Bending Stiffness Distribution Research Articles

Design optimization of a snowboard performing an ollie

The ollie, a fundamental manoeuver in snowboarding, serves as a basis for various tricks requiring high altitude and extended airtime. The maximum ollie height depends on the snowboard’s geometry and structural characteristics. In this study, the influence of these properties is investigated with a flexible multibody dynamics simulation, where the snowboard is modeled by geometrically non-linear finite elements, snow contact is considered by a penetration depth and velocity proportional normal force and ollie motion is achieved by imposing measured loads to the bindings. To maximize the height, a genetic optimization procedure is presented, which yields substantial improvements. Optimizing the camber line and the bending stiffness distribution yields enhanced performance. Less damping as well as lighter boards lead to higher jumps, no noteworthy correlation between axial stiffness and damping distribution and jump height was found, and the strain energy stored in the board during takeoff is a useful indicator for estimating ollie heights. Nevertheless, further investigations should take a more advanced and realistic rider interaction into account.

An approach for identification of bridge bending stiffness distribution using improved Gaussian peak function

Bridge damage and bending stiffness deterioration can lead to a decrease in the bearing capacity of a bridge, posing significant safety concerns. To ensure the safe operation of bridges, it is crucial to accurately identify bending stiffness deterioration and assess the bridge performance. The bridge influence line (IL), which reflects the deterioration of bending stiffness, was widely used in the assessment of bending stiffness deterioration. Existing IL-based methods mostly assume a uniform reduction in bending stiffness for identification. In reality, the deterioration of bridge bending stiffness is far more complex, which causes difficulty in accurately identifying the bending stiffness distribution using the uniform reduction model. This paper proposes a novel method for identifying bridge stiffness distribution using an improved Gaussian peak function model. The improved model incorporates additional parameters, allowing for considering a wider range of stiffness variation and thus addressing the limitations of traditional models. The parameters of the improved Gaussian peak function model are estimated by minimizing the residual between the predicted deflection influence line (DIL) and the actual DIL using the Levenberg-Marquardt (LM) algorithm. This approach enables the accurate identification of bending stiffness distribution without baseline information. Numerical simulation and laboratory experiment are used to verify the effectiveness of the proposed method in identifying bridge bending stiffness distribution. A comparison between the identified and actual bending stiffness distribution curves under various forms of damage assesses the applicability of the proposed method.

Kirigami-based inverse design for 3D surfaces formed by mechanically guided method

The mechanically guided assembly method utilizes the compressive buckling behavior of thin-film structures to transform two-dimensional (2D) precursors into three-dimensional (3D) structures. Previous research has shown that by inverse designing thickness and width distributions in 2D precursors, various 3D surfaces with target geometries can be accurately assembled. However, the variation in thickness poses significant challenges for the fabrication of the 2D precursor, especially on a small scale. In this paper, we propose a Kirigami-based inverse design framework that utilizes pre-specified incision patterns as critical parameters to control the bending stiffness distribution of 2D precursors. This enables the fabrication of target 3D structures with constant thickness, which greatly simplifies the production of 2D precursors. By studying the deformation characteristics of beam models during pure bending, we have established an analytical relationship between incision patterns and bending stiffness distribution. To validate the effectiveness of our inverse design theory, we conducted a series of simulations and experiments on 3D structures, yielding favorable comparison results. Moreover, guided by this inverse design theory, we have developed a microneedle structure through conceptual design, demonstrating the capability of Kirigami patterns in the inverse design of complex 3D structures, and highlighting the potential application of our method in the biomedical field.

Detection, localisation and quantification of stiffness loss in a bridge using indirect drive-by measurements

Drive-by health monitoring uses the measurements gathered on a vehicle while traversing a bridge to assess its condition. To date, drive-by monitoring has been mostly proposed as a pre-screening tool to detect damage under favourable conditions of low vehicle speeds and low road roughness. A major shortcoming is the potential degradation of the road profile, which is often indistinguishable from bridge damage. In this paper, the influence of vehicle dynamics, speed and road roughness is removed by applying cross-entropy optimisation to the response of individual crossings of the vehicle at different speeds. The proposed model-based algorithm locates and quantifies damage while remaining unaffected by changes in the road profile. In addition to providing the distribution of bending stiffness in the underlying bridge, the algorithm isolates the bridge deflections accurately making the reconstruction of the actual road profile on the bridge possible. The latter can be a useful feature for ensuring traffic safety as well as preventing a major dynamic amplification of the bridge response. The algorithm is successfully tested for a quarter-car driving on a 15 m simply supported beam bridge model at highway speeds of 30 m/s over a class ‘B’ road with a roughness coefficient of 64 × 10−6 m3/cycle.

Distributed bending stiffness estimation of bridges using adaptive inverse unit load method

Bending stiffness has important applications in bridge damage detection, model updating, and load bearing capacity assessment. However, accurately predicting bending stiffness is a challenging task. In this paper, a two-phase methodology named the adaptive inverse unit load method (AIULM) is developed for distributed reconstruction of bending stiffness from onboard deflection data. In the first phase, the bending stiffness is roughly estimated by uniform discretization. A global stiffness smoothing method is applied to eliminate nonphysical discontinuities of stiffness at interelement boundaries. Then, the smoothed results are applied in the second phase to define a node optimization function to adaptively adjust the element node distribution. An accurate bending stiffness distribution is provided by performing AIULM analysis again based on optimized discretization. Since only real bridge deflection influence lines (DILs) are utilized in the formulation, the AIULM provides a C0-continuous stiffness distribution without any information on internal force. The adaptive optimization of the node distribution allows the practical application of AIULM to different bridges, especially old bridges. Numerical and experimental validation cases, which demonstrate the excellent predictive capability and practical usefulness of the AIULM, have been performed.

