Differential quadrature element method for static analysis of shear deformable cross‐ply laminates

In this paper, the two‐dimensional differential quadrature element method (DQEM) is developed for the static analysis of symmetric cross‐ply laminates using the first‐order shear deformation plate theory. In this study, the laminated plate, which may contain different discontinuities in loading, geometry, material, and boundary conditions, is first divided into several simple plate elements and then the differential quadrature method (DQM) is applied to each simple element. Compatibility conditions are derived to connect the plate elements so that the overall matrix equation system for the whole plate is obtained and solved. The reliability of the DQEM for solving the titled problems is examined carefully through convergence and accuracy studies and finally some numerical test examples are given to demonstrate the applicability and flexibility of this method for practical use. The methodology presented here has overcome some critical drawbacks of the global DQM but is different from the Quadrature Element Method (QEM) since only one grid point is employed to represent the interface point. Copyright © 1999 John Wiley & Sons, Ltd.     

A novel 3D mixed finite‐element model for statics of angle‐ply laminates

Analysis of angle‐ply laminates becomes critical and computationally involved because of the presence of extension–shear coupling. A refined three‐dimensional, mixed, 18‐node finite element (FE) model has been developed to analyse angle‐ply laminates under static loading. The minimum potential energy principle has been used for the development of the mixed FE model, where the transverse stress components (τ_xz, τ_yz and σ_z, where z is the thickness direction) have been incorporated as the nodal degrees of freedom, in addition to the three displacement fields. Further, continuity of transverse stress fields through the thickness of the plate and layerwise continuity of displacement fields have been enforced in the formulation. Because all the constitutive and the compatibility conditions have been ensured within the continuum, the present formulation is unique amongst the family of mixed FE models. Results have been obtained for various angle‐ply laminates and compared with analytical and finite‐element solutions, which have been found to be in good agreement with them. Some new results on angle‐ply with clamped–clamped support condition have also been presented to serve as benchmark results. Copyright © 2003 John Wiley & Sons, Ltd.     

A computational continuum damage mechanics model for predicting transverse cracking and splitting evolution in open hole cross‐ply composite laminates

The present study focuses on a computational constitutive model which predicts the matrix cracking evolution and fibre breakage in cross‐ply composite laminates with open hole under in‐plane loading. To consider the effects of matrix cracking on the nonlinear response of laminates, a simplified crack density based model is applied which evaluates the representative damage parameters of matrix cracking. Furthermore, a developed subroutine based on continuum damage mechanics concepts is applied in ANSYS code which is capable to consider the transverse cracking/splitting evolution and predict the final failure load of mentioned laminate under monotonic loading in a progressive damage analyses. It is shown that the obtained stress–strain behaviours and the damage evaluation of considered laminates are in good agreement with the available experimental results.     

A generalized plane-strain crack density-based model for evaluating the finite fracture toughness of composite laminates

The present study focuses on a developed crack density-based model for evaluating the material properties of an orthotropic composite ply containing a specified matrix-cracking density. Furthermore, more complementary details of this model, including a closed form solution for evaluating the stress fields as well as stiffness degradation of a damaged ply, will be presented. The derived relations will be applied for evaluating the master plot curve, which is applicable for obtaining the finite fracture toughness (G_mc) of laminated composites. The obtained results will be compared with the available experimental results.     

Numerical investigation of matrix cracking propagation in cross‐ply laminated composites subjected to three‐point bending load using concurrent multiscale model

The purpose of the present study is to analyze fiber‐matrix debonding and induced matrix cracking formation as two major micromechanical damage modes in cross‐ply composite laminates using a two‐dimensional numerical approach. To this aim, the cross‐ply laminates containing 90‐degree layers are modeled, where the fibers are arranged randomly in transverse plies. Damage modes in this numerical model are simulated by the cohesive surface method. The performed analyses reveal that in the laminates with 90‐degree layers located in the outer positions, the primary micro damage mode is micro matrix cracking which is initiated from the fiber‐matrix debonding damage mode and will be followed by matrix cracking. The main benefit of the present study in comparison to other numerical methods is proposing a virtual test method for damage analysis of different cross‐ply laminates in which, the matrix cracking formation will emerge physically in a random and antisymmetric pattern similar to the experimental observations.     

