Dynamic effective thickness in laminated-glass beams and plates

In recent years, several equations have been proposed to calculate deflections and stresses in laminated-glass beams and plates under static loading using the concept of effective thickness, which consists of calculating the thickness of a monolithic element with equivalent bending properties to a laminated element. Recently, an effective thickness for the dynamic behavior of laminated-glass beams has been proposed to enable the modal parameters (natural frequencies, loss factors and mode shapes) to be determined using an equivalent monolithic model. In the present paper, the technique has been extended to the two-dimensional case of rectangular laminated-glass plates and the steps needed to estimate the modal parameters of laminated-glass elements using this methodology are presented. The dynamic effective thickness concept has been validated by experimental tests made on a laminated-glass beam and a laminated-glass plate. The results show that good accuracy is achieved in the natural frequencies and mode shapes but high scatter is encountered in the loss factors.     

Mechanical property variability in FRP laminates and its effect on failure prediction

Results are presented from an experimental study for the modeling of stochastic behavior of a unidirectional Glass/Polyester composite. An analytical approach is developed for the prediction of failure under general in-plane loading including the variability of strength, stiffness and the thermal expansion coefficients. Monte Carlo simulation and the first-order reliability method are used for comparison and the new method is proved to be in good agreement. Following international design codes, a direct comparison is also presented for failure locii at a specific reliability level as derived by the various probabilistic approaches. Results reveal that a serious overestimation of the reliability of the composite structure is being made when the stochastic nature of the material elastic properties is not taken into account.     

Crack damage mitigation and shear behavior of shear-dominant reinforced concrete beams repaired with strain-hardening cement-based composite

This research aims to study: (1) the crack damage mitigation and shear behavior of reinforced concrete (RC) beams that have been repaired using strain-hardening cement-based composite (SHCC) via experimental testing and (2) the contribution of the SHCC layers to the shear strength of the repaired RC beams via predictions. Five cantilever RC beams with a shear span-to-depth ratio of 2.8 were subjected to cyclic concentrated loading. The study variables include two types of tensile performance of the SHCC (with low or high strength in tension) and two repair methods (patching and layering). The experimental results show that the use of a SHCC layer leads to a substantial increase in the shear strength and ductility of the RC beams after the peak load. During the tests, all of the SHCC repaired beams showed delamination along the interface between the concrete and SHCC, and the shear resistance started to drop. However, the results also indicate that SHCC layers can be effective repair material for enhancing the control of cracking to help protect the concrete from the migration of aggressive agents in severe environments. In order to predict the shear strength of RC beams that have been repaired with SHCC, two methods were used in this study; one is based on Dinh's proposed model that considers the shear strength in both the compression and tension zones, and the other method considers the shear strength of the reinforcement, such as a stirrup or fiber-reinforced polymer (FRP) laminate that considers only the tensile strength across cracks. These two methods were able to predict the contribution of the SHCC layer to the shear strength of the RC beams, and the predicted shear strength values were very similar between the two methods.     

Influence of non degenerated joint on the global and local behavior of joined plates

We consider a three-dimensional transport problem (thermoconductivity, diffusion, etc.) in joined thin plates under condition that the characteristic dimension of the joint is comparable with the thickness of the plates and that the joint is made of a material with transport properties similar to the transport properties of materials of the plates (such joint is referred to as a non-degenerated joint). We expand the technique of local perturbation, developed earlier in Gaudiello and Kolpakov (2011) for beams, to plates with non-degenerated joints. Since joints between plates have more complex structure than joints between beams, the modification of the method for plates is a non-trivial task.     

Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method

 An efficient meshfree formulation based on the first-order shear deformation theory (FSDT) is presented for the static analysis of laminated composite beams and plates with integrated piezoelectric layers. This meshfree model is constructed based on the element-free Galerkin (EFG) method. The formulation is derived from the variational principle and the piezoelectric stiffness is taken into account in the model. In numerical test problems, bending control of piezoelectric bimorph beams was shown to have the efficiency and accuracy of the present EFG formulation for this class of problems. It is demonstrated that the different boundary conditions and applied actuate voltages affects the shape control of piezolaminated composite beams. The meshfree model is further extended to study the shape control of piezo-laminated composite plates. From the investigation, it is found that actuator patches bonded on high strain regions are significant in deflection control of laminated composite plates. Received: 23 October 2001 / Accepted: 29 July 2002     

Investigating the effect of machining processes on the mechanical behavior of composite plates with circular holes

