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A novel meta-material has been designed and implemented into a rotor blade to enhance aerodynamic efficiency by achieving a passive twist during rotation. The twist is induced by bend-twist coupling exhibited in the meta-material, which is created to possess anisotropic elastic properties at the bulk level. A concept design of a rectangular blade spar is proposed where the metamaterial is used as the core material to induce twist. Using finite element analysis(FEA) we demonstrate how the bend-twist property of the blade spar is governed by cell geometries of the core material. The twist is activated by a lagwise bending moment generated from a movable mass at the blade tip due to off-centre centrifugal forces. The relationship between the twist, mass location and rotational speed has been explored. Moreover, it was found that the bend-twist property achieved by the proposed blade spar is more effective compared to that of an anisotropic thin-walled composite beam.

Corners of composite curved beams can easily experience delamination under opening or closing bending moments. Existing literature on the delamination of curved laminated beams, however, is limited to unidirectional and cross-ply laminates with 0° and 90° layers and two-dimensional (2D) plane strain finite element analysis. This study experimentally and analytically investigates the failure behaviors of curved composite structures under four-point bending. Multiangle laminates manufactured using an out-of-autoclave prepreg were examined. A three-dimensional (3D) finite element model was created and analyzed with cohesive elements at the interfaces of adjacent plies. In the experiments, delamination dominated the failure of the curved laminates with several opening cracks. Multiple delamination positions were predicted in the analyses. Double cantilever beam specimens were tested and analyzed for a reference point for selecting cohesive parameters. Several cohesive parameters were selected and discussed. Predicted failure loads matched the experimental results well with 5.8% error when the model simulated a sufficient number of factors of the real test.

Tidal turbine blades experience a significant bending moment in the root area during their long-term operation in a sea water environment. This necessitates using fibre reinforced polymer as the blade material to provide the required strength/stiffness. In this study, a design methodology based on hydrodynamic and Finite Element models with a view to examine the mechanical properties of composites was developed to evaluate the structural response of two commercial scale turbine blades (1.5 and 0.35 MW). Using the output from the hydrodynamic model , Finite Element stress analysis was conducted in order to determine the likelihood of blade failure. To incorporate appropriate failure modes with the blade model, failure analysis was conducted on the composite test coupons. The results of stress analysis show that the blade root area experiences high stress values with failure modes such as resin cracking, fibre/matrix interfacial de-bonding, delamination and fibre breakage . It is also predicted that the glass fibre composite blades require three times thicker laminates than a carbon fibre composite blade of similar design to maintain the same safety factor. Reasonable agreement between the numerically and experimentally determined strain fields on a small-scale blade indicates that the result of Finite Element stress analysis is valid.

The slab spatial composite effect arises due to compatible deformation of the reinforced concrete slab with the steel beam in composite frames. This effect can significantly amplify the stiffness of composite frame beams. Current Chinese design code adopts the stiffness amplification coefficient method for the design of composite frame beams, and the equivalent moment of inertia of the composite frame beam can be calculated to conduct the global analysis. However, the current formulae are only suitable for lateral load cases and symmetric I-shaped steel section. Therefore, this study aims to propose unified design equations of the stiffness amplification coefficient considering both vertical and lateral load cases and both symmetric and asymmetric I-shaped steel sections to address the aforementioned limitations. A series of parametric finite element analyses using the beam-shell mixed element model are conducted to derive the unified design equations. The reasonability of the proposed equations is verified by comparing the critical structural indices, such as the natural vibration period, inter-storey shear, lateral displacement, bending moment, and deflection distribution of numerical examples of multi-storey composite frames. Good accuracy is obtained through the comparison between the linear beam element model modified by the proposed equations and the beam-shell mixed element model.

The von Karman large deformations are considered in the Mindlin plate theory described by the nonlocal and gradient elasticity for piezoelectric nanoplates. It is shown that electric intensity vector can be expressed by mechanical quantities. The governing equations for bending moments, normal and shear stresses are derived from the variational principle. The finite element method is developed for considered governing equations. Differences of both theories are presented.