界面脱粘对正交铺设SiC/CAS复合材料基体开裂的影响

采用细观力学方法研究了正交铺设SiC/CAS复合材料在单轴拉伸载荷作用下界面脱粘对基体开裂的影响。采用断裂力学界面脱粘准则确定了0°铺层纤维/基体界面脱粘长度, 结合能量平衡法得到了主裂纹且纤维/基体界面发生脱粘(即模式3)和次裂纹且纤维/基体界面发生脱粘(即模式5)的临界开裂应力, 讨论了纤维/基体界面剪应力、 界面脱粘能对基体开裂应力的影响。结果表明, 模式3和模式5的基体开裂应力随纤维/基体界面剪应力、 界面脱粘能的增加而增加。将这一结果与Chiang考虑界面脱粘对单向纤维增强陶瓷基复合材料初始基体开裂影响的试验研究结果进行对比表明, 该变化趋势与单向SiC增强玻璃陶瓷基复合材料的试验研究结果一致。     

Progressive damage analyses of angle‐ply laminates exhibiting free edge effects using continuum damage mechanics with layer‐wise finite element method

Capability of continuum damage mechanics (CDM) to predict the damage mechanism evolution of composite laminates has rarely been carried out, and most of the previous CDM works mainly focused on the overall response of the laminates. In this paper, progressive damage and overall response of the composite laminates under quasi‐static, monotonic increasing loading are investigated using three‐dimensional (3D) CDM implementation in a finite element method that is based on the layer‐wise laminate plate theory. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle‐ply composite laminates under quasi‐static loading that exhibit free edge effects is investigated. It is shown that using CDM global behaviour and various damage mechanisms affected by the complex nature of free edges can be qualitatively well predicted.     

Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross‐ply laminates

One of the major difficulties in interlaminar fracture tests of multidirectional laminates is the high tendency for intralaminar cracking and the resulting wavy crack propagation. Experimental work showed that this occurred in double cantilever beam (DCB) tests of cross‐ply laminates having a starter crack on a 0°/90° interface. Moreover, under steady‐state propagation conditions, the apparent values of the critical strain energy release rate G_Ic were two times higher than those of 0°/0° specimens. In this paper, a finite‐element‐based progressive damage model was used to simulate crack propagation in cross‐ply specimens. The results showed that transverse cracking alone cannot be responsible for the above difference of G_Ic values. Therefore, the higher propagation G_Ic values for cross‐plies must be attributed to the more extensive fibre bridging observed and to plastic deformations of the 90° interfacial ply.     

Variational approach development in analysis of matrix cracking and induced delamination of cross-ply composite laminates subjected to in-plane shear loading

Matrix microcracking and induced delamination propagating from the edge of microcracks in cross-ply composite laminates with [0_n/90_m]_s and [90_m/0_n]_s layups under in-plane static shear loading are investigated. An admissible stress field, which satisfies all of equilibrium equations, boundary conditions, and continuity of interfaces, is approximated. Then using the principle of the minimum complementary energy, the stress state is obtained from calculations of variation. The calculated stress state gives the stiffness reduction and the total strain energy of the laminated composite structure. Finally, the strain energy release rate of a general cross-ply laminate due to initiation and propagation of matrix cracking and induced delamination can be deduced. Results of the developed approach are in good agreement with experimental observations and finite element analyses, which confirms its accuracy.     

Efficient dynamic finite element method for 3D objects with uniform cross‐section

An efficient implicit dynamic finite element method (FEM) for elastic 3D objects with uniform cross‐sections was developed. In this method, the finite element mesh is generated in such a way that the object to be analysed is at first sliced into layers with the same thickness along its generatrix and then each layer is discretized into finite elements of the same pattern. This way of discretization makes the mass, viscosity, and stiffness matrices into the repetitive block tridiagonal matrices. The repetitive block tridiagonal matrix has the characteristic, that the sequence of matrices which appears in the Gaussian elimination for the repetitive block tridiagonal matrix is a rapid convergent sequence. The process of the Gaussian elimination can be terminated when the sequence converges. The rest of the sequence is not necessary to be stored. The present method can save the computational time and memory by utilising this characteristic of the repetitive block tridiagonal matrix. A few examples of analyses including whole Hopkinson‐bar analysis were performed to demonstrate the effectiveness of the present method. The present method is applicable not only to the elasto‐dynamics but also to many other problems, such as thermal problems, electrical problems, and plastic problems without geometric non‐linearity. Copyright © 2005 John Wiley & Sons, Ltd.     

