An investigation into the eigen-nature of cracked composite beams

It is known that the presence of cracks in composite structures introduces local flexibility associated with the changes in the dynamic characteristics of composite structures. However the nature and variations of the natural frequencies due to the presence of cracks, are still under discussion and analysis.

The present work introduces an attempt to study the variations in the eigen-nature of cracked composite beams due to different crack depths and locations. A numerical and experimental investigation has been made. The numerical finite element technique is utilized to compute the eigen pairs of laminated composite beams through several state of cracks. The model is based on elastic-plastic fracture mechanics techniques in order to consider the crack tip plasticity in the analysis. A finite element model has been developed to formulate the stiffness matrices for single edge cracked structural elements using transfer matrix theory. These matrices take into account the effects of axial, flexural and shear deformations due to crack presence. The present model has been applied to investigate the effects of state of crack, lamina code number, boundary condition on the dynamic behavior of composite beams.

The experimental tests and frequency response spectrums (FRS) is displayed on [FFT] analyzer. In experimental work the eigen pairs versus several state of cracks with various code number are measured using inductive hammering technique. The results show that the changes of the eigen parameters provide a proper indicator for detection and predication the current state of crack.     

Shape and position effects of double holes on lateral buckling of cantilever composite beams

One of the most important mechanical behavior of composite beams subjected to certain external loads and boundary conditions is lateral buckling. The effects of hole dimension, shape and position, and beam thickness on the lateral buckling behavior of woven fabric laminated composite cantilever beams, having two square or two circular holes, were investigated. Firstly, the theoretical, experimental and numerical critical buckling loads of the beams without holes were found and compared with each other. It was shown that there is a good agreement among the theoretical, experimental and numerical results. ANSYS finite element (FEM) program was used for the numerical analyses. Therefore, the numerical analysis of some models with various hole dimensions, shapes (square or circular) and fiber directions were done by changing distance between the holes. It is concluded that the circular holes are advantageous compared to the square ones in terms of lateral buckling behavior.     

Dynamic characterization of the thickness-tapered laminated plant fiber-reinforced polymer composite plates

Evolution of the laminated woven natural fiber fabric-reinforced polymer composite structures makes a way to the development of the non-uniform laminated composite structures in order to achieve the stiffness variation throughout the structure. An attempt is made in this work to carry out the experimental and numerical investigations on the dynamic characteristics of the thickness-tapered laminated woven jute/epoxy and woven aloe/epoxy composite plates. The governing differential equations of motion for the thickness-tapered laminated composite plate are developed using the h-p version FEM based on higher order shear deformation theory. The validation of the present finite element formulation is carried out by comparing the natural frequencies obtained using the finite element formulation with those natural frequencies determined experimentally. The developed model is further validated with the available literature works on tapered composite plate to confirm the efficiency of h-p version FEM. This work also explores the study of the vibrational characteristics of composite plates under the influence of plant fiber’s transverse isotropic material characteristics and porosity associated with plant fiber composites through the elastic constants evaluated in the author’s previous work. Also the influences of aspect ratios, ply orientations, and taper angles under various end conditions on the natural frequencies of the woven jute/epoxy composite plate are studied using the present finite element formulation. The forced vibration response of the thickness-tapered laminated woven jute/epoxy composite plate under the harmonic force excitation is carried out considering CFCF and CFFF end conditions.     

Shear coefficients for thin-walled composite beams

The shear coefficient in Timoshenko beam theory is obtained for thin-walled beams constructed of laminated panels of composite material using a variation of the method due to Cowper. Formulae are presented for a class of such composite beams. Comparisons are made with Cowper's original formulae for the case of an isotropic beam. The effect of shear deformation under static loading of typical composite beams is investigated. A procedure is outlined for the distribution of plies in the laminated panels to achieve optimal response under static or dynamic loading.     

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.     

The restrained torsional response of open section carbon fibre composite beams

The analysis procedure outlined in this paper essentially makes use of the existing isotropic theories of torsion suitability modified to account for the non isotropic nature of typical carbon fibre composite material.

The warping and St Venant torsional stiffnesses of the beams are determined using the appropriate equivalent engineering elastic constants of the composite material which correspond to the membrane and bending modes of action respectively.

The differential equation governing the constrained torsional equilibrium of the open section beams is solved exactly in the paper for Z and channel sections with some emphasis being given to the influence of ply stacking sequence.

Theoretical results are presented in graphical form and these depict the variations in warping displacement, warping shear flow and longitudinal or axial constraint force intensity with applied torque for the cantilever beam condition with torque applied at the free end.

