Three dimensional stress analysis of a composite patch using stress functions

A stress function-based analysis is proposed to provide a simple and efficient approximation method of three-dimensional (3D) state of stress that exists near the free edge of bonded composite patches. In order to apply plane strain assumption in a composite patch, a linear superposition of sliced section from a bonded patch is used. In addition, to describe the load transfer mechanism from the substrate to the composite patch, a simple shear lag model is introduced. The 3D stress behavior at the free edge of the composite patch is modeled by Lekhnitskii stress functions, and the governing equations of the given composite patch are obtained by applying the principle of complementary virtual work. After a suitable expansion of the functions, the governing equations are transformed into two coupled ordinary differential equations, and they are solved by a general eigenvalue solution procedure. As the number of base functions increases, the interlaminar stresses converge. The interlaminar stresses reach maximum at the free edge and decrease sharply at the inner part of the patch. The interlaminar stresses are concentrated at the interface between the layers because of the mismatch of material properties and the geometric singularity. Since the proposed method accurately predicts the 3D stresses in a composite patch bonded on the metal substrate, it can be used as a simple and efficient analytical tool for designing such structural components.     

Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory

Natural frequencies and buckling stresses of cross-ply laminated composite circular cylindrical shells are analyzed by taking into account the effects of higher-order deformations such as transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for laminated composite circular cylindrical shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate higher-order theories are applied to solve the vibration and buckling problems of laminated composite circular cylindrical shells subjected to axial stresses. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the first natural frequency and corresponding buckling stress for the fundamental mode r=s=1 are examined in detail. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite circular cylindrical shells within small number of unknowns.     

A new hybrid-mixed composite laminated curved beam element

In this study, we piesent a new efficient hybrid-mixed composite laminated curved beam element The present element, which is based on the Helhnger-Reissnet vatiational principle and the first-order shear deformation lamination theory, employs consistent stress parameters coriespondmg to cubic displacement polynomials with additional nodeless degrees in order to lesolve the numerical difficulties due to the spurious constraints The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the (6X6) element stiffness matrix The present study also incorporates the straightforwaid prediction of interlaminar stresses from equilibrium equations Seveial numencal examples confirm the superioi behavior of the present composite laminated curved beam element     

Interlaminar stress analysis of general composite laminates

In this study, based on the reduced from of elasticity displacement field for a long laminate, an analytical method is established to exactly obtain the interlaminar stresses near the free edges of generally laminated composite plates under the extension and bending. The constant parameters, which describe the global deformation of a laminate, are properly computed by means of the improved first-order shear deformation theory. Reddy's layerwise theory is subsequently utilized for analytical and numerical examinations of the boundary layer stresses within arbitrary laminated composite plates. A variety of numerical results are obtained for the interlaminar normal and shear stresses along the interfaces and through the thickness of laminates near the free edges. Finally the effects of end conditions of laminates on the boundary-layer stress are examined.     

Measurement of residual stress in thick section composite laminates using the deep-hole method

The deep-hole method is a method of measuring residual stress in large metallic components. In this paper, an extension to the deep-hole method is described to allow the residual stresses in thick section composite laminated plates to be evaluated. The method involves first drilling a small hole through the laminate perpendicular to the surface. The material around the hole is then machined away, resulting in a change in diameter of the hole due to the release of residual stress. This change in diameter is measured and used to calculate the residual stress. The calculation requires the evaluation of coefficients that depend on the properties of the composite. In this work, the finite element method is used to evaluate these coefficients. Using this method, the residual stresses in a 22 mm thick carbon/epoxy composite plate are measured and reported.     

Vibration and stability of angle-ply laminated composite plates subjected to in-plane stresses

Natural frequencies and buckling stresses of angle-ply laminated composite plates are analyzed by taking into account the effects of shear deformation, thickness change and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for thick rectangular laminates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported thick laminated plate. In order to assure the accuracy of the present theory, convergence properties of the fundamental natural frequency are examined in detail. Numerical results are compared with those of the published existing theories. The modal displacement and stress distributions in the thickness direction are obtained and plotted in figures. The present global higher-order approximate theories can predict the natural frequencies, buckling stresses and modal stresses of thick multilayered angle-ply composite laminates accurately within small number of unknowns which is not dependent on the number of layers.     