One‐dimensional analysis of thin‐walled closed beams having general cross‐sections

This paper presents a new one‐dimensional theory for static and dynamic analysis of thin‐walled closed beams with general cross‐sections. Existing one‐dimensional approaches are useful only for beams with special cross‐sections. Coupled deformations of torsion, warping and distortion are considered in the present work and a new approach to determine sectional warping and distortion shapes is proposed. One‐dimensional C⁰ beam elements based on the present theory are employed for numerical analysis. The effectiveness of the present theory is demonstrated in the analysis of thin‐walled beams having pillar sections of automobiles and excavators. Copyright © 2000 John Wiley & Sons, Ltd.     

Non‐linear dynamic stability analysis of composite laminates under periodic in‐plane compressive loads

This work deals with the investigation of the non‐linear instability behaviour of the composite laminates subjected to periodic in‐plane/axial load, through the finite element formulation with dynamic response analysis. Here, C¹ eight‐noded shear‐flexible plate element, based on a new kind of kinematics which allows to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers of the laminate, and also the boundary conditions at the top and bottom surfaces of the laminate, is employed. The non‐linear governing equations obtained are solved using the Newmark direct integration method coupled with a modified Newton–Raphson iteration procedure. The analysis brings out various characteristic features of the dynamic stability such as existence of beats, their dependency on the forcing frequency, and the typical character of vibrations in the different regions. Numerical results are also presented to highlight the influence of ply‐angle and lay‐up of the laminate on dynamic stability behaviour of the composite laminates. Copyright © 1999 John Wiley & Sons, Ltd.     

Induced out‐of‐plane mode at the tip of blunt lateral notches and holes under in‐plane shear loading

As it is well known the Poisson's effect in a cracked plate subjected to anti‐symmetric plane loading leads to the generation of a coupled out‐of‐plane singular mode. Recent theoretical and numerical analyses have shown that this effect is present also in plates weakened by sharp V‐notches and might play a role in failure initiation phenomena of notched plates subjected to Mode II loading, especially in the presence of a large notch opening angle. Dealing with blunt notches with a large notch radius, and not just with sharp notches, the presence or not of an out‐of‐plane mode does not appear to have been systematically investigated in the past. The main aim of this work is to confirm the existence of the stress field associated with the out‐of‐plane mode (Mode O) and to describe its main features in the presence of a notch radius significantly different from zero. The analyses include U‐notches, as well as circular and elliptic holes. The strain energy density in a 3D control volume is utilized to identify the most critical zone (with respect to failure initiation) through the plate thickness at the notch tip.     

Damage analysis of laminated composites using a new coupled micro‐meso approach

In this study, the simplicity and strong physical meaning of micromechanics approach and capability of mesomechanics approach for damage analysis of structures with complex loadings are employed to develop a new micro‐meso approach. For this purpose, a new micromechanics model is developed to predict the matrix cracking initiation and evolution in laminated composites. These damage initiation and evolution are replaced with the damage criteria and flow rule in the continuum damage approach, respectively. The results of this procedure are used in the FEM damage analyses of laminated composites to predict constitutive response of layered composites. It is shown that, the predicted stress distribution and strain energy in a lamina unit cell are in good agreement with the finite element results. Furthermore, it is shown that the predicted stress–strain behaviours are in good agreement with the available experimental results for various laminates with different lay‐ups.     

Contact between 3D beams with rectangular cross‐sections

In this paper frictionless contact between 3D beams is analysed. The beam model is used in which large displacements but small strains are allowed. The element is derived on the basis of updated Lagrangian formulation using physical shape functions with shear effect included. An effective contact‐search algorithm, which is necessary to determine an active set for the contact contribution treatment, is elaborated. The contact element uses the same set of physical shape functions as the beam element. A consistent linearization of contact contribution is derived and expressed in suitable matrix form, easy to use in FEM approximation. Several numerical examples depict the efficiency of the presented approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

In this paper, the free vibration analysis of simply‐supported and clamped composite laminates, especially thick laminates, is carried out. The three‐dimensional theory of elasticity is integrated into a layerwise model via differential quadrature discretization. All physical governing equations are satisfied, including the additional constraints of the characteristics of continuity and discontinuity of interfacial transverse and in‐plane strains and stresses along the interfaces of composite laminates. Effects of plate aspect and thickness ratios on the free vibration of these laminates are examined in detail. This study demonstrates the applicability, accuracy, and stability of the present methodology, for vibration analyses of composite structures of thick laminated constitution. Copyright © 2003 John Wiley & Sons, Ltd.     

