Deflection analysis of hybrid laminated composite plates

In this paper an attempt is made to obtain deflections of hybrid, laminated, rectangular and skew composite plates. Analysis is performed by employing the Galerkin technique. Numerical results have been obtained for two types of layups employing Kevlar/epoxy and Boron/epoxy laminae. It is observed that for a given aspect ratio the rigidity of the skew plate increases with an increase in the skew angle. Further, for a specified deflection, the hybrid laminates turn out to be lighter.

Stability of laminated composite plates with cut-outs

Critical buckling loads of laminated fibre-reinforced plastic square panels have been obtained using the finite element method. Various boundary conditions, lay-up details, fibre orientations, cut-out sizes are considered. A 36 degrees of freedom triangular element, based on the classical lamination theory (CLT) has been used for the analysis. The performance of this element is validated by comparing results with some of those available in literature. New results have been given for several cases of boundary conditions for [0°/ ± 45°/90°]s laminates. The effect of fibre-orientation in the ply on the buckling loads has been investigated by considering [±?]6s laminates.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

The effect of shear strength on the ballistic response of laminated composite plates

The ballistic performance of clamped circular carbon fibre reinforced polymer (CFRP) and Ultra High Molecular Weight Polyethylene (UHMWPE) fibre composite plates of equal areal mass and 0/90 lay-up were measured and compared with that of monolithic 304 stainless steel plates. The effect of matrix shear strength upon the dynamic response was explored by testing: (i) CFRP plates with both a cured and uncured matrix and (ii) UHMWPE laminates with identical fibres but with two matrices of different shear strength. The response of these plates when subjected to mid-span, normal impact by a steel ball was measured via a dynamic high speed shadow moiré technique. Travelling hinges emanate from the impact location and travel towards the supports. The anisotropic nature of the composite plate results in the hinges travelling fastest along the fibre directions and this results in square-shaped moiré fringes in the 0/90 plates. Projectile penetration of the UHMWPE and the uncured CFRP plates occurs in a progressive manner, such that the number of failed plies increases with increasing velocity. The cured CFRP plate, of high matrix shear strength, fails by cone-crack formation at low velocities, and at higher velocities by a combination of cone-crack formation and communition of plies beneath the projectile. On an equal areal mass basis, the low shear strength UHMWPE plate has the highest ballistic limit followed by the high matrix shear strength UHMWPE plate, the uncured CFRP, the steel plate and finally the cured CFRP plate. We demonstrate that the high shear strength UHMWPE plate exhibits Cunniff-type ballistic limit scaling. However, the observed Cunniff velocity is significantly lower than that estimated from the laminate properties. The data presented here reveals that the Cunniff velocity is limited in its ability to characterise the ballistic performance of fibre composite plates as this velocity is independent of the shear properties of the composites: the ballistic limit of fibre composite plates increases with decreasing matrix shear strength for both CFRP and UHMWPE plates. © 2013 Elsevier Masson SAS. All rights reserved.

Recent advances of finite elements for laminated composite plates

A large amount of finite elements have been developed for finite element analysis of laminated composite plates. The laminated plate theories are reviewed and summarized in this paper. The focus of this review is on the recently developed laminated finite elements since 1990. The 2-D triangular and quadrilateral displacement-based and mixed/hybrid-based finite element models, which were developed based on the first-order shear deformation theories, the higher-order shear deformation theories, the zig-zag theories and the global-local higher-order deformation theories, and the layer-wise laminated plate theories are reviewed in this paper and also their related patents. Finally, some points on the development of the laminated finite elements are summarized.

A family of simple and robust finite elements for linear and geometrically nonlinear analysis of laminated composite plates

A family of simple, displacement-based and shear-flexible triangular and quadrilateral flat plate/shell elements for linear and geometrically nonlinear analysis of thin to moderately thick laminate composite plates are introduced and summarized in this paper.

The developed elements are based on the first-order shear deformation theory (FSDT) and von-Karman’s large deflection theory, and total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from Timoshenko’s laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates and shear-locking problem is avoided naturally.