Thermo-viscoelastic residual stress analysis of metal liner-inserted composite cylinders

One of the most significant problems in the processing of composite material is residual stress. The high residual stress may cause cracking in the matrix without external loads and degrade tile integrity of composite structures. In this Study, thermo-viscoelastic residual stresses occurred in an aluminum liner-inserted composite cylinder are investigated. This type of the structure is used for rocket fuselage due to the convenience to attach payloads and equipment to the metal liner by machining. The time and degree of cure dependent thermo-viscoelastic constitutive equations are developed and coupled with a thermo-chemical process model. Thee equations are solved with the finite element method to predict the residual stresses in the composite cylinder and also in the interface between the liner and file composite dining cure.     

Pre-stressed adhesive strap joints for thick composite sandwich structures

A simple but effective design to improve the strength of thick adhesive composite strap joints is validated with experiment and finite element method. The strap joint under investigation, with a particular application to naval ship structures, consists of two thick woven E-glass/vinyl ester laminates joined together with two steel doublers. Longitudinal tensile loads are applied to the joints, resulting in large concentrated shear and peel stresses near the free edges of bondlines. The new design intends to reduce the adhesive peel stress by application of through-the-thickness compressive pre-stress along the bondline and thus leads to an increase of joint strength. Experiment results show that all the joint failures are delamination of the top layer of the laminated adherends. The test further confirms that joint strength increases significantly by applying the transverse pre-stress. Finite element analysis reveals that the pre-stress can effectively reduce the magnitude even reverse the sign of the peel stress in the adhesive layer and the adherends. Recessing the adhesive leading edge could magnify the pre-stress effect and reduce the adhesive peel stress, but would increase the shear stress. For those composite joints with low transverse interlaminar strength and susceptible to delamination, this simple design/technique can considerably improve their joint strength.     

确定复合材料对称层板层间应力的边界层近似计算法

提出了一种有效的确定复合材料对称层板自由边附近层间应力分布的边界层近似法。所确定的应力场满足０阶边界层控制方程和自由边上的应力边界条件以及层间界面上的应力连续条件。对几种复合材料层板的分析表明，本文提出的方法可以较好地估算工程应用中几层至几十层的复合材料对称层板听层间应力分布。     

Modeling and analysis of curved beams with debonded piezoelectric sensor/actuator patches

In this paper, a mathematical model for thin-walled curved beams with partially debonded piezoelectric actuator/sensor patches is presented for investigating the effect of debonding of the actuator/sensor on their open- and closed-loop behaviors. The actuator equations and the sensor equations of the curved beam in perfectly bonded and debonded regions are derived. In the perfect bonding region, the adhesive layer is modeled to carry constant peel and shear stresses; while in the debonding area, it is assumed that there is no peel and shear stress transfer between the host beam and the piezoelectric layer. Both displacement continuity and force equilibrium conditions are imposed at the interfaces between the bonded and debonded regions. Based on the model and the sensing equation of the sensor, a closed-loop vibration control for the curved beams is performed. To obtain the frequency response from the presented model, a solution scheme for solving the complex governing equations is given. Using this model and the solution scheme, the effects of the debonding of actuator and sensor patches on open- and closed-loop control are investigated through an example. The results show that edge debonding of the piezoelectric patch has a significant side effect on the closed-loop control of the curved beams.     

Buckling of laminated composite plates subjected to mechanical and thermal loads using meshless collocations

Meshless collocations utilizing Gaussian and Multiquadric radial basis functions for the stability analysis of orthotropic and cross ply laminated composite plates subjected to thermal and mechanical loading are presented. The governing differential equations of plate are based on higher order shear deformation theory considering two different transverse shear stress functions. The plate governing differential equations are discretized using radial basis functions to cast a set of simultaneous equations. The convergence of both radial basis functions is studied for different values of shape parameters. Several numerical examples are undertaken to demonstrate the accuracy of present method and the effects of orthotropy ratio of the material, span to thickness ratio of the plate, and fiber orientation on critical load/temperature are also presented.     

