were calculated and compared to experimentally determined values for different fiber orientations and laminate sequences, and a nominally good qualitative agreement was observed. Finally, the experimentally extracted model parameters were substituted in the analytical model, and the model predictions in terms of frequency shifts were compared against experimental observations. Nominally good agreement was observed for 45° and 90° fiber orientations, however the experimental observations didn't match well for 0°.

Dynamic analysis of tapered laminated composite magnetorheological elastomer (MRE) sandwich plates

In the present study, the dynamic performance of the sandwich plate with magneto rheological elastomer (MRE) as the core layer and tapered laminated composite plates as the face layers is investigated. Various MRE tapered laminated composite sandwich plate models are formulated by dropping-off the plies longitudinally in top and bottom composite layers to yield tapered plates as the face layers and uniform MRE layer as the core layer. The governing equations of motion of tapered composite MRE sandwich plates are derived using classical laminated plate theory and solved numerically. Further, silicon based MRE is being fabricated and tested to obtain the shear and loss moduli using MR rheometer. The efficacy of the finite element formulation is validated by carrying out experiments on the various prototypes of tapered composite silicon based MRE sandwich plates and comparing the results in terms of natural frequencies obtained at various magnetic fields with those obtained numerically and with available literature. Also, the effects of magnetic field, taper angle of the top and bottom layers, aspect ratio, ply orientations and various end conditions on the various dynamic properties of tapered laminated composite MRE sandwich plate are investigated. Further, the transverse vibration responses of three different tapered composite MRE based sandwich plates under harmonic force excitation are analyzed at various magnetic fields.

Buckling analysis of piezoelectric cylindrical composite panels reinforced with carbon nanotubes

The current article analyses the buckling response of piezoelectric cylindrical composite panels reinforced with carbon nano-tubes subjected to axial load. Classical laminated plate theory (CLPT) is employed to reach stress and displacement correlations embracing mechanical and magnetic terms. Stress–strain equations for piezoelectric cylindrical panels reinforced with carbon nanotubes are then written by using Mori–Tanaka method. The coupled electro-mechanical governing equations, Donnell theory as well as minimum potential energy method are thereafter utilized to calculate buckling loads and modes. The effects of such parameters as volume fraction of nano-tube, geometrical characteristics as well as two loading types of axial and biaxial on buckling load of the composite panel are investigated. The results show that increasing the volume fraction of nano-tube eventuates in increasing the buckling load. The results were compared with those already available in the existed literature using different shell theories for isotropic and composite cylindrical panels and a very good agreement was observed.

Stress Distribution of Bolted Joints With Different Lay-Up Types

A parametric study of the stress distribution in the composite plates is undertaken to show the effect of different lay-ups. Full 3-D elastic properties are required in the modelling. These properties are calculated using equations taken from the literature and derivation from simple Classical Laminate Plate Theory (CLPT). In previous experimental work, it was shown that tensile failure involved the development of a damage zone at the edge of the hole. In a double-lap joint, it is assumed that uniform stresses are exhibited throughout the plate thickness. Different lay-ups system give different tangential stress distributions and insignificant variation in the radial stress distribution along the hole boundary.

Free vibrations of laminated rectangular plate reinforced with carbon nanotubes

This article presents the analysis of free vibration of cross ply and angle ply laminated rectangular plate reinforced with carbon nanotubes. The methods were used for analysis, are based on classical laminated plate theory (CLPT), first order shear deformation theory (FSDT) and third order shear deformation theory (TSDT) with simply supported boundary conditions. The effective material properties of reinforced polymer with nanotubes are estimated according to the Cox model. Also to calculate the material of properties, the rule of mixture and Halpin‐Tsai relations were used. In this analysis, the effect of weight fraction of CNTs and width‐to‐thickness ratio are investigated. It is shown that analytical and FEM results have good agreements. POLYM. COMPOS., 38:2128–2139, 2017. © 2015 Society of Plastics Engineers

Some aspects of interactive dynamic stability of thin-walled trapezoidal FGM beam-columns under axial load

The present paper deals with a dynamic interactive response of FG beam-columns subjected to in-plane pulse loading when the shear lag phenomenon and distortional deformations are taken into account. The structures are assumed to be simply supported at the ends. In order to obtain the equations of motion of individual plates, the classical laminate plate theory (CLPT) has been modified in such a way that it additionally accounts for all components of inertial forces. Thin-walled trapezoidal FGM beam-columns are considered. A dynamic interaction of the global mode with the lowest primary local buckling mode and the secondary local mode has been analysed. Attention has been drawn to some unexpected aspects related to the fact that a two- and three-modal approach has been assumed in the analysis of dynamic interactive buckling.