The influence of the machining quality on the mechanical behavior of CFRP composites is yet not fully understood. There are only few works in the literature that have investigated the effect of the machining quality on CFRP. In fact, most of these works focus only on conventional machining such as axial or orbital drilling. The aim of this paper is to examine the influence of two machining processes namely conventional machining (CM) and abrasive water jet machining (AWJM) on the mechanical behavior of composite plates under cyclic loading. For this purpose, an experimental study using several composite plates drilled with a cutting tool and an abrasive water jet machining was carried out. In order to study the impact of the process of machining on the mechanical behavior, thermographic infrared testing and fatigue cyclic tests were performed to assess temperature evolutions, stiffness degradation, and the damage evolution in these plates. Fatigue testing results have shown that the damage accumulation in specimens drilled with CM process was higher than the AWJM specimens. Furthermore, the endurance limit for a composite plate drilled with CM was approximately 10% inferior compared to specimens drilled with AWJM. This difference can be related to the initial surface integrity after machining induced by the difference in the mechanism of material’s removal between the two processes used.     

Wide-shallow beams with and without steel fibres: A peculiar behaviour in shear and flexure

This paper reports an experimental campaign on Reinforced Concrete (RC) Wide-Shallow Beams (WSBs) with or without fibres, tested under shear and flexure. A wide-shallow beam is a rather frequent structure in residential buildings in Southern Europe (as in Italy and in Spain). In order to study both the shear and flexural behaviour of WSBs and evaluate the possibility of substituting the minimum conventional transverse reinforcement required by Eurocode 2 with steel fibres, full-scale beams have been tested. Specimens, all 250 mm deep, had two different widths, fibre contents and also, minimum amount of classical shear reinforcement. Results evidenced that a relatively low volume fraction of fibres can significantly increase shear bearing capacity and beam ductility. Moreover, WSBs did not show the typical brittle failure in shear, even without any shear reinforcement, as the effect of fibres was more prominent than in deep beams. Peculiarities of WSBs were evidenced in terms of enhancements both in shear and in flexure. Experimental results have been evaluated in terms of strength, ductility, post-cracking stiffness, shear and flexural cracking, collapse mechanism and fibre effect.     

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.     

Flexural strengthening of RC beams using Hybrid Composite Plate (HCP): Experimental and analytical study

Hybrid Composite Plate (HCP) is a reliable recently proposed retrofitting solution for concrete structures, which is composed of a strain hardening cementitious composite (SHCC) plate reinforced with Carbon Fibre Reinforced Polymer (CFRP). This system benefits from the synergetic advantages of these two composites, namely the high ductility of SHCC and the high tensile strength of CFRPs. In the material-structural of HCP, the ultra-ductile SHCC plate acts as a suitable medium for stress transfer between CFRP laminates (bonded into the pre-sawn grooves executed on the SHCC plate) and the concrete substrate by means of a connection system made by either chemical anchors, adhesive, or a combination thereof. In comparison with traditional applications of FRP systems, HCP is a retrofitting solution that (i) is less susceptible to the detrimental effect of the lack of strength and soundness of the concrete cover in the strengthening effectiveness; (ii) assures higher durability for the strengthened elements and higher protection to the FRP component in terms of high temperatures and vandalism; and (iii) delays, or even, prevents detachment of concrete substrate. This paper describes the experimental program carried out, and presents and discusses the relevant results obtained on the assessment of the performance of HCP strengthened reinforced concrete (RC) beams subjected to flexural loading. Moreover, an analytical approach to estimate the ultimate flexural capacity of these beams is presented, which was complemented with a numerical strategy for predicting their load-deflection behaviour. By attaching HCP to the beams' soffit, a significant increase in the flexural capacity at service, at yield initiation of the tension steel bars and at failure of the beams can be achieved, while satisfactory deflection ductility is assured and a high tensile capacity of the CFRP laminates is mobilized. Both analytical and numerical approaches have predicted with satisfactory agreement, the load-deflection response of the reference beam and the strengthened ones tested experimentally.     

Static and free vibration analysis of multilayered functionally graded shells and plates using an efficient zigzag theory

Accurate zigzag theory is presented for static and free vibration analysis of multilayered functionally graded material (FGM) cylindrical shells and rectangular plates by approximating inplane displacements as a combination of linear layerwise and cubic global terms. Governing equations of motion are derived using Hamilton’s principle. The theory yields accurate results for displacements, stresses and natural frequencies in simply-supported functionally graded multilayered cylindrical shell panels and rectangular plates. Effect of changing the volume fraction ratio, aspect ratio and thickness of FGM layer between two homogeneous layers are investigated for a number of multilayered shell and plate laminates.     