Dynamic analysis of smart composite beams by using the frequency-domain spectral element method

To excite or measure the dynamic responses of a laminated composite structure for the active controls of vibrations or noises, wafer-type piezoelectric transducers are often bonded on the surface of the composite structure to form a multi-layer smart composite structure. Thus, for such smart composite structures, it is very important to develop and use a very reliable mathematical and/or computational model for predicting accurate dynamic characteristics. In this paper, the axial-bending coupled equations of motion and boundary conditions are derived for two-layer smart composite beams by using the Hamilton??s principle with Lagrange multipliers. The spectral element model is then formulated in the frequency domain by using the variation approach. Through some numerical examples, the extremely high accuracy of the present spectral element model is verified by comparing with the solutions by the conventional finite element model provided in this paper. The effects of the lay-up of composite laminates and surface-bonded wafer-type piezoelectric (PZT) layer on the dynamics and wave characteristics of smart composite beams are investigated. The effective constraint forces at the interface between the base beam and PZT layer are also investigated via Lagrange multipliers.     

Analysis of rectangular laminated composite plates via FSDT meshless method

A meshless approach based on the reproducing kernel particle method is developed for the flexural, free vibration and buckling analysis of laminated composite plates. In this approach, the first-order shear deformation theory (FSDT) is employed and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency conditions. The essential boundary conditions are enforced by a singular kernel method. Numerical examples involving various boundary conditions are solved to demonstrate the validity of the proposed method. Comparison of results with the exact and other known solutions in the literature suggests that the meshless approach yields an effective solution method for laminated composite plates.     

Effect of fiber orientation on interfacial fracture toughness for adhesively bonded composite plates

In this study, interfacial fracture toughness was investigated experimentally and numerically in laminated composite plates with different fiber reinforcement angles bonded with adhesive. The composite plates are four-layered and the layer sequence is [0º/θ]_s. DCB test was applied to composite plates reinforced with epoxy resin matrix and unidirectional carbon fiber. The experimental sample model for the DCB test was made using the ANSYS finite element package program. In the numerical study, four layered composites were prepared in three dimensions. Under critical displacement value; mode I fracture toughness at the crack tip was calculated using VCC (virtual crack closure) technique. Numerical values consistent with experimental results have presented in graphical forms. At 60o and 75° the greatest fracture toughness was obtained. In addition, numerical results have shown that fiber orientation prevents the uniform distribution of stress on the interface crack tip and causes stress accumulation, especially at the edge of the plate.

     

3-D finite element analysis for thermo-mechanical behavior of laminated carbon-phenolic composite ring

In this paper, the thermal insulator structure of a real rocket which is fabricated in a way that laminated composite rings are connected in series is analyzed using 3-dimensional axisymmetric finite element models. Simulation of cowl zone using real operating conditions provides that the stress distribution in the laminated composite ring is largely influenced by ply-angles, axial dimensions, and boundary conditions. It is hypothesized that notably the ply-lift that is the precursor to the wedge-out occurs in the ring-to-ring bonding region to a limited ply angle. Moreover, it is suggested that the wedge-out is dropped out due to the maximum shear stress in a fixed ply-angle direction and the axial compressive stress.     

On the thermal expansion effects in the transverse direction of laminated composite plates by means of a global-local higher-order model

In this paper, a new efficient global-local higher-order model is proposed for the thermoelastic analysis of laminated composite and sandwich plates. The proposed model takes into account explicitly the contribution of thermal expansion in the transverse displacement component. To satisfy the transverse displacement continuity along the thickness direction, the continuity condition of transverse displacement at interfaces, which is not satisfied in many other schemes, has been a priori enforced. This model fully satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. As the number of variables of the proposed model is independent of the number of layers of laminates, compared to the 1,2-3 theory proposed by Li and Liu (1997) [20], the present model offers some significant improvements, and is able to predict accurately thermoelastic response of laminated plates under uniform temperature without a corresponding increase in the number of unknowns. The governing equations of equilibrium are derived by means of the principle of virtual displacements involving the thermal strain field. Applying Navier's technique, analytical solutions in terms of a double trigonometric series for simply supported laminated plates are presented. Results of benchmark examples are compared with the three-dimensional thermoelastic solutions as well as other published works. Numerical results show that the proposed model is more rigorous and can better predict the thermoelastic response in comparison with the 1,2-3 theory and other two-dimensional models.     