The paper also gives details of finite element studies of the composite beams and of an experimental programme of work pertaining solely to the behaviour of composite Z beams.

Comparisons between theory, finite element and experiment are presented and these are seen to give exceptionally close agreement.

It is clearly indicated that fibre orientation significantly influences the restrained torsional behaviour of thin-walled open-section composite beams. It is also clear that the use of the appropriate equivalent engineering elastic material constants in the theory is able to closely predict actual behaviour.     

Nonlinear damping and forced vibration analysis of laminated composite beams

The purpose of the present work it to study the damping and forced vibrations of three-layered, symmetric laminated composite beams. In the analytical formulation, both normal and shear deformations are considered in the core by using the higher-order zig-zag theories. The harmonic balance method is coupled with a one mode Galerkin procedure for a simply supported beam. The geometrically nonlinear coupling leads to a nonlinear frequency amplitude equation governed by several complex coefficients. In the first part of the paper, linear and nonlinear damping parameters of laminated composite beams are obtained. In the second part, nonlinear forced vibration analysis is carried out for small and large vibration amplitudes. The frequency response curves are presented and discussed for various geometric and material properties.     

Numerical modeling on pultrusion of composite I beam

Pultrusion is one of the most efficient methods for making fiber reinforced polymer composite parts. However, more work needs to be done to develop scientific means for the pultrusion tooling design and process control. This paper describes numerical simulation on the pultrusion of fiberglass–vinyl ester composite I beams using a numerical procedure based on general-purpose FE packages. The theory and numerical implementation of the procedure is briefly introduced. The procedure is verified by good agreement between the predicted temperature profiles and the experimental ones. The effect of various process parameters and/or heating configurations on the temperature and curing profiles in the composite I beams are investigated numerically. The results are used to determine preferred process conditions and/or heating configurations for the pultrusion of the composite I beams.     

Dynamic investigation of laminated composite beams with shear and rotary inertia effect subjected to the moving oscillators using FEM

An algorithm based on the finite element method (FEM) has been developed to study the dynamic response of composite laminated beams subjected to the moving oscillator. The first order shear deformation theory (FSDT) is assumed for the beam model. The algorithm accounts for the complete dynamic interaction between the components of system. The proposed method can also be applied to the general moving mass and the simplified moving force problems. After deriving the governing equations of motion of beam and oscillator, the corresponding equations of motion are integrated by applying the Newmark’s time integration procedures to obtain the system responses in each time step. The numerical results of free vibration and moving force problems analysis of isotropic and composite laminated beams are presented and, whenever possible, compared to the available analytical solution and other numerical results in order to demonstrate the accuracy of the present method. In addition, parametric analysis is carried out over a wide range of velocities and mass, frequency and damping ratios of system components.     

Analytical solutions of thermal buckling and postbuckling of symmetric laminated composite beams with various boundary conditions

Based on the first-order shear deformation beam theory, considering geometric nonlinearity, the governing equations for symmetric laminated composite beams subjected to uniform temperature rise are derived by using Hamilton’s principle, and then three solving methods are presented to deal with it. By introducing an auxiliary function, which is shown in method one, the governing equations are reduced to be a single fourth-order integral-differential equation, and the exact solutions for the thermal buckling and postbuckling of symmetric laminated composite beams with combination of in-plane immovable simply supported and clamped boundary conditions are presented for the first time. On the basis of the results given in the method one, the explicit solutions for the thermal buckling and postbuckling of the beams are presented by giving accurate displacement functions (method two) and Ritz method (method three), respectively. Then, the effects of the transverse shear effects and boundary conditions on the thermal buckling and postbuckling of the beams are qualitatively discussed. What is more, a preliminary discussion on the probability and difference of extending the giving methods to the higher-order shear deformation beam theory with various boundary conditions is conducted. In the numerical examples, the good agreements between the present results and existing solutions verify the validity and efficiency of the present analysis and numerical results. And then the symmetric cross-ply laminated composite beam (0/90/0) is taken as an example to numerically evaluate the effects of the length-to-thickness ratio, beam theories, and boundary conditions on the thermal buckling and postbuckling of symmetric laminated composite beams. Some meaningful conclusions have been drawn.     

