Edge delamination in a laminated composite strip under generalized plane deformations

Edge delamination cracks in an elastic laminated composite strip are considered within the range of generalized plane deformations. By way of a simple regular finite element method, the method of mutual integral, wherein generalized plane strain solutions are employed as auxiliary fields, is applied to edge delamination cracks to obtain the complex stress intensities. The proposed numerical scheme is found to be very efficient and accurate. Moreover, the crack growth stability is examined for various loadings, including compression, bending and torsion, in terms of the energy release rate and mode mixity.     

An investigation on the post-buckling behavior of symmetric cross-ply laminated plates using a semi-energy finite strip approach

A geometrically non-linear finite strip for the post-buckling analysis of geometrically perfect thin symmetric cross-ply laminated plates under uniform end shortening is presented in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von Kármán’s compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von Kármán’s compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the Principle of Minimum Potential Energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyze the post-local-buckling behavior of thin flat laminates. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. It should be mentioned that the FEM analysis was carried out employing the general purpose ANSYS package. The study of the results has provided confidence in the validity and capability of the developed finite strip in handling the post-buckling problem of symmetric cross-ply laminated plates.     

Flutter of delaminated cross-ply laminated cylindrical shells

In this study, the instability of delaminated cross-ply thin laminated cylindrical shells and panels when subjected to supersonic flow parallel to its length edge is investigated. The delamination is parallel to the shell reference and it extends along the entire length of the cylindrical shell. The Love’s shell theory and Von-Karman–Donnell type of kinematic relations along with first-order potential theory have been employed to construct the aeroelastic equations of motion. The effects of several parameters such as length to radius ratio, delamination position, size and thickness on the critical values are discussed in the details. The results indicate that the presence of delamination reduced the overall stiffness of the structure and thereby decreases the flutter critical boundaries.     

Thermal buckling of cross-ply laminated composite beams

Summary Thermal buckling of thick, moderately thick and thin cross-ply laminated beams subjected to uniform temperature distribution are analyzed. Exact analytical solutions of refined beam theories are developed to obtain the critical buckling temperature of cross-ply beams with various boundary conditions. The state space concept in conjunction with Jordan canonical form will be used to solve exactly the governing equations of the thermal buckling problems. The effects of length to thickness ratio, modulus ratio, thermal expansion coefficients ratio, various boundary conditions and number of layers on the critical buckling temperature are investigated.     

Thermally induced vibrations of cross-ply laminated shallow shells

Summary An exact analytical solution of the dynamic response of cross-ply laminated shallow shells subject to rapid heating is presented. The classical theory (based on Love-Kirchhoff assumption), involving three coupled partial differential equations, is used. The solution is applicable to shells whose parallel edges are simply supported and the remaining ones are clamped. A generalized modal approach is used to obtain the solution. The equations of motion are converted into a single-order system of equations by using state variables. The biorthogonality conditions of principal modes of the original and adjoint eigenfunctions are used to decouple the state space equation. Histories of deflection of graphite-reinforced aluminum shell panels are presented through numerical examples.     

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.     

Non-homogeneous response of cross-ply laminated elastic plates using a higher-order theory

A consistent formulation for the bending of cross-ply laminated composite plates that possess non-homogeneous elastic properties is presented. Based on a third-order shear deformation plate theory, the governing equations are obtained using the principle of virtual work. With the help of the small parameter method, a wide variety of results are presented for the symmetric and antisymmetric analysis of non-homogeneous rectangular laminated plates. The influence of non-homogeneity, lamination schemes, aspect ratio and material anisotropy on the deflections and stresses is investigated. The new results for non-homogeneous response of composite plates should serve as bench marks for future comparisons.     

Transverse cracks in a strip with reinforced surfaces

The symmetrical problem of two transverse cracks in an elastic strip with reinforced surfaces is formulated in terms of a singular integral equation. The special cases of one central crack or two edge cracks are discussed. Numerical methods for solving the problems with internal cracks are outlined and stress intensity factors are presented for various geometries and degrees of surface reinforcement.     

Stresses in cross-ply laminated circular cylinders of axially variable thickness

Summary This paper presents the results from an analytical investigation of the behavior of composite circular cylinders subjected to internal and external surface loading. The present cylinder consists of a number of homogeneous ply groups of axially variable thickness. Each ply group forming a layer is treated as an individual thin elastic cylinder of generally orthotropic material with interfacial stresses on the inner and outer surfaces of the layer as boundary loading. The deformation and stresses in each layer can be expressed in terms of interfacial stresses along the exterior surfaces of each layer. All displacement and stresses throughout the composite cylinder can be determined subsequently after satisfying boundary conditions at the inside and outside surfaces of the cylinder in conjunction with the recurrence relationship among interfacial stresses. Numerical results are presented for different values of the inner-to-outer ratio, number of layers, stacking sequence, axially-variable-thickness parameter, and load factor. Based on the presented results, conclusions can be drawn concerning the cylinder behavior and its sensitivity to different parameter variations.     

