Showing papers in "Composite Structures in 2014"

Abstract: The analysis of flexural strength and free vibration of carbon nanotube reinforced composite cylindrical panels is carried out. Four types of distributions of uniaxially aligned reinforcements are considered, i.e. uniform and three kinds of functionally graded distributions of carbon nanotubes along thickness direction of the panels. Material properties of nanocomposite panels are estimated by employing an equivalent continuum model based on the Eshelby–Mori–Tanaka approach. The governing equations are developed based on the first-order shear deformation shell theory. Detailed parametric studies have been carried out to reveal the influences of volume fraction of carbon nanotubes, edge-to-radius ratio and thickness on flexural strength and free vibration responses of the panels. In addition, effects of different boundary conditions and types of distributions of carbon nanotubes are examined.

Abstract: Utilization of silica fume in CNT/cement composites was recently proposed as a mean of improving the dispersion of CNTs and enhancing the interfacial interaction between CNTs and the hydration products. The present study focuses on the enhanced effect of CNTs on mechanical and electrical properties of cement composites by incorporation of silica fume. A qualitative analysis using SEM images was carried out to observe the surface morphology and microstructure of cement composites with different amounts of silica fume and CNT addition. The effects of silica fume addition on the porosity, compressive strength, and electrical resistance of the CNT/cement composites were then systematically investigated. It was found that the improved dispersion of CNTs by incorporation of silica fume might yield the enhancement of the mechanical and electrical properties of CNT/cement composites, whereas the CNT additions in cement composite without silica fume had an insignificant effect on the mechanical and electrical properties of the cement composites.

Abstract: This contribution hopes to give a comprehensive review of past and current research work published on the dynamic response of fibre-metal laminates subjected to low velocity impact. The historical development of fibre-metal laminates is first reviewed in details, and notable researchers and their contributions are chronologically tabulated and reviewed. Included are also reviews on published experimental, numerical and analytical work on the low velocity impact of fibre-metal laminates. Detailed discussions on the two main groups of parameters namely geometry and material based parameters that influenced the structural response of fibre metal laminates to low-velocity impact. The review concludes with detailed discussions on the future works needed for fibre-metal laminates subjected to low velocity impact loads.

Abstract: The mechanical and thermal buckling behaviors of ceramic–metal functionally grade plates (FGPs) were studied by using a local Kriging meshless method. The local meshless method was developed based on the local Petrov–Galerkin weak-form formulation combined with shape functions having the Kronecker delta function property, constructed by the Kriging interpolation. The cubic spline function of high continuity was used as the weight function to simplify the local weak form of governing equations with the integration on the internal boundaries vanishing. The transverse shear strains of FGPs were incorporated by employing the first-order shear deformation plate theory and plate material properties were assumed to change exponentially along the thickness direction. Convergence and comparison studies examined the stability and accuracy of the presented method. Two types of FGMs, Al/Al2O3 and Ti–6Al–4V/Aluminum oxide, were chosen for mechanical and thermal buckling analyses. The influences of volume fraction exponent, boundary condition, length-to-thickness ratio and loading type on the buckling behaviors of FGPs were discussed.

Abstract: In this paper, a first-known dynamic stability analysis of carbon nanotube-reinforced functionally graded (CNTR-FG) cylindrical panels under static and periodic axial force by using the mesh-free kp-Ritz method is presented. The cylindrical panels are reinforced by single-walled carbon nanotubes (SWCNTs) with different types of distributions, i.e. uniform and three kinds of functionally graded distributions of carbon nanotubes along thickness direction of the panels. Eshelby–Mori–Tanaka approach is employed to estimate effective material properties of the resulting nanocomposite panels. By applying the Ritz minimization procedure to the energy expressions, a system of Mathieu–Hill equations is formulated. Then the principal instability regions are analyzed through Bolotin’s first approximation. Detailed parametric studies have been carried out to reveal the influences of volume fraction of carbon nanotubes, edge-to-radius ratio and radius-to-thickness ratio. In addition, effects of different boundary conditions and types of distributions of carbon nanotubes are examined in detail.