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

Nonlinear bending analysis of polymeric laminated composite plate is examined considering material nonlinearity for viscoelastic matrix material through a Micro–macro approach. The micromechanical Simplified Unit Cell Method (SUCM) in three-dimensional closed-form solution is used for the overall behavior of the unidirectional composite in any combination of loading conditions. The elastic fibers are transversely isotropic where Schapery single integral equation in multiaxial stress state describes the matrix material by recursive-iterative formulation. The finite difference Dynamic Relaxation (DR) method is utilized to study the bending behavior of Mindlin annular sector plate including geometric nonlinearity under uniform lateral pressure with clamped and hinged edge constraints. The unsymmetrical laminated plate deflection is predicted for different thicknesses and also various pressures in different time steps and they are compared with elastic finite element results. As a main objective, the deflection results of viscoelastic laminated sector plate are obtained for various fiber volume fractions in the composite system.     

轴压复合材料组合梁的振动与稳定性相关性研究

应用分布参数传递函数法分析了复合材料组合梁在轴压作用下的振动与稳定性问题及其相关性。建立了组合梁在任意边界条件下振动与稳定性的状态空间控制方程和振动频率与轴压载荷之间的相互关系式。分析中同时考虑了一阶和高阶横向剪切变形、转动惯量、细长比、各向异性、扭转变形等多种因素对组合梁固有频率和屈曲载荷的影响。并将数值例子的结果与试验值或文献所提供的结果相比较。      

Vibration characteristics of laminated composite beams with magnetorheological layer using layerwise theory

Vibration characteristics of laminated composite beams with magnetorheological (MR) layer are investigated using layerwise theory. In most studies, shear strain across the thickness of MR layer has been considered as a constant value, which does not precisely describe the shear strain. In this study, layerwise theory is employed to develop a finite element formulation to investigate MR-laminated beams. Experimental tests under different magnetic fields are carried out to verify the numerical results. Layerwise numerical results are compared with the experimental results and other theories. An empirical expression for complex shear modulus is presented. The effects of MR layer thickness on vibration of MR-laminated beams are examined.     

Bending Response of Foldcore Composite Sandwich Beams

In order to solve bending behavior difference of corrugated structure in L andWorientation, bending response for composite sandwich beams with foldcores of three different wall thicknesses were experimentally and numerically investigated. Effect of the cell walls thickness on the strength and failure behavior of the composite sandwich beams with L and W orientations was also examined. The deformation mode was obtained by the numerical method; a constitutive law of laminated material has been incorporated into a finite element (FE) analysis program. Numerical calculations give accurate prediction to the bending response of foldcore composite sandwich beams comparing with experiments. Structural flexural stiffness, strength and failure mechanism at a given topological geometry depended on the nature of core itself: the bending stiffness and strength of the sandwich beam increased with the core wall thickness (relative density). Also, bending isotropy was shown in this study for foldcore composite sandwich beams with selected core geometry.     

Free Vibration Analysis of Generally Layered Composite Beams with Arbitrary Boundary Conditions

A hyperbolic shear deformation theory is used for the free vibration analysis of generally layered composite beams with arbitrary boundary conditions. The variationally consistent governing differential equations and boundary conditions are derived by employing Hamilton's principle. The dynamic stiffness method is applied to calculate the vibration frequencies of the laminated beams with the help of Wittrick–Williams algorithm. Examples of application of the hyperbolic shear deformation theory for the free vibration analysis of the laminated beams with a couple of different boundary conditions are presented. The present results are compared to the numerical solutions and experimental results available in the literature.     

Multi-material topology optimization of laminated composite beam cross sections

This paper presents a novel framework for simultaneous optimization of topology and laminate properties in structural design of laminated composite beam cross sections. The structural response of the beam is evaluated using a beam finite element model comprising a cross section analysis tool which is suitable for the analysis of anisotropic and inhomogeneous sections of arbitrary geometry. The optimization framework is based on a multi-material topology optimization model in which the design variables represent the amount of the given materials in the cross section. Existing material interpolation, penalization, and filtering schemes have been extended to accommodate any number of anisotropic materials. The methodology is applied to the optimal design of several laminated composite beams with different cross sections. Solutions are presented for a minimum compliance (maximum stiffness) problem with constraints on the weight, and the shear and mass center positions. The practical applicability of the method is illustrated by performing optimal design of an idealized wind turbine blade subjected to static loading of aerodynamic nature. The numerical results suggest that the proposed framework is suitable for simultaneous optimization of cross section topology and identification of optimal laminate properties in structural design of laminated composite beams.     