Quasi-Three-Dimensional Crack Tip Element Analysis for Evaluation of Total Energy Release Rate in Composite Laminates

An analytical quasi-three-dimensional crack tip element model is developed to provide a quick assessment of the delamination behavior for composite laminates. A closed-form solution for the average total strain energy release rate is obtained by taking into consideration of all the displacement components defined in the classical laminated plate theory. By means of numerical experiments, it is shown that the presented method can predict the average total strain energy release rates with satisfactory accuracy for a relatively large variety of composite layups under opening and in-plane-shearing loading conditions. It indicates that the influence of out-of-plane transverse displacements on the total energy release rate can be significant for certain type of layups even under in-plane loading conditions. Furthermore, an orthotropic parameter is introduced to represent the influence of out-of-plane transverse effects.

Evaluation of dimensional accuracy and material properties of the MakerBot 3D desktop printer

Purpose – This paper aims to evaluate the material properties and dimensional accuracy of a MakerBot Replicator 2 desktop 3D printer. Design/methodology/approach – A design of experiments (DOE) test protocol was applied to determine the effect of the following variables on the material properties of 3D printed part: layer height, per cent infill and print orientation using a MakerBot Replicator 2 printer. Classical laminate plate theory was used to compare results from the DOE experiments with theoretically predicted elastic moduli for the tensile samples. Dimensional accuracy of test samples was also investigated. Findings – DOE results suggest that per cent infill has a significant effect on the longitudinal elastic modulus and ultimate strength of the test specimens, whereas print orientation and layer thickness fail to achieve significance. Dimensional analysis of test specimens shows that the test specimen varied significantly (p < 0.05) from the nominal print dimensions. Practical implications – Although desktop 3D printers are an attractive manufacturing option to quickly produce functional components, this study suggests that users must be aware of this manufacturing process’ inherent limitations, especially for components requiring high geometric tolerance or specific material properties. Therefore, higher quality 3D printers and more detailed investigation into the MakerBot MakerWare printing settings are recommended if consistent material properties or geometries are required. Originality/value – Three-dimensional (3D) printing is a rapidly expanding manufacturing method. Initially, 3D printing was used for prototyping, but now this method is being used to create functional final products. In recent years, desktop 3D printers have become commercially available to academics and hobbyists as a means of rapid component manufacturing. Although these desktop printers are able to facilitate reduced manufacturing times, material costs and labor costs, relatively little literature exists to quantify the physical properties of the printed material as well as the dimensional consistency of the printing processes.

Stability and Dynamic Analysis of Laminated Composite Plates

Buckling and free vibration analysis of laminated rectangular plates with uniform and non uniform distributed in-plane compressive loadings along two opposite edges is performed using the Ritz method. Classical laminated plate theory is adopted. The static component of the applied in- plane loading are assumed to vary according to uniform, parabolic or linear distributions. Initially, the plate membrane problem is solved using the Ritz method; subsequently, using Hamilton’s variational principle, linear homogeneous algebraic equations in terms of unknown are generated, the set of linear algebraic equations can be solved as an Eigen-value problem. Buckling loads for laminated plates with different combinations of boundary conditions are obtained and their effect on the natural frequencies of plate are also investigated. The proposed method is verified by comparing results to data obtained by the finite element method (FEM) using ANSYS program, from experimental program and that obtained by other researchers. Analytical results are also presented to bring out the effects of aspect ratio, boundary conditions, lamination angle, and loading type on the critical buckling load and natural frequency.
 

Predictions of Delamination Growth for Quasi-Static Loading of Composite Laminates

This paper presents an exact, two-dimensional (2D) quasi-static elastic analysis of predelaminated composite panels subject to arbitrary transverse pressure loads. The piecewise linear spring model and the shear bridging model are, respectively, used to simulate the normal contact and shear frictional behavior between the interfaces of the existing delamination. This general contact model can be further reduced to the “friction-free model” and the “constrained model” by assigning extreme values to the spring stiffnesses. The analysis yields a closed-form solution for the 2D displacement and stress fields. To predict the delamination propagation, different propagation criteria as suggested in the literature are used. Calculated load–displacement responses and delamination threshold loads are in good agreement with existing experimental data. The results are further compared against simple fracture models and a model that uses a modified classical laminated plate theory for the predelaminated composite with fracture criteria, showing an overestimation of the delamination threshold loads. The 2D elasticity theory that is formulated can be used with confidence to study other multilayered structures with multiple delaminations and subject to arbitrary loading profiles.

Numerically validated reduced-order model for laminates containing shape memory alloy wire meshes

The incorporation of active materials into composites is an active area of research. However, the design and optimization of such composites is challenging because detailed analysis using finite element analysis (FEA) is computationally intensive. This work presents a new reduced-order model for laminates containing shape memory alloy (SMA) wire meshes that significantly reduces the computational burden on design analysis while maintaining good accuracy. The approach is based on a foundation of classical laminated plate theory (CLPT). It considers fully non-linear stress distributions and incorporates a detailed phenomenological model of the hysteretic SMA constitutive behavior. The reduced-order CLPT-based model and its numerical implementation are fully described and unique laminate responses are presented. The model is validated against a corresponding high-fidelity FEA model of an SMA-based laminate. The reduced-order model produces accurate predictions at significantly less expense than the high-fidelity FEA approach, with normalized root-mean-squared error below 10% for most design cases.