Abstract: Modelling the mechanical performance of textile composites is typically based on idealised unit cell geometry. However, 3D woven composites feature more complex textile architecture then 2D woven materials, and in reality nominally straight warp and weft yarns can also possess significant waviness. For such textiles, idealising yarns as straight entities becomes an oversimplification. In this study, the voxel method and a continuum damage model are used in a finite element analysis to compute stress–strain curves for an orthogonal 3D woven composite under tensile loading. The main goal of this study was to compare results produced using idealised geometry with realistic geometry obtained from detailed simulation of the preform during weaving and compaction. Significant variation in predictions was obtained using the different geometrical models. The idealised model lead to an overestimation of stiffness and strength compared to experiment due to the neglecting of yarn waviness, whereas the simulated geometry models produced more conservative results closer to experiment. 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://

Abstract: This research deals with the forced vibration behavior of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on the Timoshenko beam theory along with von Karman geometric nonlinearity. For the carbon-nanotube reinforced composite (CNTRC) beams, uniform distribution (UD) and three types of functionally graded (FG) distribution patterns of SWCNT reinforcements are considered. It is assumed that the material properties of FG-CNTRC beams are graded in the thickness direction and estimated through the rule of mixture. The nonlinear governing equations and corresponding boundary conditions are derived based on the Hamilton principle and discretized by means of the generalized differential quadrature (GDQ) method. After that, a Galerkin-based numerical technique is employed to reduce the set of nonlinear governing equations into a time-varying set of ordinary differential equations of Duffing type. Since the nanobeam responds periodically to harmonic excitations, a set of periodic differential matrix operators is introduced to discretize the Duffing equations on the time domain using the derivatives of a periodic base function. The vectorized form of final nonlinear parameterized equations is then solved through the use of pseudo-arc length continuum technique. Numerical results are presented to examine the effects of different parameters such as nanotube volume fraction, slenderness ratio, dimensionless damping parameter, dimensionless transverse force, CNT distributions and boundary conditions on the natural frequencies and frequency responses of FG-CNTRC beams.

Abstract: A meshless local Petrov–Galerkin approach based on the moving Kriging interpolation technique is developed for geometrically nonlinear thermoelastic analysis of functionally graded plates in thermal environments (prescribed a temperature gradient or heat flux). The Kriging interpolation method makes the constructed shape functions possess Kronecker delta function property and thus special techniques for enforcing essential boundary conditions are avoided. In the thermal analysis, the dependency of thermal conductivity of functionally graded materials on temperature is involved, which gives rise to a nonlinear partial differential heat conduction equation. The nonlinear formulation of large deflection of the functionally graded plates is based on the first-order shear deformation plate theory in the von Karman sense by taking small strains and moderate rotations into account. The incremental form of nonlinear equations is obtained by Taylor series expansion and the tangent stiffness matrix is explicitly developed in two different ways within the framework of the local meshless method. The nonlinear solutions are computed using the Newton–Raphson iteration method. Parametric and convergence studies are conducted to examine the stability of the proposed method and then several selected numerical examples are presented to demonstrate the accuracy and effectiveness of the method for nonlinear bending problems of functionally graded plates in thermal environments.

Abstract: An effective, simple, robust and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple first-order shear deformation theory (S-FSDT), which was recently presented in Thai and Choi (2013) [11], is naturally free from shear-locking and captures the physics of the shear-deformation effect present in the original FSDT, whilst also being less computationally expensive due to having fewer unknowns. The S-FSDT requires C1-continuity that is simple to satisfy with the inherent high-order continuity of the non-uniform rational B-spline (NURBS) basis functions, which we use in the framework of isogeometric analysis (IGA). Numerical examples are solved and the results are compared with reference solutions to confirm the accuracy of the proposed method. Furthermore, the effects of boundary conditions, gradient index, and geometric shape on the mechanical response of functionally graded plates are investigated.

Abstract: The influences of centrifugal and Coriolis forces on the free vibration behavior of rotating carbon nanotube reinforced composite (CNTRC) truncated conical shells are examined. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and are estimated through a micromechanical model. The governing equations are derived based on the first-order shear deformation theory (FSDT) of shells using Hamilton’s principle. The initial mechanical stresses are obtained by solving the dynamic equilibrium equations. The differential quadrature method (DQM) is adopted to discretize the equations of motion and the related boundary conditions. After demonstrating the convergence and accuracy of the presented approach, the effects of angular velocity, Coriolis acceleration, geometrical parameters, type of distribution and volume fractions of carbon nanotubes on the frequency parameters of the CNTRC truncated conical shells are studied. The results reveal that the influences of the type of carbon nanotube distribution and its volume fraction on the frequency parameters depend on the semi vertex angle and angular velocity of the shells and the frequency parameters of the shell with FG asymmetric carbon nanotube distribution can become greater than those of the case with FG symmetric distribution ones.