Radial bone shaft fractures are commonly treated with bone plates. Flexible bone plates made of fiber-reinforced polymer composites have advantages over complications, such as stress shielding, corrosion, harmful ions, X-ray artifacts, resulting from metallic bone plates. Postoperative rehabilitation exercise is an important factor influencing the healing outcomes of radial bone fractures. A finite element model of radial shaft fracture was treated with Twintex [0]2nT composite bone plate and six stainless steel bicortical screws. Axial compression (10 N), bending moment (0.1 Nm), and torsion (0.1 Nm) as single, combined, and alternative loads (10% loads of daily activities) were used in the finite element study. A mechano-regulation algorithm based on deviatoric strain was used to predict the healing of bone fractures. The healing performance and bending stiffness were evaluated and compared to estimate the healing status of bone fractures. The best exercise mode, which gave the highest healing performance (68%) and bending stiffness (89%), was suggested. These results can be successfully utilized for the design of healing devices for the rehabilitation of fractured bones.

New closed-form, analytical solutions are derived for the strain energy release rate (SERR) and mode partitioning of uneven bending moments-loaded tests on layered beams with bending-extension coupling and residual hygrothermal stresses. The analytical modeling utilizes Timoshenko beam kinematics, a semi-rigid interface model, and the global method to perform mode partitioning. The proposed solutions are validated via the finite element method in two typical examples of metal-composite joints. In addition, experiments using the double cantilever beam with uneven bending moments test setup are performed in a titanium-carbon fiber reinforced plastic adhesive joint, and data reduction is performed utilizing the new analytical solutions. We demonstrate that the residual thermal stresses effect on the SERR and mode mixity of the metal/composite interfaces can be non-negligible and, thus, should be considered in the design and analysis of such structures. The proposed formulas serve as a data reduction scheme for the fracture toughness and mode mixity determination in the general case of layered beams with bending-extension coupling and hygrothermal stresses, when utilizing uneven bending moments for the characterization tests.

An analytical method for partitioning mixed-mode fractures on rigid interfaces in orthotropic laminated double cantilever beams (DCBs) under through-thickness shear forces, in addition to bending moments and axial forces, is developed by extending recent work by the authors (Harvey et al., 2014). First, two pure through-thickness-shear-force modes (one pure mode I and one pure mode II) are discovered by extending the authors’ mixed-mode partition theory for Timoshenko beams. Partition of mixed-mode fractures under pure through-thickness shear forces is then achieved by using these two pure modes in conjunction with two thickness ratio-dependent correction factors: (1) a shear correction factor, and (2) a pure-mode-II energy release rate (ERR) correction factor. Both correction factors closely follow an elegant normal distribution around a symmetric DCB geometry. The principle of orthogonality between all pure mode I and all pure mode II fracture modes is then used to complete the mixed-mode fracture partition theory for a general loading condition, including bending moments, axial forces, and through-thickness shear forces. Excellent agreement is observed between the present analytical partition theory and numerical results from finite element method (FEM) simulations.

In this paper, a first order shear deformation theory is proposed for cylindrical sandwich pipes subjected to undersea water pressure. The new model examines the change of the circumferential radius due to the radial deflection of the cylindrical sandwich shell and its effect on the bending moments. Differential equations of equilibrium for the non-shallow cylindrical sandwich shell are derived and are expressed in terms of the components of displacement and the rotation angles of the middle planes of the face sheets with respect to the neutral surface. The proposed theory is applied to investigate the buckling of a thermal insulating sandwich pipe laid on the seabed with fully constraint ends. Numerical analyses are conducted by developing MATLAB program to obtain the buckling pressures as well as the corresponding half wave numbers in circumferential direction for cylindrical sandwich pipes for different slenderness ratio, radius-to-thickness ratio and core-to-facesheet thickness ratio. The efficiency and accuracy of the presented theory is confirmed by comparing the analytical solutions with finite element results from ABAQUS, both showing a good agreement with each other.

