Analysis of adhesively bonded CFRE composite scarf joints modified with MWCNTs

The main objective of the present work is to improve the performance of bonded joints in carbon fiber composite structures through introducing Multi-Walled Carbon Nanotubes (MWCNTs) into Epocast 50-A1/946 epoxy, which was primarily developed for joining and repairing of composite aircraft structures. Results from tension characterizations of structural adhesive joints (SAJs) with different scarf angles (5–45°) showed improvement up to 40% compared to neat epoxy (NE)–SAJs. Special attention was considered to investigate the performance of SAJs with 5° scarf angle under different environments. The tensile strength and stiffness of both NE-SAJs and MWCNT/E-SAJs were dramatically decreased at elevated temperature. Water absorption showed a marginal drop of about 2.0% in the tensile strength of the moist SAJs compared to the dry one. Cracks initiation and propagation were detected effectively using instrumented-SAJs with eight strain gauges. The experimental results agree well with the predicted using three-dimensional finite element analysis model.     

Stochastic free vibration analyses of composite shallow doubly curved shells – A Kriging model approach

This paper presents the Kriging model approach for stochastic free vibration analysis of composite shallow doubly curved shells. The finite element formulation is carried out considering rotary inertia and transverse shear deformation based on Mindlin’s theory. The stochastic natural frequencies are expressed in terms of Kriging surrogate models. The influence of random variation of different input parameters on the output natural frequencies is addressed. The sampling size and computational cost is reduced by employing the present method compared to direct Monte Carlo simulation. The convergence studies and error analysis are carried out to ensure the accuracy of present approach. The stochastic mode shapes and frequency response function are also depicted for a typical laminate configuration. Statistical analysis is presented to illustrate the results using Kriging model and its performance.     

A case-deletion diagnostic for penalized calibration estimators and BLUP under linear mixed models in survey sampling

The penalized calibration technique in survey sampling combines usual calibration and soft calibration by introducing a penalty term. Certain relevant estimates in survey sampling can be considered as penalized calibration estimates obtained as particular cases from an optimization problem with a common basic structure. In this framework, a case deletion diagnostic is proposed for a class of penalized calibration estimators including both design-based and model-based estimators. The diagnostic compares finite population parameter estimates and can be calculated from quantities related to the full data set. The resulting diagnostic is a function of the residual and leverage, as other diagnostics in regression models, and of the calibration weight, a singular feature in survey sampling. Moreover, a particular case, which includes the basic unit level model for small area estimation, is considered. Both a real and an artificial example are included to illustrate the diagnostic proposed. The results obtained clearly show that the proposed diagnostic depends on the calibration and soft-calibration variables, on the penalization term, as well as on the parameter to estimate.     

Design criterion for fatigue strengthening of riveted beams in a 120-year-old railway metallic bridge using pre-stressed CFRP plates

This study presents a design criterion developed for fatigue strengthening of a 120-year-old metallic railway bridge in Switzerland and presents a pre-stressed un-bonded reinforcement (PUR) system developed to apply the strengthening. The PUR system uses carbon fiber reinforced polymer (CFRP) plates; however, unlike conventional pre-stressed CFRP reinforcement methods, preparation of the existing metallic bridge surface is not required. This decreases the time required for on-site strengthening procedures. The principle of the constant life diagram (CLD) and two fatigue failure criteria (Johnson and Goodman) are described. Analytical formulations are developed based on the CLD method to determine the minimum CFRP pre-stress level required to prevent fatigue crack initiation. The PUR system uses an applied pre-stress force to reduce the mean stress level (and stress ratio) to shift an existing fatigue-susceptible metallic detail from the ‘at risk’ finite life regime to the ‘safe’ infinite life regime. The applied CLD method is particularly valuable when the stress history of the detail is not known and it is difficult to assess the remaining fatigue life. Moreover, it is shown that the currently adopted approach in many structural codes which emphasizes stress range as the dominant parameter influencing fatigue life are non-conservative for tension–tension stress patterns (i.e., stress ratios of 0 < R < 1). Analyses show that the modified Johnson formula accurately reflects the combined effect of stress range, mean stress level, and material properties, and offers a relatively easy design procedure. Details of a retrofit field application on members of a riveted wrought iron railway bridge are given. A wireless sensor network (WSN) system is used for long-term monitoring of the on-site CFRP stress levels and temperature of the retrofitted details. WSN measurements indicate that increases in ambient temperature result in increased CFRP pre-stress levels.     