Abstract: Progressive damage models based on continuum damage mechanics were used in combination with cohesive interface elements to predict the structural response and the failure mechanisms of composite laminates subjected to low-velocity impact. The potential of this simulation approach for correctly predicting the through-thickness distribution of internal damage was specifically examined in the study. The constitutive models for intralaminar and interlaminar damage modes were incorporated into the ABAQUS/Explicit FE code by user-defined VUMAT material subroutines. The results of numerical simulations were compared with experimental data obtained by drop-weight impact testing and stereoscopic X-radiography. The developed FE model provided a correct prediction of the structural impact response of laminated samples over the range of impact energies examined and successfully simulated the temporal sequence of the major damage mechanisms. A reasonably good agreement was also achieved between numerical predictions and experimental observations in terms of shapes, orientations and sizes of individual delaminations induced by impact at the different interfaces. Additional numerical analyses were also conducted to investigate the influence of simulated intralaminar damage modes on the prediction of interface delaminations. The analyses show that implementation of intralaminar damage modes may be required for accurate simulation of the three dimensional delamination pattern induced by impact.

Abstract: This paper presents a physics based modelling procedure to predict the thermal damage of composite material when struck by lightning. The procedure uses the Finite Element Method with non-linear material models to represent the extreme thermal material behaviour of the composite material (carbon/epoxy) and an embedded copper mesh protection system. Simulation predictions are compared against published experimental data, illustrating the potential accuracy and computational cost of virtual lightning strike tests and the requirement for temperature dependent material modelling. The modelling procedure is then used to examine and explain a number of practical solutions to minimize thermal material damage.

Abstract: In this paper, nonlinear free vibration of functionally graded (FG) nanobeams with immovable ends, i.e. simply supported-simply supported (SS) and simply supported-clamped (SC), is studied using the nonlocal elasticity within the frame work of Euler–Bernoulli beam theory with von karman type nonlinearity. The material properties are assumed to change continuously through the thickness of the FG nanobeam according to a power-law distribution. The analytical solution for the nonlinear natural frequency is established using the method of multiple scale. The small scale effects on the linear/nonlinear nonlocal frequency to the linear/nonlinear classical frequency ratios (the linear/nonlinear frequency ratios) are examined for various parameters such as the FG nanobeam length, the FG nanobeam thickness to length ratio (the thickness ratio), the vibration amplitude to the radius of gyration ratio (the amplitude ratio), and the boundary condition. As a main result, it is observed that while the linear frequency ratios are independent of the gradient index, the nonlinear frequency ratios vary with the gradient index.

Abstract: The goal of this work is to identify the best strategy for clustering of AE events, originated from damage initiation and development of 2D and 3D glass/epoxy woven composites loaded in tension. Two AE features – peak amplitude and peak frequency – were selected as the best cluster-definition features from nine AE parameters by (a) Laplacian score and correlation analysis, (b) principal component analysis and k-means++ algorithm and (c) repeatability and similarity analysis of the clusters in AE registration of different specimens. Peak amplitude and peak frequency represent adequately and in a reproducible way the AE events clustering for both 2D and 3D woven glass/epoxy composites, resulting in the clusters of similar shape. Cluster bounds are identified for different reinforcement type and different loading directions. The cluster identification creates a framework for analysis of a link between damage mode and AE parameters of the corresponding AE event.

Abstract: This paper investigates the large amplitude vibration behavior of nanocomposite cylindrical panels resting on elastic foundations in thermal environments. Two kinds of carbon nanotube-reinforced composite (CNTRC) panels, namely, uniformly distributed and functionally graded reinforcements, are considered. The material properties of FG-CNTRC panels are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Karman-type of kinematic nonlinearity. The panel-foundation interaction and thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion are solved by a two-step perturbation technique to determine the nonlinear frequencies of the CNTRC panels. Numerical results demonstrate that the natural frequencies of the CNTRC panels are reduced but the nonlinear to linear frequency ratios of the CNTRC panels are increased as the temperature rises. In contrast, natural frequencies are increased but the nonlinear to linear frequency ratios are decreased by increasing the foundation stiffness. The results reveal that the natural frequencies are increased by increasing the CNT volume fraction, whereas the CNTRC panels with intermediate CNT volume fraction do not necessarily have intermediate nonlinear to linear frequency ratios.