The flat triangular plate/shell element is of 3-node, 18-degree-of-freedom, and the plane displacement interpolation functions of the Allman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. The flat quadrilateral plate/shell element is of 4-node, 24-degree-of-freedom, and the linear displacement interpolation functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements.

The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the elements are convergent, not sensitive to mesh distortion, accurate and efficient for linear and geometric nonlinear analysis of thin to moderately thick laminates.

Flexure of composite plates

A new higher order shear deformation theory of laminated composite plates is developed. The basic displacement variables in this theory are two partial normal displacements and two in-plane displacement parameters. The governing equations are presented in the form of four simultaneous partial differential equations. The shear deformation theories of Bhimareddy and Stevens, and of Reddy are special cases of this formulation. In their models, transverse shear strains will become zero at points in the plate where displacements are constrained to be zero such as those on fixed edges. This limitation has been overcome in the present formulation.

On higher order shear deformation theory of laminated composite panels

In this paper we examine the suitability of higher order shear deformation theory based on cubic inplane displacements and parabolic normal displacements, for stress analysis of laminated composite plates including the interlaminar stresses. An exact solution of a symmetrical four layered infinite strip under static loading has been worked out and the results obtained by the present theory are compared with the exact solution. The present theory provides very good estimates of the deflections, and the inplane stresses and strains. Nevertheless, direct estimates of strains and stresses do not display the required interlaminar stress continuity and strain discontinuity across the interlaminar surface. On the other hand, ‘statically equivalent stresses and strains’ do display the required interlaminar stress continuity and strain discontinuity and agree very closely with the exact solution.

A simple displacement-based quadrilateral laminated composite plate element : Part II : linear analysis

The 4-node, 24-dof quadrilateral displacement-based element (Zhang et al. 2004), which have been developed successfully for linear analysis of thin to thick laminated composite plates, is extended further for geometrically nonlinear analysis in this paper. The proposed element is based on the first-order shear deformation theory (FSDT) and von-Karman's large deflection theory, and the total Lagrangian approach is employed to formulate the element. The deflection and rotation functions of the element boundary are obtained from Timoshenko's laminated composite beam functions. The developed element is simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the element is accurate and efficient for large deformation, small rotation geometrically nonlinear analysis of thin to moderately thick laminated composite plates.

Estimation of low-velocity impact damage in laminated composite circular plates using nonlinear finite element analysis

Nonlinear finite element analysis is used for the estimation of damage due to low-velocity impact loading of laminated composite circular plates. The impact loading is treated as an equivalent static loading by assuming the impactor to be spherical and the contact to obey Hertzian law. The stresses in the laminate are calculated using a 48 d.o.f. laminated composite sector element. Subsequently, the Tsai-Wu criterion is used to detect the zones of failure and the maximum stress criterion is used to identify the mode of failure. Then the material properties of the laminate are degraded in the failed regions. The stress analysis is performed again using the degraded properties of the plies. The iterative process is repeated until no more failure is detected in the laminate. The problem of a typical T300/N5208 composite [45 degrees/0 degrees/-45 degrees/90 degrees](s) circular plate being impacted by a spherical impactor is solved and the results are compared with experimental and analytical results available in the literature. The method proposed and the computer code developed can handle symmetric, as well as unsymmetric, laminates. It can be easily extended to cover the impact of composite rectangular plates, shell panels and shells.

Large deformation finite element analysis of laminated circular composite plates

A 48 d.o.f., four-noded quadrilateral laminated composite shell finite element is particularised to a sector finite element and is used for the large deformation analysis of circular composite laminated plates. The strain-displacement relationships for the sector element are obtained by reducing those of the quadrilateral shell finite element by substituting proper values for the geometric parameters. Subsequently, the linear and tangent stiffness matrices are formulated using conventional methods. The Newton-Raphson method is employed as the nonlinear solution technique. The computer code developed is validated by solving an isotropic case for which results are available in the literature. The method is then applied to solve problems of cylindrically orthotropic circular plates. Some of the results of cylindrically orthotropic case are compared with those available in the literature. Subsequently, application is made to the case of laminated composite circular plates having different lay-up schemes. The computer code can handle symmetric/unsymmetric lay-up schemes. The large displacement analysis is useful in estimating the damage in composite plates caused by low-velocity impact.