Five Reinforced Concrete (RC) beams strengthened with Basalt Fiber Reinforced Polymer (BFRP) grid in conjunction with Engineered Cementitious Composite (ECC) were tested along with one conventional RC beam for reference to investigate their performance improvement, particularly in shear capacity, due to strengthening. The test results highlighted that the failure modes of the tested beams were dominated with shear-compression failure in the shear/bending moment regions and concrete crushing in the compression part of the pure bending zone. A good bonding performance between the BFRP-ECC composite and concrete substrate was exhibited during the testing process, which can effectively suppress the propagation of diagonal cracks in the shear/bending moment regions. The shear capacity of strengthened RC beams was greatly improved with the increase of BFRP grid reinforcement ratio. Moreover, the reinforcement effect of this strengthening technique was much more effective with the increase of shear-span ratio of the tested RC beams. Furthermore, finite element analyses based on ABAQUS/Standard software were conducted to provide analytical estimations of the shear capacity of the strengthened RC beams. The analytical results revealed that the predicted values agree very well with the test data, which can effectively predict the shear capacity of RC beams strengthened with BFRP-ECC composite.

The GFRP elastic gridshell is a type of spatial structure composed of long continuous hollow GFRP members and has been used in large-span roof structures. The elastic gridshell achieves its shape as the result of elastic deformations during the construction process of lifting or pushing. The shape-forming mechanism of such structures is very complicated due to significant geometric non-linearity. This research aims to propose analytic formulations to estimate the structural features of the GFRP elastic gridshell under lifting construction. An analytical theory, considering the large geometric deformations, is first presented for analyzing single lifted member. Based on the given theory and an iteration process, a form-finding method is further proposed for predicting the deformation, nodal forces and bending moment of biaxial symmetrical GFRP elastic gridshells during the lifting construction. The form-finding method is realized on the Matlab platform and a case study is carried out. Finite element analysis is further conducted to validate the accuracy and practicability of the proposed method. Results show that, the analytic theory is highly accurate for the analysis of lifted members, and the proposed form-finding method is applicable in predicting the structural behaviors of GFRP elastic gridshells for which the lifting construction is adopted.

This paper presents a beam finite element model for non-linear global buckling analysis of composite laminated beam type structures. To perform the non-linear stability analysis, the framework of updated Lagrangian incremental formulation is used. The non-linear displacement field of thin-walled cross-section is adopted in order to insure the geometric potential of semitangential type for both the internal torsion and bending moments. The cross-section mid-line contour is assumed to remain not deformed in its own plane and the shear strains of middle surface are neglected. The laminates are modeled on the basis of classical lamination theory. In order to illustrate the application of the proposed formulation, several numerical examples are presented. For validation purposes, the obtained results are compared with results reported in the literature and the ones obtained with shell finite elements by Nastran.

Solution of the buckling problem for the CCFF orthotropic plate subjected to in-plane pure bending is presented. The two parallel clamped edges of the plate are loaded by linearly distributed in-plane loads statically equivalent to the in-plane bending moments. The problem is solved using method of lines for partial differential equations and Galerkin’s method. The buckling problems are solved for isotropic, orthotropic and multilayered CFRP composite plates with various aspect ratios. Results of calculations of critical loads are compared with those based on finite-element modelling and analyses. The comparisons demonstrate efficiency of the proposed approach to the buckling analysis of composite CCFF plates with various dimensional and stiffness parameters.