Abstract: The behaviour of RC beams strengthened with NSM FRP bars was experimentally investigated. Eight beams were tested under four point bending. The effects of material type, epoxy properties, bar size and the number of NSM bars were studied. The tested beams were strengthened with a limited bond length in order to imitate as much as possible work-place conditions, as the grooves could only be cut up to the faces of the supporting columns with difficulty. The load capacity, deflection, mode of failure, FRP strain, concrete strain, free end slip and the transverse strain in epoxy and concrete of the tested beams were all analysed. Comparison of strengthened and control beams showed enhancement of 155.8% and 129.8% in the yielding loads, while the increase in the ultimate loads was 166.3% and 159.4% for beams strengthened with carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) respectively. The beams strengthened with CFRP bars experienced higher stiffness than the corresponding beams with GFRP bars. Epoxy properties, size and number of bars had little effect on the load capacity of the strengthened beams with failures mainly occurring either in epoxy or as a result of concrete cover separation.

Abstract: Thermo-electro-mechanical vibration of piezoelectric cylindrical nanoshells is studied using the nonlocal theory and Love’s thin shell theory. The governing equations and boundary conditions are derived using Hamilton’s principle. An analytical solution is first given for the simply supported piezoelectric nanoshell by representing displacement components in the double Fourier series. Then, the differential quadrature (DQ) method is employed to obtain numerical solutions of piezoelectric nanoshells under various boundary conditions. The influence of the nonlocal parameter, temperature rise, external electric voltage, radius-to-thickness ratio and length-to-radius ratio on natural frequencies of piezoelectric nanoshells are discussed in detail. It is found that the nonlocal effect and thermoelectric loading have a significant effect on natural frequencies of piezoelectric nanoshells.

Abstract: In this paper, the bending and free flexural vibration behavior of sandwich plates with carbon nanotube (CNT) reinforced facesheets are investigated using QUAD-8 shear flexible element developed based on higher-order structural theory. This theory accounts for the realistic variation of the displacements through the thickness, and the possible discontinuity in slope at the interface, and the thickness stretch affecting the transverse deflection. The in-plane and rotary inertia terms are considered in the formulation. The governing equations obtained using Lagrange’s equation of motions are solved for static and dynamic analyses considering a sandwich plate with homogeneous core and CNT reinforced face sheets. The accuracy of the present formulation is tested considering the problems for which solutions are available. A detailed numerical study is carried out based on various higher-order models deduced from the present theory to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness and the plate thickness ratio on the global/local response of different sandwich plates.

Abstract: The behavior of single bricks and small masonry pillars strengthened by means of fabric reinforced cementitious matrix systems made with glass-fiber grids is discussed both from an experimental and numerical standpoint. A standard Push–pull double lap test is performed on three different series of experimental set-ups for reinforced single bricks and on masonry pillars, evaluating the role played by the anchorage length on the overall behavior of the strengthened system. Standard Italian bricks with very good mechanical properties are used, in order to evaluate the ultimate strength of the grid for delamination within the mortar. The masonry pillar is built with 3 bricks spaced out by two thick mortar joints. When dealing with the single bricks, three different anchorage lengths were tested, equal to 5, 10 and 15 cm, in order to evaluate the reduction of the ultimate strength induced by an insufficient anchorage. To suitably interpret experimental results, both a newly developed analytical–numerical approach and a recently presented 3D FEM model were utilized to have an insight into experimental results. In the analytical–numerical approach only the glass-fiber grid was considered and modeled by means of 1D Finite Elements interacting with the surrounding mortar by means of interfaces exhibiting a non-linear stress–slip behavior deduced from experimental data. The 3D model uses 8-noded rigid elements interconnected by inelastic interfaces exhibiting softening. The incremental non-linear problem is solved by means of a robust Sequential Quadratic Programming routine already tested on medium and large scale examples with softening materials. The grid is modeled through non-linear truss elements, interacting with surrounding mortar by means of non-linear interfacial tangential stresses. Stress–slip behavior of the interface between the mortar and the textile is deduced through ad hoc experimentation conducted on a mortar specimen reinforced with a single yarn and subjected to a standard tensile test. Good agreement was found between experimental evidences and numerical simulations, meaning that the combined approach proposed may be considered as reference for design considerations.