Vibration analysis of cross-ply laminated truncated conical shells using a spline method

Free vibration of symmetric and antisymmetric cross-ply composite laminated truncated conical shells using the spline function technique is studied. The equilibrium equations for a truncated conical shells are formulated including first-order shear deformation theory. The equations of motion are derived in terms of displacement functions and rotational functions using stress–strain and strain–displacement relationships. The coupled differential equations are solved using Bickley-type splines to obtain the generalized eigenvalue problem by combining suitable boundary conditions. The convergence and comparative results are presented. Both symmetric and anti-symmetric cross-ply shells are considered using various types of material properties. Parametric studies are made to investigate the effect of transverse shear deformation on the frequency parameter with respect to the thickness ratio, length ratio, cone angle, and circumferential mode number using different numbers of layers under various types of boundary conditions.     

Dynamic behavior of cross-ply laminated beams with piezoelectric layers

The dynamic behavior of cross-ply non-symmetric composite beams, having uniform piezoelectric layers is analysed. A first-order Timoshenko type analysis is applied to obtain the equations of motion, which include shear deformation, rotary inertia, bending-stretching coupling terms and induced axial strains caused by the piezoelectric material. Using the principle of virtual work, the coupled equations of motion and the relevant boundary conditions are obtained. For a laminated beam having uniform piezoelectric layers the induced strains appear only in the boundary conditions yielding time dependent ones. Therefore, a special procedure involving orthogonality of the coupled Timoshenko type natural vibrational modes of the beam is applied to help understanding of the dynamic behavior of the non-symmetric laminated beam and to investigate the influence of the induced strains (by the piezoelectric layers) on the dynamic behavior while keeping an ‘open-loop’ control. Typical types of laminates and piezoelectric materials are used to calculate natural frequencies and mode shapes. Numerical results for various parameters of laminated beams are presented to stress the better applicability and suitability of the present approach to the analysis of dynamic behavior of laminated composite beams with piezoelectric layers.     

Effective widths of compression-loaded of perforated cross-ply laminated composites

In this study the influence of eccentric circular cutouts on the prebuckling and postbuckling stiffness, and effective widths of compression loaded laminated composite plates are presented. The effective-widths concept is derived based on nonlinear finite element analysis for the plates with and without cutout. Several behavioral trends are described that initially appear to be nonintuitive. The results demonstrate a complex interaction between cutout size and the degree of plate orthotropy that affects the axial stiffness and effective width of plate subjected to compression loads. Also these investigations show that the cutout dimension have a more considerable effect on prebuckling stiffness compare to postbuckling one. It will show that the stiffness ratio of the postbuckling over prebuckling is increased by cutout size. Considering the effective-width ratios concept provide a simple means for incorporating the postbuckling strength and stiffness of plate subcomponents into the design of stiffened structures.     

Edge cracks in a transversely isotropic hollow cylinder

The analytical solution for the linear elastic, axisymmetric problem of inner and outer edge cracks in a transversely isotropic infinitely long hollow cylinder is considered. The z = 0 plane on which the crack lies is a plane of symmetry. The loading is uniform crack surface pressure. The mixed boundary value problem is reduced to a singular integral equation where the unknown is the derivative of the crack surface displacement. An asymptotic analysis is done to derive the generalized Cauchy kernel associated with edge cracks. It is shown that the stress intensity factor is a function of three material parameters. The singular integral equation is solved numerically. Stress intensity factors are presented for various values of material and geometric parameters.     

Edge effects of uniformly loaded cross-ply composite laminates

Interlaminar stresses resulting from bending of rectangular cross-ply composite laminates are determined using a layer wise laminate theory. Two types of laminates are considered. First a fully simply supported laminate subjected to bi-directional bending is analyzed. The results obtained from this theory are compared with those of the published three-dimensional elasticity solutions to verify the validity and accuracy of the present theory. Then laminates with two edges simply supported and the other two edges free are examined. The results indicate the presence of significant interlaminar stresses near the free edges.     

On the transient response of cross-ply laminated circular cylindrical shells

Transient response of simply-supported circular cylindrical shells is investigated using a higher-order shear deformation theory (HSDT). The theory is a modification of the Sanders' shell theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the bounding surfaces of the shell. The results obtained using the classical shell theory (CST) and the first-order shear deformation theory (FSDT) are compared with those obtained using the higher-order theory. The state-space approach is used to develop the analytical solutions to the equations of motion of the three theories.     

Free vibration of cross-ply laminated beams with arbitrary boundary conditions

Analytical solutions of refined beam theories are developed to study the free vibration behavior of cross-ply rectangular beams with arbitrary boundary conditions in conjunction with the state space approach. The study concludes that the disagreement between different shear deformation theories is much less than the disagreement between any of them and Euler-Bernoulli theory.     

Buckling analysis of cross-ply laminated conical panels using GDQ method

The buckling analysis of cross-ply laminated conical shell panels with simply supported boundary conditions at all edges and subjected to axial compression is studied. The conical shell panel is a very interesting problem as it can be considered as the general case for conical shells when the subtended angle is set to 2π and also cylindrical panels and shells when the semi-vertex angle is equal to zero. Equations were derived using classical shell theory of Donnell type and solved using generalized differential quadrature method. The results are compared and validated with the known results in the literature. The effects of subtended angle, semi-vertex angle, length, thickness and radius of the panel on the buckling load and mode are investigated.     

Edge crack in a strip of an elastic solid

The problem of determining the distribution of stress and the deformation of a long strip of an elastic material, damaged by a crack normal to an edge of the strip, is investigated. The strip is deformed by pressure applied to the faces of the crack. The stress intensity factor is calculated and its variation with the depth of the crack, relative to the width of the strip, in the special case of uniform pressure, is illustrated.