Maximum Bending Stiffness Research Articles

Numerical study on the design of flax/bamboo fiber reinforced hybrid composites under bending load

Natural fiber-based composites are essential for the environment in this era of depletion of petroleum resources and for new green environmental rules, as they have limited detrimental behavior or response against the environment. In this paper, firstly, the suitability of replacing glass fiber with natural bamboo fiber in a flax/glass/epoxy hybrid composite under a fixed bending load is investigated using Finite Element Analysis (FEA) software ABAQUS with proper model validation. Finally, five different lay-up sequences of flax/bamboo/epoxy hybrid composite laminate for fixed volume fractions of flax and bamboo strips are investigated numerically to develop design strategies for binary hybrid composite. It is found that the bending stiffness and equivalent modulus of elasticity for model FB-1 are increased by 37.53 % and 37.52 % respectively compared to the base model while the energy absorption for model FB-3 is highest which is 105.89 % higher than the base model. Analysis of various lay-up sequences showed that flexural behavior can be improved by fabricating binary hybrid composites using the concept of a sandwich structure. It is shown that all highly stiff laminas should be placed on the outer sides of the composite to achieve the maximum bending stiffness whereas they should be placed at the center to attain the maximum energy absorption.

Soft Robotic Fabric Actuator With Elastic Bands for High Force and Bending Performance in Hand Exoskeletons

In current designs soft robotic bending actuators, the need for high force capabilities is not adequately addressed. In this article, we present a new inflatable actuator that exploits textile manufacturing techniques, using an elastic band to improve both bend and force performance. At a pressure of 102 kPa, the index finger sized actuator exerts 24.8 N of force on the environment. It is also capable of a full 360 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> bending angle for pressures between 30 kPa and 102 kPa with a maximum bending stiffness of 288.4 N/m. We further demonstrate feasibility of this new actuator in a case study of an entirely fabric based soft robotic hand exoskeleton that increases robustness and user comfort. Our results suggest that textile robotics could provide an attractive solution in terms of the development of user-friendly hand exoskeletons.

A Novel Jamming Structure With Interlocking Mechanism Towards Applications in Wearable Robots

The adoption of variable stiffness actuators allows robots to take advantages of both rigid and soft structures. Jamming based variable stiffness structures are receiving increased attentions due to advantages of light weight, easy fabrication, and so on. However, the maximum bending stiffness and stiffness variation ratio achieved by most existing jamming structures are relatively small and unable to provide sufficient assistance to human joints when used in wearable robots. In this study, we proposed a novel jamming structure called gear jamming. Be different from most existing jamming structures that adopt frictional effects between internal components for resistance generation, the proposed jamming structure relies on an interlocking mechanism consisting of a series of gear-shape components and two layers distributed with teeth. A geometrical model was built to provide guidance for structure design, and experiments were performed to investigate effects of different factors on bending stiffness. A stiffness variation ratio up to 29.09 folds was achieved with the structure when the vacuum pressure increased from 0 to 90 kPa. To evaluate its performance for human joint assistance, a 64-g prototype was worn on subject's wrist to assist static holding of a 3-kg weight under a low vacuum pressure (30 kPa). Muscular activities of three representative muscles on the forearm reduced by 74.31±5.24%, 39.31±11.03%, and 71.48±3.00% in average over five subjects when compared to the condition without wearing the gear jamming prototype, which implied the promise of applying the proposed gear jamming structure in wearable robots.

A Method to Determine the Geometry-Dependent Bending Stiffness of Multilayer Graphene Sheets

Abstract We consider how the bending stiffness of a multilayer graphene sheet relies on its bending geometry, including the in-plane length L and the curvature κ. We use an interlayer shear model to characterize the periodic interlayer tractions due to the lattice structure. The bending stiffness for the sheet bent along a cylindrical surface is extracted via an energetic consideration. Our discussion mainly focuses on trilayer sheets, particularly the complex geometry-dependency of their interlayer stress transfer behavior and the overall bending stiffness. We find that L and κ dominate the bending stiffness, respectively, in different stable regions. These results show good quantitative agreement with recent experiments where the stiffness was found to be a non-monotonic function of the bending angle (i.e., Lκ). Besides, for a given in-plane length, the trilayer graphene in the flat state (κ → 0) is found to have the maximum bending stiffness. According to our analytical solution to the flat state, the bending stiffness of trilayer graphene sheet can vary by two orders of magnitude. Furthermore, once multilayer graphene sheets are bent along a cylindrical surface with small curvature, the sheets perform similar characteristics. Though the discussion mainly focuses on the trilayer graphene, the theoretical framework presented here can be readily extended for various van der Waals materials beyond graphene of arbitrary layer numbers.