Abstract: This article introduces the concept of stacking sequence table (SST) for the optimal design of laminated composite structures with ply drops. The SST describes the sequence of ply-drops ensuring the transition between a thick guide laminate and a thinner one. A blended design is represented by a SST combined with a thickness distribution over the regions of the structure. An evolutionary algorithm is specialized for SST-based blending optimization. Optimization of the sequence of ply-drops with the proposed algorithm enables satisfying design guidelines that could not have been considered in previous studies. An extensive set of design guidelines representative of the actual industrial requirements is introduced. The method is applied to an 18-panel benchmark problem from the literature with convincing results. In particular, the present results show that strength-related guidelines can be enforced without significantly penalizing the stiffness behavior and consequently the mass of the structure.

Abstract: Buckling and free vibration of magnetoelectroelastic nanoplate resting on Pasternak foundation is investigated based on nonlocal Mindlin theory. The in-plane electric and magnetic fields can be ignored for nanoplates. According to Maxwell equations and magnetoelectric boundary conditions, the variation of electric and magnetic potentials along the thickness direction of the nanoplate is determined. Using the Hamilton’s principle, the governing equations of the magnetoelectroelastic nanoplate are derived. Numerical results reveal the effects of the electric and magnetic potentials, spring and shear coefficients of the Pasternak foundation on the buckling load and vibration frequency. These results can serve as benchmark solutions for future numerical analyses of magnetoelectroelastic nanoplates.

Abstract: A new three-dimensional exact solution for the free vibrations of arbitrarily thick functionally graded rectangular plates with general boundary conditions is presented. The three-dimensional elasticity theory is employed to formulate the theoretical model. According to a power law distribution of the volume of the constituents, the material properties change continuously through the thickness of the functionally graded plates. Each of displacements of the plates, regardless of boundary conditions, is expanded as a three-dimensional (3-D) Fourier cosine series supplemented with closed-form auxiliary functions introduced to eliminate all the relevant discontinuities with the displacements and its derivatives at the edges. Since the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on Rayleigh–Ritz procedure by the energy functions of the plate. The excellent accuracy and reliability of the current solutions are demonstrated by numerical examples and comparison of the present results with those available in the literature, and numerous new results for thick FG plates with elastic boundary conditions are presented. The effects of gradient indexes are also illustrated.

Abstract: The simulation at meso-scale of textile composite reinforcement deformation provides important information. In particular it gives the direction and density of the fibres that condition the permeability of the textile reinforcement and the mechanical properties of the final composite. These meso FE analyses are highly dependent on the quality of the initial geometry of the model. Some softwares have been developed to describe composite reinforcement geometries. The obtained geometries imply simplification that can disrupts the reinforcement deformation computation. The present paper presents a direct method using computed tomography to determine finite element models based on the real geometry of the textile reinforcement. The FE model is obtained for any specificity or variability of the textile reinforcement. The interpenetration problems are avoided. The determination of the fibre direction at each point of the model is detailed. It is a key point for the quality of the deformation simulation. A comparison between FE models obtained from μCT and from a textile geometrical modeller shows that the description of the variability taken into account by the first one leads to a better result.

Abstract: In previous studies by the authors, it was found that a lower water–binder ratio led to enhanced dispersion of carbon nanotube (CNT) in the cement matrix. The objective of this study was to investigate the piezoresistive sensitivity and stability of CNT/cement mortar composites with low water–binder ratio. The effect of absorbed water on the piezoresistivity of the composites was also investigated, since it strongly affects the electrical properties of the composites. The changes in the electrical resistance of composite specimens induced by external cyclic loading were measured to investigate their piezoresistive sensitivity and stability. The experimental results indicates that the stability of piezoresistivity under cyclic loading and their time-based sensitivity can be improved by decreasing the water–binder ratio of the cement composites. Moreover, the variation of piezoresistivity induced by the moisture content can be decreased by low water–binder ratio.

Abstract: The present paper investigates the static behavior of doubly-curved laminated composite shells and panels. A two dimensional General Higher-order Equivalent Single Layer (GHESL) approach, based on the Carrera Unified Formulation (CUF), is proposed. The geometry description of the middle surface of shells and panels is computed by means of differential geometry tools. All structures have been solved through the generalized differential quadrature numerical methodology. A three dimensional stress recovery procedure based on the shell equilibrium equations is used to calculate through-the-thickness quantities, such as displacements components and the strain and stress tensors. Several lamination schemes, loadings and boundary conditions are considered in the worked out applications. The numerical results are compared with the ones obtained with commercial finite element codes. New profiles, concerning displacements, strains and stresses, for doubly-curved multi-layered shell structures are presented for the first time by the authors.