A homogenized limit analysis model for the prediction of collapse loads and failure mechanisms of masonry walls reinforced with near surface bed joint GFRP bars is presented. Reinforced masonry homogenized failure surfaces are obtained by means of a compatible identification procedure, where each brick is supposed interacting with its six neighbors by means of finite thickness mortar joints, filler epoxy resin and FRP rods. In the framework of the kinematic theorem of limit analysis, a simple constrained minimization problem is obtained on the unit cell, suitable to estimate – with a very limited computational effort – reinforced masonry homogenized failure surfaces. A FE strategy is adopted to solve the homogenization problem at a cell level, modeling joints, bricks, filler and FRP rods by means of eight-noded infinitely resistant parallelepiped elements. A possible jump of velocities is assumed at the interfaces between contiguous elements, where plastic dissipation occurs. For mortar and bricks interfaces, a frictional behavior with possible limited tensile and compressive strength is assumed, whereas for epoxy resin and FRP bars some formulas available in the literature are adopted in order to take into account in an approximate but effective way, the delamination of the bar from the epoxy and the failure of the filler at the interface with the joint. In order to validate the model proposed, two meaningful examples are critically analyzed. The first relies on a reinforced masonry beam in four-point bending, whereas the second is a full scale wall constrained at three edges and loaded until failure with a distributed out-of-plane pressure. While the first example is useful to test the model at a cell level, since only horizontal ultimate bending moment is involved in the failure mechanism, the second provides a full assessment of the procedure proposed at a structural level. In both cases, very good agreement is found with literature data, meaning that the model proposed may provide useful information for all practitioners interested in the design of masonry walls reinforced with bed joint FRP bars.

This work studied the mechanical performance of GFRP woven composites under combined tension-bending loading. Special fixtures were used to apply the bending moments through offset shims of various thicknesses placed between the specimen and the loading axis. Different experimental setups were performed to determine failure stresses, strains at different locations, out of plane displacement, and stress–strain relation. The experimental results showed that failure occurred near the fixture where maximum bending stress existed. In addition to the experimental study, theoretical analysis and finite element modeling of the specimen and the loading condition were also carried out. The out of plane displacement of the specimen under combined tension-bending loading as determined from the theoretical and finite element model had very good matching with the experimental data. The out of plane deflection of the specimen at the center increased rapidly with loading until it reaches the limiting value, the eccentricity. The stress distribution computed by the finite element model showed that the maximum resultant stress occurred near the fixture, where the failure had been observed experimentally. In addition, the stain computed by the finite element model had very good agreement with the experimental data. Hence, the finite element model is capable of simulating the performance of the composite under different loading conditions.

Analytical treatment of the deformations in adhesively bonded joints on elastic foundations is presented, with special attention to the specific case of adhesive joints between the face sheets of sandwich beams. While the subject of deformations in adhesively bonded joints has been studied in detail over the past six decades, no work on the subject of modeling adhesive joints on elastic foundations exist. The analytical model idealizes the overlap region as a single cylindrically bent plate, and thus applies to both balanced and unbalanced joint types of various configurations. The influence of the elastic foundation parameters on the magnitude of the edge moment is studied in detail. Results show that the elastic foundation acts to reduce the magnitude of the bending moments at the ends of the overlap, and alleviate the geometric non-linearity in the adhesive joint response. The integrity of the model is verified through good agreement with non-linear finite element model results, and other analytical models found in the literature. Strain energy release rates in adhesively bonded sandwich beams are computed using the proposed model, and are shown to correlate well with experimental results.

In this study, bending analysis of a moderately thick orthotropic sector plate subjected to various loading conditions is presented. Different boundary conditions including clamped, simply supported and free are considered. The governing equations, assuming Reissner shear deformation theory, include eight first order partial differential equations in terms of r and θ with eight unknowns, i.e. displacements, rotations, bending and twisting moments and shear forces within the domain. Assuming unknown variables as separable functions of r and θ together with the extended Kantorovich method (EKM) leads to dual sets of eight first order ordinary differential equations. Iterative solutions are then presented for the resulted ODE systems. It is shown that the method provides accurate predictions for all displacement and stress resultant components with very fast convergence. The accuracy of the predicted results is examined using other published data in the literature. Finite element analysis is used to validate results for a wide range of loading and boundary conditions of sector plates for possible future studies.