Generalized differential quadrature for free vibration of rotating composite laminated conical shell with various boundary conditions

By using the generalized differential quadrature (GDQ) method, this paper presents the orthotropic influence of composite materials on frequency characteristics for a rotating thin truncated circular symmetrical cross-ply laminated composite conical shell with different boundary conditions. The present governing equations of free vibration include the effects of initial hoop tension and the centrifugal and Coriolis accelerations due to rotation. Frequency characteristics are obtained to study in detail the orthotropic influences. Effects of boundary condition, rotating speed, circumferential wave number and geometric property are also discussed. To ensure the accuracy of the present results by the GDQ method, comparisons are made with those available in open literature and very good agreements are achieved.     

Dynamic response and damage of composite shell under impact

The dynamic response and damage of laminated composite cylindrical shell subjected to impact load is numerically investigated using the finite element method. A nine-node isoparametric quadrilateral element based on Sander's shell theory is developed, in which the transverse shear deformation is considered. A semi-empirical contact law that accounts for the permanent indentation is incorporated into the finite element program to evaluate the contact force. The Newmark time ingegration algorithm is used for solving the time dependent equations of the shell and the impactor. The Tsai-Wu failure criterion is used to estimate the failure of the laminated shell. Numerical results, including the contact force history, interlaminate damage zone, and failure indices in the shell are presented. Effects of curvature, impact velocity and mass of impactor on the composite shell behaviors are discussed.     

Optimum design of multi-ring composite flywheel rotor using a modified generalized plane strain assumption

A numerical method for calculating the stress and strength ratio distribution of the hybrid rim-type composite flywheel rotor is presented with a consideration of the thermally induced residual stresses. The axisymmetric rotor is divided into several rings and the stiffness matrix for each ring is derived by solving the radial equilibrium equation and the stress–strain–temperature relations. The ring stiffness matrices are assembled into a symmetric global matrix satisfying the continuity equations at each interface with the assumptions of a modified generalized plane strain (MGPS). In the MGPS, the z-directional axial strains are assumed to vary linearly along the radial direction; ε_z=ε₀+ε₁r. The conditions that the z-directional force and the circumferential moment resultants vanish are thus used to solve the z-directional axial strains as well as the radial and circumferential strains. After solving the strain distributions, the on-axis stresses and the strength ratios are calculated at each ring. Three-dimensional finite element method (3D FEM) is then used to verify the accuracy of the present method. The results are also compared with those based on the assumption of a plane stress (PSS). In this case, the analysis of MGPS better matches with 3D FEM results than PSS. An optimum design is then performed maximizing total stored energy (TSE) with the thickness of each composite rim as design variables. The optimal design obtained in this study, which considers material sequence, provides a more effective way of maximizing TSE. It is found that the consideration of the residual stress in the design of the hybrid flywheel rotor is crucial. The result of the optimal designs shows that TSE with consideration of ΔT reduces by about 30%.     

Improved flexural–torsional stability analysis of thin-walled composite beam and exact stiffness matrix

A simple but efficient method to evaluate the exact element stiffness matrix is newly presented in order to perform the spatially coupled stability analysis of thin-walled composite beams with symmetric and arbitrary laminations subjected to a compressive force. For this, the general bifurcation-type buckling theory of thin-walled composite beam is developed based on the energy functional, which is consistently obtained corresponding to semitangential rotations and semitangential moments. A numerical procedure is proposed by deriving a generalized eigenvalue problem associated with 14 displacement parameters, which produces both complex eigenvalues and multiple zero eigenvalues. Then the exact displacement functions are constructed by combining eigenvectors and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently exact element stiffness matrices are evaluated by applying member force–displacement relationships to these displacement functions. As a special case, the analytical solutions for buckling loads of unidirectional and cross-ply laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of this study, the numerical, analytical, and the finite element solutions using the Hermitian beam elements are presented and compared with those from ABAQUS's shell elements. The effects of fiber orientation and the Wagner effect on the coupled buckling loads are also investigated intensively.