Development of a biocomposite based on green epoxy polymer and natural cellulose fabric (bark cloth) for automotive instrument panel applications

Natural fiber reinforced composites have attracted interest due to their numerous advantages such as biodegradability, dermal non-toxicity and with promising mechanical strength. The desire to mitigate climate change due to greenhouse gas emissions, biodegradable resins are explored as the best forms of polymers for composites apart from their synthetic counterparts which are non-renewable. In this study biodegradable bark cloth reinforced green epoxy composites are developed with view of application to automotive instrument panels. The optimum curing temperature of green epoxy was shown to be 120 °C. The static properties showed a tensile strength of 33 MPa and flexural strength of 207 MPa. The dynamic mechanical properties, frequency sweep showed excellent fiber-matrix bonding of the alkali treated fabric with the green epoxy polymer with glass transition temperature in the range of 160 °C–180 °C. Treatment of the fabric with alkali positively influenced the mechanical properties of the fabric reinforced biocomposites.     

An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions

Extending the previous work on isotropic beams and plates by the second author [Li WL, et al. An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports. J Sound Vib 2009;321:254–69], this paper describes an accurate analytical method for calculating the static deflections and modal characteristics of orthotropic plates with general elastic boundary supports. The displacement function is expressed as a 2-D Fourier cosine series supplemented with several terms in the form of 1-D series. The series expansions for all the relevant derivatives can be directly obtained through term-by-term differentiations of the displacement series. Thus, a classical solution can be derived by letting the series exactly satisfy the governing differential equation at every field point and all the boundary conditions at every boundary point, respectively. Several numerical examples are presented to demonstrate the excellent accuracy and convergence of the current solutions.     

Frequency equation and mode shape formulae for composite Timoshenko beams

Exact expressions for the frequency equation and mode shapes of composite Timoshenko beams with cantilever end conditions are derived in explicit analytical form by using symbolic computation. The effect of material coupling between the bending and torsional modes of deformation together with the effects of shear deformation and rotatory inertia is taken into account when formulating the theory (and thus it applies to a composite Timoshenko beam). The governing differential equations for the composite Timoshenko beam in free vibration are solved analytically for bending displacements, bending rotation and torsional rotations. The application of boundary conditions for displacement and forces for cantilever end condition of the beam yields the frequency equation in determinantal form. The determinant is expanded algebraically, and simplified in an explicit form by extensive use of symbolic computation. The expressions for the mode shapes are also derived in explicit form using symbolic computation. The method is demonstrated by an illustrative example of a composite Timoshenko beam for which some published results are available.     

Fully plastic J-integral solutions for surface cracked plates under biaxial loading

In this paper, surface cracked plates under biaxial tension are studied. Three-dimensional elastic-plastic finite element analyses have been carried out to calculate the J-integral for surface cracked plate for a wide range of geometry, biaxiality and material properties. Fully plastic J-integral solutions along the front of the surface cracks are presented for Ramberg-Osgood power law hardening material of n = 3, 5, 10 and 15. Geometries considered are a/c = 0.2, 1.0 and a/t = 0.2, 0.4, 0.6 and 0.8 and the biaxial ratios of 0, 0.5 and 1. Based on these results, the J-integral along the crack front for general elastic-plastic loading conditions can be estimated using the EPRI scheme. These solutions are suitable for fracture analyses for surface cracked plates under biaxial loading.     

First-ply failure prediction of an unsymmetrical laminated ellipsoidal woven GFRP composite shell with incorporated surface-bounded sensors and internally pressurized

First-ply failure of an unsymmetrical laminated ellipsoidal woven Glass Fiber Reinforced Polymer (GFRP) composite shell internally pressurized was investigated analytically using the linear interpolation technique. The shell's boundary was fixed at its end. Tsai-Wu failure criterion was used as the composite failure design factor. The analytical results, including critical internal pressure and strains in global directions, were validated with the experimental results for some arbitrarily selected points on the shell surface along meridian axis. Manufacturing of laminated ellipsoidal composite shells was performed by using the Vacuum Infusion Process (VIP), a novel method commonly adopted for the fabrication of laminated composite shells. Surface-bounded sensors were installed on the shells' surface to measure the strain values after the internal pressure was applied. According to the analytical investigation findings, the failure factor was critical at the innermost ply. In addition, for each ply, the shell's edge was observed to be the region with the highest failure factor. The experimental findings confirmed that the failure occurred in the regions close to the shell's edge, as predicated by the analytical approach. The results from both approaches were in a close agreement. Subsequently, the effect of various parameters including thickness, aspect ratio, and stacking sequence on the first-ply failure of laminated ellipsoidal woven GFRP composite shell were investigated and the critical mechanical factors to avoid failure were determined.     