对称非均匀层合板梁的弯扭耦合效应

为了研究复合材料风力机叶片的弯扭耦合效应,将风力机叶片简化为对称非均匀铺层层合板梁,采用实验和数值分析方法研究耦合区域对叶片弯扭耦合效应的影响。给出了对称非均匀层合板梁的铺层方式及其制作工艺,设计了对称非均匀层合板梁的弯扭耦合效应实验,给出了实验原理及测量方法,测量了对称非均匀层合板梁的挠度和扭转角。基于ANSYS软件建立了对称非均匀层合板梁的有限元模型,计算了在集中力载荷作用下梁的变形。通过有限元数值分析结果与实验结果对比,结果表明:耦合区域对对称非均匀层合板梁的变形行为产生重要影响,采用中部耦合区域铺层方式可以获得显著的弯扭耦合效应。     

The behaviour of open and closed section carbon fibre composite beams subjected to constrained torsion

A simple engineering theoretical approach is presented in this paper which is able to predict the initial constrained torsional response of a specific class of thin-walled open-section and single-cell closed-section carbon fibre composite beams. The flat walls of the composite beams are symmetrically laminated about their own mid-planes and possess membrane orthotropy. The laminated flats are assembled in such a way that the stiffness distribution round the section is of a symmetrically disposed nature and thus the flanges of a composite box-section, for example, can have a different lay-up configuration to that of the section webs. Beams of this type are essentially uncoupled in their overall stiffnesses and thus it is possible to apply axial load or bending to the sections without inducing torsional behaviour.

The analysis procedures for such beams will, of course, be considerably less complex in nature than those associated with beams of a more general lay-up configuration. Indeed, the analysis approach adopted in this paper simply makes use of the existing theories of torsion appropriate to isotropic construction and these are then suitably modified to account for the non-isotropic nature of the composite material. The torsional and warping rigidities for use in the analysis of the composite beams are thus duly determined through the use of the appropriate equivalent engineering elastic constants of the individual thin composite walls and the concept of effective thickness is employed to account for the different stiffnesses in the walls.

In the paper some detailed attention is paid to the effects of primary and secondary warping restraint on the torsional response of open section beams and the distinct differences between sections whose behaviour is governed predominantly by primary effects and those whose response is associated solely with secondary effects are discussed. The stress systems set up in open-section and single-cell closed-section carbon fibre composite beams when subjected to torsion with variable twist are examined in the paper and in particular it is shown that although the shear flow due to primary warping restraint in open-section beams serves in part to equilibrate the applied torque, that in closed box section beams is completely self equilibrating. Comparisons are given in the paper between theory and experiment and between theory and finite element solutions and these are shown to give good agreement for the Z, angle and box section beams considered.     

Hole effects on lateral buckling of laminated cantilever beams

In this study, the effects of hole diameter and hole location on the lateral buckling behaviour of woven fabric laminated composite cantilever beams have been investigated. In the experimental studies, two different groups of samples were used; samples with a single circular hole and samples with no hole. The critical buckling load for each sample was then determined experimentally. For the numerical analyses, ANSYS 10.0 finite element program was utilized. It has been noted that there is a good agreement between experimental results and those of finite element analyses. On the basis of this harmony, the numerical analyses of some models having different dimensions and fiber orientations have been done by changing length and width of the beam, diameter and location of the hole. It has been concluded that the effects of the hole diameter and hole location on the lateral buckling behaviours is very important, especially for the short beams.     

Nonlinear numerical modelling of FRP reinforced glued laminated timber

Fibre-reinforced polymers (FRPs) are effective in the flexural stiffening and strengthening of structural members. Such systems can be optimised if accurate numerical models are developed. At present, limited information is available in the literature on numerical models that can predict with good accuracy the nonlinear behaviour of FRP reinforced low-grade glued laminated timber beams. This paper discusses the development of a finite element model, which incorporates nonlinear material modelling and nonlinear geometry to predict the load–deflection behaviour, stiffness, ultimate moment capacity and strain distribution of FRP plate reinforced glued laminated timber beams manufactured from mechanically stress graded spruce. Beams with and without sacrificial laminations are modelled and their performance is compared to unreinforced glued laminated timber beams. The model employed anisotropic plasticity theory for the timber in compression. The failure model used was the maximum stress criterion. Strong agreement was obtained between the predicted behaviour and the associated experimental findings. It was deduced from comparing the results from the numerical model with experimental findings that the FRP plate succeeds in increasing the performance of the adjacent timber significantly. The model is a useful tool for examination of the effect of reinforcement percentage and will be used for optimisation of the hybrid beam.