Structural design of composite stiffened panel for a flat wing micro-aircraft

In this study, the integral micro-sized composite wings are designed and manufactured by using carbon fiber reinforced plastics and low-density foam. The analytical expressions of bending stiffness of a multilayer sandwich structures for variable cross-section panel are determined. The obtained analytical bending stiffness is numerically verified using results of compressive buckling modes on wing panels from a numerical FE program and experimental tests by a series of stiffened structures which are empirically designed. Contrastive results demonstrate that the stiffener configuration tremendously affects the global buckling of the wing panels and the shapes, locations and intervals of the stiffeners which should be adjusted to construct a structure with maximum bending stiffness. Finally, with the use of the bi-directional evolutionary structural optimization method, the optimum design of the wing cross-section was determined by topology optimization method to pursue the best weight/stiffness. Compared with the initial structure, the optimum material layout of the topology structure performs better at reducing stress concentration and improving load carrying capacity of wing panels.

Prediction of fracture risk of a distal femur reconstructed with bone cement: QCSRA, FEA, and in-vitro cadaver tests

Lack of quantitative, biomechanical criteria to predict the risk of fracture for a bone affected by giant cell tumor (GCT) has made the decision for the necessary surgical technique a dilemma. The purpose of this study is to critically assess the usefulness of quantitative computed tomography (QCT) based structural rigidity analysis (QCSRA) and QCT-based finite element analysis (FEA) in predicting the fracture risk for long bones reconstructed with bone cement. QCSRA, QCT-based FEA, and in-vitro mechanical tests on five pairs of cadaveric distal femora were employed to quantitatively assess the compressive failure load of the human femur affected by GCT and reconstructed with bone cement. QCT was utilized to investigate the bone’s structural rigidity properties as well as to generate heterogeneous finite element models using written material mapping codes. In order to validate the QCSRA and QCT-based FEA results, their outcomes were compared with the results of in-vitro mechanical tests on human cadavers. Results of this study demonstrated an acceptable correlation between QCSRA fracture loads and fracture loads found in in-vitro mechanical tests on cadavers (R2 = 0.85). Also, QCSRA procedure is developed in order to estimate the axial stiffness and the maximum bending stiffness of the bone, employing the QCT-scans. It is shown that these two features, describing the structural rigidity, are linked to the experimental fracture loads (R2 = 0.72 for axial stiffness, R2 = 0.79 for maximum bending stiffness). Moreover, a good correlation was found between the fracture loads determined by QCT-based FEA and the experimental in-vitro fracture loads (R2 = 0.92). Results of this study confirm the usefulness of the applications of QCSRA and QCT-based FEA as clinically tools for predicting the failure load of a long bone.

Shear-lag influence on maximum specific bending stiffness and strength of composite I-beam wing spar

Beams with low height and high strength, used in modern unmanned aerial vehicles (UAVs) can be especially problematic considering the efficiency of material usage. This FEM study analyses the influence of shear-lag effect on maximum specific bending stiffness and strength of a composite I-beam wing spar with unidirectional carbon fibre-reinforced plastic flanges. Elliptical load distribution, which is characteristic of airplane wings, was used. For 12 different flanges, width-to-thickness aspect ratios and three different web skin thicknesses, stresses, and end deflections were observed. The flanges cross-section area and beam height were kept the same and constant in all cases. After a certain value of the flanges aspect ratio, the bending stiffness starts to decrease, because the shear-lag effect starts dominating over the still increasing moment of inertia of the cross-section. Maximum specific bending stiffness was reached at much lower aspect ratios of flanges than maximum bending stiffness. Maximum axial stresses start to increase in an almost linear fashion beyond a certain aspect ratio. The highest specific strength was found at relatively low aspect ratios. The influence of web shear stiffness on shear-lag magnitude was also analysed. Changing web stiffness in a selected range showed a negligible influence on shear-lag magnitude for all aspect ratios.

Triangular core as a universal strategy for stiff nanostructures in biology and biologically inspired materials

Recent findings in protein structure prediction have revealed a new class of fibrous proteins called beta-solenoids. In stark resemblance to amyloid structures and prion proteins, these self-assembling peptides feature a triangular cross-sectional structure with non-specific biological significance. Using basic geometric and mechanical arguments and finite element simulations, here we point out that the equilateral triangle, as the most anisotropic regular convex polytope, is an ideal shape that leads to a maximum bending stiffness at minimum material usage. Considering the mechanical stability of the cell-puncture needle of the bacteriophage T4 virus and the extreme efficiency of aggregation in amyloids and prion proteins, possibly due to their capacity of acting as rigid binding and nucleation sites, we propose that the triangular core may reflect a universal biological paradigm for achieving exceptionally stiff nanostructures, overcoming the limitations of the underlying weak molecular interactions such as hydrogen bonds. Stiff nanostructures employing a triangular core geometry may be particularly useful for nanomechanical applications such as puncture and cutting devices where maximum rigidity has to be achieved using a minimal cross-sectional area.