Constitutive modeling of woven composites considering asymmetric/anisotropic, rate dependent, and nonlinear behavior

The mechanical performance of woven composites was analyzed focusing on their nonlinear and rate dependent asymmetric/anisotropic deformation behavior. Three key characteristics were identified which are indispensable for realistically simulating the mechanical performance of woven composites: the asymmetric material behavior between tension and compression, its anisotropic and nonlinear evolution and rate dependency. To include all three characteristics into the nonlinear finite element analysis for woven composites, a phenomenological constitutive equation was developed based on an elasto-viscoplastic theory using the modified Drucker–Prager yield criterion and, in particular, developing the anisotropic nonlinear hardening law. A characterization method using both uniaxial tensile and compressive tests at different strain rates was proposed to determine the material properties for the constitutive equation. Then, the developed constitutive equation was incorporated into a finite element code and was validated by comparing the finite element simulation of the three points bending test with experiments.     

A conforming unified finite element formulation for the vibration of thick beams and frames

Beams and frames are common features in many engineering structures and in this paper an approach is given to model their dynamic behaviour adequately. Whilst the eigen‐frequencies of continuous systems comprising of slender beams can be identified, in most cases of practical interest, by means of Euler or Timoshenko beam theory, for structures comprising of thick beam models this is not necessarily true since such idealizations constrain the cross‐sections to remain planar. This paper suggests an alternative approach by means of a unified fully conforming plane stress rectangular finite element which is believed to allow for more realistic representation of the shear effects and hence the strain field around the joints of such structures. The usefulness and functionality of this improved numerical approach is explored via comparison against a non‐conforming two‐dimensional plate as well as one‐dimensional Euler–Bernoulli and Timoshenko finite element formulations corresponding to a variety of beam aspect ratios representing the structures of a rotor and a portal frame. The idealization is shown to be particularly advantageous for simulating the effects of shear distortion where beams join at right angles and the transverse forces in one member interact with the extensional forces of the adjoining structure. Copyright © 2004 John Wiley & Sons, Ltd.     

Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories

In this study, two dimensional (2D) and quasi three-dimensional (quasi-3D) shear deformation theories are presented for static and free vibration analysis of single-layer functionally graded (FG) plates using a new hyperbolic shape function. The material of the plate is inhomogeneous and the material properties assumed to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori–Tanaka model, in terms of the volume fractions of the constituents. The fundamental governing equations which take into account the effects of both transverse shear and normal stresses are derived through the Hamilton's principle. The closed form solutions are obtained by using Navier technique and then fundamental frequencies are found by solving the results of eigenvalue problems. In-plane stress components have been obtained by the constitutive equations of composite plates. The transverse stress components have been obtained by integrating the three-dimensional stress equilibrium equations in the thickness direction of the plate. The accuracy of the present method is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.     

Collapse of clamped and simply supported composite sandwich beams in three-point bending

Composite sandwich beams, comprising glass–vinylester face sheets and a PVC foam core, have been manufactured and tested quasi-statically. Clamped and simply supported beams were tested in three-point bending in order to investigate the initial collapse modes, the mechanisms that govern the post-yield deformation and parameters that set the ultimate strength of these beams. Initial collapse is by three competing mechanisms: face microbuckling, core shear and indentation. Simple formulae for the initial collapse loads of clamped and simply supported beams along with analytical expressions for the finite deflection behaviour of clamped beams are presented. The simply supported beams display a softening post-yield response, while the clamped beams exhibit hardening behaviour due to membrane stretching of the face sheets. Good agreement is found between the measured, analytical and finite element predictions of the load versus deflection response of the simply supported and clamped beams. Collapse mechanism maps with contours of initial collapse load and energy absorption are plotted. These maps are used to determine the minimum mass designs of sandwich beams comprising woven glass face sheets and a PVC foam core.