Nonlinear response in glass fibre non-crimp fabric reinforced vinylester composites

This paper addresses the nonlinear stress-strain response in glass fibre non-crimp fabric reinforced vinylester composite laminates subjected to in-plane tensile loading. The nonlinearity is shown to be a combination of brittle and plastic failure. It is argued that the shift from plastic to brittle behaviour in the vinylester is caused by the state of stress triaxiality caused by the interaction between fibre and vinylester. A model combining damage and plasticity is calibrated and evaluated using data from extensive experimental testing. The onset of damage is predicted using the Puck failure criterion, and the evolution of damage is calibrated from the observed softening in plies loaded in transverse tension. Shear loading beyond linear elastic response is observed to result in irreversible strains. A yield criterion is implemented for shear deformation. A strain hardening law is fitted to the stress-strain response observed in shear loaded plies. Experimental results from a selection of laminates with different layups are used to verify the numerical models. A complete set of model parameters for predicting elastic behaviour, strength and post failure softening is presented for glass fibre non-crimped fabric reinforced vinylester. The predicted behaviour from using these model parameters are shown to be in good agreement with experimental results.     

Homogenization with uncertainty in Poisson ratio for polymers with rubber particles

The main aim of this work is dual computer analysis of probabilistic coefficients for the homogenized tensor of the polymer filled with the rubber particles having randomized Poisson ratios of both constituents. The major issue is to verify an influence of a randomness in rubber Poisson ratio close to the compressibility limit on the uncertainty of the effective tensor probabilistic characteristics. Probabilistic analysis presented here is carried out using mainly the stochastic perturbation technique provided by the common application of the traditional FEM commercial code ABAQUS and the symbolic computations package MAPLE. This FEM-based technique employs polynomial response function of the optimum order recovered from the weighted least squares method and following a set of deterministic solutions obtained for various values of the randomized input parameter. Optimization procedure is released entirely into a symbolic environment, where maximization of the correlation factor together with minimization of the fitting variance and approximation error are applied. Homogenization technique consists in equating of deformation energies for the real composite and the artificial one characterized by the effective elasticity tensor with uncertainty.     

Pull out of FRP reinforcement from masonry pillars: Experimental and numerical results

In this paper, debonding phenomena between carbon fiber reinforced polymer (CFRP) strips and masonry support were investigated on the basis of single-lap shear tests, considering different dimensions of the bond length. To capture the post-peak response of the CFRP–masonry joint, the slip between the support and the reinforcement strip was controlled using a clip gauge positioned at the end of the reinforcement. The tests were simulated by means of a finite element model able to capture the post-peak snap-back behavior due to the failure process. The numerical model is based on zero-thickness interface elements and on a proper non-linear cohesive law. The comparison between experimental and numerical results was performed in terms of overall response, measured by both the machine stroke and the clip gauge positioned at the free end of the reinforcement. The cases of effective bond length greater and lesser than the minimum anchorage length, suggested by the CNR Italian recommendation, were considered.     

A Constitutive Equation of Thermoelasticity for Solid Materials

A new constitutive equation of thermoelasticity for crystals is presented based on the interatomic potential and solid mechanics at finite temperature. Using the new constitutive equation, the calculations for crystal copper and graphene are carried out under different loading paths at different temperatures. The calculated results are in good agreement with those of the previous thermoelasticity constitutive equation based on quantum mechanics, which clearly indicates that our new constitutive equation of thermoelasticity is correct. A lot of comparisons also show that the present theory is more concise and efficient than the previous thermal stress theory in the practical application.     

An element-based displacement preconditioner for linear elasticity problems

Finite element analysis of problems in structural and geotechnical engineering results in linear systems where the unknowns are displacements and rotations at nodes. Although the solution of these systems can be carried out using either direct or iterative methods, in practice the matrices involved are usually very large and sparse (particularly for 3D problems) so an iterative approach is often advantageous in terms of both computational time and memory requirements. This memory saving can be further enhanced if the method used does not require assembly of the full coefficient matrix during the solution procedure. One disadvantage of iterative methods is the need to apply preconditioning to improve convergence. In this paper, we review a range of established element-based preconditioning methods for linear elastic problems and compare their performance with a new method based on preconditioning with element displacement components. This new method appears to offer a significant improvement in performance.     

A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow

 A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation. The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest. Sponsored by The Research Council of Norway, project number 125676/410 Dedicated to the memory of Prof. Mike Crisfield, a respected colleague