Normalization Process Technique of Composite Foam-filled Sandwich Wind Turbine Blades

In this paper, the resin transfer molding (RTM) and compression molding manufacturing processes were used to fabricate composite wind turbine blades by stacking pieces of glass-fiber fabric, expandable polystyrene (EPS) foam and inserting parts in an interior pressure mold. The blade preform is a composite foam-filled sandwich structure, where the interior is an EPS foam layer while the exterior is coated with a main fiber layer, root reinforcing fiber layer and the parts are inserted. The inserted parts that were investigated were the I-beam, LED, conductor, root connection joint and repair patch. The reinforcing fiber layer was designed to provide maximum bending stiffness in the flexure to resist the stress concentration of the composite wind turbine blade. This research will also be used to develop adhesive bonding repair techniques for life extension of the damaged components in a wind turbine blade. A number of composite wind turbine blade constructions were fabricated to demonstrate the feasibility and applications of the proposed manufacturing method.

A New Model for Maximizing the Bending Stiffness of a Symmetric Three-Ply Paper or Board

Based on the theoretical bending stiffness model for a symmetrical three-ply structure, researchers developed a model that could predict the maximum bending stiffness of a three-ply symmetric structure as a function of density and elastic modulus. The model was tested with experimental data either generated in the authors’ laboratory or reported in the literature. The model accurately predicted the maximum bending stiffness based on the middle-layer share of basis weight. Model results indicate that it is possible to increase the middle-layer share without loss of bending stiffness, leading to reduced costs and lower virgin fiber requirements. Results show that the model is a useful and rapid tool for papermakers to predict the maximum bending stiffness of either coated papers or three-ply boards for a given furnish. Furthermore, the model has potential to be developed further to predict maximum bending stiffness for boards with more than three plies.

Global analysis of secondary bifurcation of an elastic bar

In a three dimensional framework of finite deformation configurations, this paper investigates the secondary bifurcation of a uniform, isotropic and linearly elastic bar under compression in a large range of parameters. The governing differential equations and finite dimensional equations of this problem are discussed. It is found that, for a bar with two ends hinged, usually many secondary bifurcation points appear on the primary branches which correspond to the maximum bending stiffness. Results are shown on parameter charts. Secondary modes and branches are also calculated with numerical methods.

繊維複合材料平板の最大曲げ剛性設計

An optimization procedure is proposed for design of fibrous composite plates having angle-ply for maximum bending stiffness. Strain energy was taken as the objective function, while the lamination parameters by which a general laminate construction can be considered were taken as the design variables. Deformation analysis was carried out using the Rayleigh-Ritz method for bending under any loading conditions. Numerical results are presented for graphite/epoxy symmetric laminates, resting on simple supports and subjected to either distributed or concentrated loading. As a result, it was found that the application of the present optimization procedure yielded an optimum design of a laminate construction, and the effects of the loading condition and aspect ratio became clear.

A Note on the Optimum Distribution of Material in a Beam for Stiffness

T HAS BEEN STATED by some authors1 that the maximum stiff­ ness of a beam for a given weight is attained when the strain energy is a minimum or when the stress is constant. It can be shown that this condition does not, generally, result in maximum stiffness; however, it closely approximates the optimum condition in some cases. The optimum distribution of material for torsional stiffness of tubular beams is such that the thickness is constant around any cross section, and, for positions along the axis of the tube, the wall thickness should be proportional to the square root of the torsional moment and inversely proportional to the enclosed area. For maximum bending stiffness, the effective flange thick­ ness should be proportional to the square root of the bending moment or the square root of the product of the moment and the axial length on the beam, depending on whether angular or linear deflections are being considered. For the case of torsion, stiffness is measured by the amount of angular rotation, and, if t is independent of s, is given by:

Tubes of Optimum Bending Stiffness: An Analogy

The torsional stiffness of a thin-walled tube of given perimeter and thickness varies as the square of the enclosed area. The shape giving maximum torsional stiffness is therefore a circle, this being the curve with maximum area for given perimeter. We consider here the nature of the corresponding curve for maximum bending stiffness. The quantity to be made a maximum is now, not the area within the curve, but the second moment for the whole curve about the bending axis. This will give the greatest “moment of inertia” for a tube of uniform thickness. The theory is given in the Appendix and typical forms are shown in Fig. 3. A finite length of base has to be assumed; otherwise the curve reduces to a single straight line normal to the axis.