Abstract: In this paper, the polyurethane foam filled pyramidal lattice core sandwich panel is fabricated in order to improve the energy absorption and low velocity impact resistance. Based on the compression tests, a synergistic effect that the foam filled sandwich panels have a greater load carrying capacity compared to the sum of the unfilled specimens and the filled polyurethane block is found. Moreover, the energy absorption efficiency of foam filled sandwich panels with higher relative density (2.58% and 3.17%) lattice cores is lower than that of the unfilled specimens when the compressive strain is small, while it exhibits superior when the compressive strain arrives at about 0.25, and the superiority enlarges as the strain increase. However, the energy absorption of foam filled sandwich panels owning lower relative density (1.83%) lattice cores is inferior to that of the unfilled specimens. During the low velocity impact tests, it is found that the contact duration between the impactor and the sandwich specimens is shorter and the impact peak load has a slight increase for the foam filled specimens.

Abstract: A numerical model for accurately predicting the delamination propagation in multidirectional laminates under mode I and mixed-mode I/II loadings using the cohesive element is proposed in this paper. Instead of a constant fracture toughness, a fracture toughness function which reflects the variation of fiber bridging tractions, accompanying with a group of appropriate interface stiffness, interface strength, the number of cohesive elements in cohesive zone and viscosity coefficient determined by the trial and error method among recommended guidelines or values in literatures, can provide accurate simulations on the delamination growth in the multidirectional laminates. The predicted delamination behaviors of the multidirectional laminates with interfaces 0°/5°, 45°/−45° and 90°/90° in both the DCB and MMB tests are consistent with experimental outcomes, which give evidence of the effectiveness of the proposed model.

Abstract: This study focuses on the static analysis of functionally graded conical shells and panels and extends a previous formulation by the first three authors. A 2D Unconstrained Third order Shear Deformation Theory (UTSDT) is used for the evaluation of tangential and normal stresses in moderately thick functionally graded truncated conical shells and panels subjected to meridian, circumferential and normal uniform loadings. To investigate the behavior of the functionally graded structures at issue, a four parameter power law function is considered. The initial curvature effect is discussed and the role of the parameters in the power law function is shown. The conical shell problem described in terms of seven partial differential equations is solved by using the generalized differential quadrature (GDQ) method. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. The stress recovery is worked out to reconstruct the correct distribution of transverse stress components. Accurate stress profiles for general loading combinations applied at the extreme surfaces are obtained. The influence of the semi vertex angle is pointed out.

Abstract: This paper presents a general two-dimensional approach for solving doubly-curved laminated composite shells using different kinematic expansions along the three orthogonal directions of the curvilinear shell model. The Carrera Unified Formulation (CUF) with different thickness functions along the three orthogonal curvilinear directions is applied to completely doubly-curved shells and panels, different from spherical and cylindrical shells and plates. Furthermore, the fundamental nuclei for doubly-curved structures are presented in their explicit form for the first time by the authors. These fundamental nuclei also allow to consider doubly-curved structures with variable thickness. In addition, the theoretical model includes the Murakami’s function (also known as zig-zag effect). For some problems it is useful to have an in-plane kinematic expansion which is different from the normal one. The 2D free vibration problem is numerically solved through the Local Generalized Differential Quadrature (LGDQ) method, which is an advanced version of the well-known Generalized Differential Quadrature (GDQ) method. The main advantage of the LGDQ method compared to the GDQ method is that the former can consider a large number of grid points without losing accuracy and keeping the very good stability features of GDQ method as already demonstrated in literature by the authors.

Abstract: Variable stiffness composite laminates can be manufactured using Automated Fiber Placement (AFP) technology. An improvement in structural performance can be achieved by tailoring their material properties in directions that are more favorable to carry loads. During AFP manufacturing, however, the formation of defects, mainly gaps and overlaps, is inevitable. The extent of a defected zone is generally controlled by two sets of parameters: design parameters; and manufacturing parameters. In this work, we investigate how the parameters governing the formation of defects impact the set of optimal solutions for a multi-objective optimization problem, where in-plane stiffness and buckling load are simultaneously maximized. It is found that increasing the number of tows within a course reduces the amount of defected areas, where the course width is kept constant. Furthermore, the amount of defect areas significantly reduces by using a wide course, which has the effect of both increasing the deviation from the designed fiber path and reducing the number of manufacturable designs. The results show that a complete gap strategy shifts the defect-free Pareto front, obtained without considering the effect of defects, towards lower in-plane stiffness and buckling load; on the other hand, a complete overlap strategy shifts the Pareto front towards higher structural properties.