Exact dynamic stiffness matrix for a thin‐walled beam of doubly asymmetric cross‐section filled with shear sensitive material

An exact dynamic stiffness matrix is developed for the flexural motion of a three‐dimensional, bi‐material beam of doubly asymmetric cross‐section. The beam comprises a thin walled outer layer that encloses and works compositely with its shear sensitive core material. The outer layer may have the form of an open or closed section and provides flexural, warping and Saint‐Venant rigidity, while the core material provides Saint‐Venant and shear rigidity. The uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick–Williams algorithm, which enables the required natural frequencies to be converged upon to any required accuracy with the certain knowledge that none have been missed. Such a formulation enables the powerful modelling features associated with the finite element technique to be utilized when establishing structural models. Three examples are included to validate and illustrate the method. The work also holds considerable potential in its application to the approximate analysis of asymmetric, multi‐storey, three‐dimensional wall‐frame structures. Copyright © 2006 John Wiley & Sons, Ltd.     

The effect of fatigue pre‐cracking forces on fracture toughness

Testing procedures for the determination of the fracture toughness of a material by monotonic loading of fatigue pre‐cracked specimens are well established in standards such as BS 7448, BS EN ISO 15653, ISO 12135, ASTM E1820 and ASTM E1921. However, a review of these standards indicates a wide range of permitted fatigue pre‐cracking forces, whilst the underlying assumption in each standard is that the pre‐cracking conditions do not affect the fracture toughness determined. In order to establish the influence of different fatigue pre‐cracking forces on the fracture toughness, tests were carried out on specimens from an API 5L X70 pipeline steel. Single‐edge notch bend specimens of Bx2B geometry were notched through thickness and tested at temperatures of +20 °C, ?80 °C and ?140 °C to show the fracture behaviour in different regions of the fracture toughness ductile‐to‐brittle transition curve. Fatigue pre‐cracking was conducted on a high‐frequency resonance fatigue test machine over a range of pre‐cracking forces permissible within the various standards and beyond. The results showed that an excessively high pre‐cracking force can result in a significant overestimation of the value of fracture toughness for material exhibiting brittle behaviour, whilst very low fatigue pre‐cracking forces appeared to result in an increase in scatter of fracture toughness. A review of standards indicated that there was a possibility to misinterpret the intention of the ISO 12135 standard and potentially use excessively high pre‐cracking forces. Suggested clarifications to this standard have therefore been proposed to avoid the risk of overestimating fracture toughness.     

Assessing the contact‐activation of coagulation during hemodialysis with three different polysulfone filters: A prospective randomized cross‐over trial

Introduction: During hemodialysis (HD) the interaction of the blood with the dialyzer triggers both an inflammatory reaction and an activation of the coagulation cascade. An accepted parameter to quantify the extent of coagulation activation during HD is not available. This study aims to evaluate its amplitude, comparing dialyzers made of different polysulfone polymers, by measuring D‐dimers in the filter‐rinsing fluids (Frf) and to test whether Frf D‐dimers are suitable candidate markers to assess contact coagulation activation during HD. Methods: In a prospective, cross‐over study 41 hemodialysis patients were randomly allocated to nine HD sessions with three types of polysulfone membranes: Filter A: Poliflux®RevaclearMAX; Filter B: Helixone®Fx80, Filter C: Polyflux®H210. Findings: A total of 117 HD sessions were studied. The mean (SD) filter (Frf) D‐dimers were 0.19 µg/L (0.56) for Filter A; 0.66 µg/L (2.81) for Filter B; 0.33 µg/L (1.13) for Filter C. Significant differences were found: A vs. B (P < 0.01), A vs. C (P = 0.01); B vs. C not significant. A large between‐patient variability of D‐dimer filter levels was found. D‐Dimers in blood showed a similar trend but differences were not significant. Discussion: The contact activation of coagulation during HD may also vary among filters made up with similar polysulfones. D‐dimer in the filter rinsing fluid but not in the blood can be considered a candidate marker for the evaluation of thrombogenicity during HD. Further studies are needed to elucidate the mechanism(s) and to confirm the usefulness of filter rinsing fluid D‐Dimers as a clotting activation marker during HD.