Effect of matrix cracking and material uncertainty on composite plates

A laminated composite plate model based on first order shear deformation theory is implemented using the finite element method.Matrix cracks are introduced into the finite element model by considering changes in the A, B and D matrices of composites. The effects of different boundary conditions, laminate types and ply angles on the behavior of composite plates with matrix cracks are studied.Finally, the effect of material property uncertainty, which is important for composite material on the composite plate, is investigated using Monte Carlo simulations. Probabilistic estimates of damage detection reliability in composite plates are made for static and dynamic measurements. It is found that the effect of uncertainty must be considered for accurate damage detection in composite structures. The estimates of variance obtained for observable system properties due to uncertainty can be used for developing more robust damage detection algorithms. (C) 2010 Elsevier Ltd. All rights reserved.

Stress and strength analysis of pin joints in laminated anisotropic plates

Mechanical joints in composites can be tailored to achieve improved performance and better life by appropriately selecting the laminate parameters. In order to gain the best advantage of this possibility of tailoring the laminate, it is necessary to understand the influence of laminate parameters on the behaviour of joints in composites. Most of the earlier studies in this direction were based on simplified assumptions regarding load transfer at the pin-plate interface and such studies were only carried out on orthotropic and quasi-isotropic laminates. In the present study, a more rigorous analysis is carried out to study pin joints in laminates with anisotropic properties. Two types of laminates with (0/ + ?4/90)s and (0/ ± ?2/90)s layups made out of graphite epoxy T300/5208 material system are considered. The analysis mainly concentrates on clearance fit in which the pin is of smaller diameter compared to the hole. The main aspect of the analysis of pin joints is the changing contact between the pin and the plate with increasing load levels. The analysis is carried out by an iterative finite element technique and a computationally efficient routine is developed for this purpose. Numerical studies indicate that the location and magnitude of the peak stresses along the hole boundary are functions of fibre angle and the overall anisotropic properties. It is also shown that the conventional assumption of cosine distribution for the contact pressure between pin and the plate in the analysis lead to underestimation of bearing failure load and overestimation of shear and tensile failure loads in typical (0/905)s cross-ply laminates.

A simple displacement-based quadrilateral laminated composite plate element - part I : linear analysis

Based on the first-order shear deformation theory (FSDT) and Timoshenko's laminated composite beam functions, a simple displacement-based 4-node, 24-dof quadrilateral laminated plate element is proposed in this paper for linear analysis of thin to moderately thick laminates. The deflection and rotation functions of the element boundary are obtained from the Timoshenko's laminated composite beam functions, hence convergence to the thin plate solution can be achieved theoretically and shear-locking problem is avoided naturally. The in-plane displacement functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements of the proposed quadrilateral element. Some numerical examples of linear analysis of composite laminated plates are calculated, and the results show that the proposed element is convergent, shear-locking free, efficient, accurate and not sensitive to mesh distortion.

Fasteners in Composite Plates - Effects of Interfacial Friction

The effects of tangential friction at pin—hole interfaces are appropriately modelled for the analysis of fasteners in large composite (orthotropic) plate loaded along its edges. The pin—hole contact could be of interference, clearance or neat fit. When the plate load is monotonically increased, interference fits give rise to receding contact, whereas clearance fits result in advancing contact. In either case, the changing contact situations lead to non-linear moving boundary value problems. The neat fit comes out as a special case in which the contact and separation regions are invariant with the applied load level and so the problem remains linear. The description of boundary conditions in the presence of tangential friction, will depend on whether the problem is one of advancing or receding contact, advancing contact presenting a special problem. A model is developed for the limiting case of a rigid pin and an ideally rough interface (infinitely large friction coefficient). The non-linearity resulting from the continuously varying proportions of contact and separation at the interface, is handled by an “Inverse Formulation” which was successfully applied earlier by the authors for smooth (zero friction) interfacial conditions. The additional difficulty introduced by advancing contact is handled by adopting a “Marching Solution”. The modelling and the procedure are illustrated in respect of symmetric plate load cases. Numerical results are presented bringing out the effects of interfacial friction and plate orthotropy on load-contact relations and plate stresses.