Composite cylindrical shells and panels are widely used in aerospace structures. These are often subjected to defects and damage from both in-service and manufacturing events. Delamination is the most important of these defects. This paper deals with the instability analysis of delaminated composite cylindrical shells subject to pure bending and also combined bending and axial compression, using the finite element method. The combined double-layer and single-layer of shell elements are employed, which in comparison with the three-dimensional finite elements requires less computing time and space for the same level of accuracy. The effect of contact in the buckling mode has been considered, by employing contact elements between the delaminated layers. The interactive buckling curves and postbuckling response of delaminated cylindrical shells have been obtained. In the analysis of post-buckled delaminations, a study using the virtual crack closure technique has been performed to find the distribution of the strain energy release rate along the delamination front. The results show that under pure bending, laminated cylindrical shells are more sensitive to the presence of delamination, than they are under pure axial compression. It was also observed that the effects of delamination are more apparent when the composite cylindrical shells are subjected to combined axial compression and bending. In this case, with a slight increase of the applied bending moment, the strain energy release rate distribution on the compressive side of the cylinder changes drastically. © 2007 Elsevier Ltd. All rights reserved.

The formulation of a non-linear composite 4-node co-rotational resultant shell element is presented for the solution of bending, free vibration, critical buckling and postbuckling analysis of composite plates and shells. Using the ANS (assumed natural strain) method the present shell element generates shear locking behavior, and such element performs very well as much as shells get thin. The formulation of the geometrical stiffness presented here is exactly defined on the mid-surface and is efficient for analyzing stability problems of thin and thick laminated plates, and shells by incorporating bending moment and transverse shear resultant forces. The transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The adoption of a second-order co-rotational formulation makes it computationally efficient compared to the most existing composite shell elements. The proposed formulation is computationally efficient and the test results showed good agreement.

This paper presents a stress analysis method for web-core sandwich beams. The beam is a transverse cut from a sandwich plate. The analysis is carried out by transforming the initially periodic web-core sandwich beam, constructed from a set of unit cells, into an equivalent homogenous sandwich beam. Certain deformation components are set equal both in periodic and homogenous beams when a unit cell is considered. The structural analysis of the homogenized beam follows thick face plate kinematics giving the deflection, bending moment and shear force distributions. Then the normal stress components can be calculated accurately by reconsidering the periodic structure of the beam. The validation of the proposed method is carried out with FE-analyses.

Box-girder analysis and design should take into consideration stresses due to longitudinal bending moment, shear force, torsion, distortion, shear-lag and transverse bending as well as instability of the flange under compression and web under shear as plates and stiffened panels. The orthotropic nature of FRP has to be taken into consideration in all these analyses. Although general purpose finite element software can be used to accurately analyse such a bridge considering all these effects, the time consumed is too high to practically use it in the preliminary and optimum design stages, which involve a large number of trials. A simplified and computationally efficient procedure for the analysis of single cell FRP box-girder bridges made of blade angle or T stiffened panels, for efficient use at these stages, is presented in this paper. This has been validated by comparison with results available in literature or results obtained from finite element analysis.

The free-edge effect in unsymmetrically laminated plates subjected to a uniformly distributed tensile force or bending moment is studied. A variational asymptotic formulation, leading to a finite element scheme in the free-edge layer, is presented. A stress field is determined for symmetric and unsymmetric laminates subjected to tension and bending loadings. Based on two criteria, the edge effect is compared between the different sample cases. It is found that the edge effect is more dominant in tension than in bending loading for symmetric and unsymmetric laminates, and more pronounced for symmetric angle-ply than for unsymmetric angle-ply laminates.

Stiffened panels are structures that can be designed to efficiently support in-plane compression, bending, and shear loads. Although the stiffeners are usually discrete elements which are fastened or bonded to a flat or continuously curved plate, manufacturing methods such as thermoforming allow integral formation of the stiffeners in a panel. Such a configuration offers potential advantages in terms of a reduced number of parts and manufacturing operations. For thermoplastic composite panels stiffened by integrally formed open-section beads, the effects of bead spacing and bend cross-section geometry on the initiation of buckling under uniaxial compression and uniform shear loading were investigated. Finite elements results for a range of stiffened panel sizes and bead geometries are presented and compared with approximate closed-form solutions based on an effective flat plate size. Experimental verification of analytical predictions for one of the shear panels and one of the compression panels is described. Compensation of the forming tool to reduce the degree of initial curvature of the panels was found to be necessary.