Experimental study of moment redistribution before yielding in precast prestressed concrete beams made continuous

AbstractThe bending stiffness distribution of beams composed of simple‐span precast prestressed beams, which are made continuous by deck reinforcement at intermediate supports, is not constant. As the structure undergoes loading, the deck slab at the intermediate support cracks earlier than the prestressed span soffit and due to that the bending stiffness distribution changes along the beam length. The effect of nonconstant bending stiffness distribution on the moment redistribution of the structure before the yielding is studied experimentally and analytically. Two continuous beams with spans of 10 m + 10 m were manufactured, loaded to failure, and studied. It was concluded that the studied structure undergoes considerable moment redistribution before yielding although it would be designed for zero redistribution at the ultimate limit state. If this elastic redistribution is neglected in the structural analysis, the service limit state sagging moment at midspan may end up on the unconservative side. Elastic redistribution can be predicted quite accurately with the help of nonlinear analysis or roughly with simplified idealization as proposed in this article.

Analysis of Track Bending Stiffness and Loading Distribution Effect in Rail Support by Application of Bending Reinforcement Methods

Railway track is a linearly inhomogeneous object that consists of geometrical and elastic discontinuities such as bridges, transition zones, rail joints and crossings. The zones are subjected to the development of local instabilities due to quicker deterioration than the other tracks. Until now, there have been no efficient approaches that could fully exclude the problem of accelerated differential settlements in the problem zones. Many structural countermeasures are directed at controlling the sleeper/ballast loading with the help of fastenings/under-sleeper pad elasticities, sleeper forms and additional bending stiffness reinforcements. However, the efficiency of the methods is difficult to compare. The current paper presents a systematic approach in which the loading distribution effect in the rail support by application of two bending reinforcement methods is compared: auxiliary rail and under-sleeper beam. The study considers only the static effects to reach a clear understanding the influence of the main factors. The track equivalent bending stiffness criterion is proposed for comparing reinforcement solutions. The analysis shows that the activation of the bending stiffness of the reinforcement beams depends on the relative ratio of the rail fastenings stiffness and track support stiffness under sleepers (or under the under-sleeper beam). The comparison demonstrates that conventional auxiliary rail reinforcement solutions are ineffective due to their weak bending because of the high elasticity of fastening clips and the main rail fastenings. The share of an auxiliary rail is maximally 20% in the track bending stiffness and cannot be significantly improved by additional rails. The under-sleeper beam-based reinforcement solutions show noticeably higher efficiency. The highest effect can be achieved by the activation of the horizontal shear interaction between the under-sleeper beam and the rail. The additional track bending stiffness of the under-sleeper-based solutions is about 3.5 times more of the rail one and could be potentially increased to 6–10 times.

Effect of non-uniform stiffness distribution on the dynamics of inverted plates in a uniform flow

The stability of the inverted flexible plate with non-uniform stiffness distribution in a free stream is studied by numerical simulation and mathematical theory. In our study, the bending stiffness distribution is expressed as the function of the leading edge's bending stiffness K∗ and the polynomial of the plate's coordinate. Based on the former theoretical work on the stability of inverted plates with uniform stiffness distribution, we derive the upper limit value of K∗ at which the zero-deflection equilibrium loses its stability for the plate with non-uniform stiffness distribution. The critical K∗ derived from the mathematical theory agrees well with that obtained from the numerical simulation. An effective bending stiffness is defined, which can be used to unify the regimes of the motion modes between uniform plates and non-uniform plates. Moreover, three orders of mass ratio [O(10−2), O(10−1), and O(1)] are investigated, and the underlying mechanism for large amplitude flapping is clarified for the inverted plate with different mass ratios. An appropriate bending stiffness distribution can greatly improve the deformation of the plate. The findings shed some light on the energy harvesting of the inverted plate.

Wrapping of a vesicle nanoparticle with variable bending stiffness by membrane

Cellular uptake of nanoparticle (NP) is an important biological process involving mechanically and structurally heterogeneous environments, such as biophysical heterogeneity of single extracellular vesicles and biomechanical heterogeneity of small viral capsids. Despite of these heterogeneous environments, poor understanding of membrane interacting with vesicle NP of non-uniform mechanical properties still exists. To address this issue, combining the continuum Canham–Helfrich theory of membrane and the stochastic Markov method on state transition, we establish a theoretical model of the wrapping of a NP with any variable bending stiffness. As NPs are hypothesized with two typical types of non-uniform bending stiffness distributions (Gaussian-like and piecewise), through both minimum energy and stochastic dynamic approaches, it is identified that the membrane tends to encapsulate the NP with a sealing near soft region of NP. Because complete wrapping of NP with a sealing near its stiff region requires large elastic deformation of membrane. In addition, during cellular uptake, rotation phenomenon of the NP with variable bending stiffness is found, which is reminiscent of previous observations on homogeneous NP as reported in literature. These predictions are verified by relevant Monte Carlo simulations. Our findings are of interest to not only the fundamental understanding of cellular uptake but also the applications in the design of nanocarriers for drug delivery.

Non-centrosymmetric solid core photonic crystal fiber for suppressing parasitic twist in fiber sensing coil

During the fabrication of fiber sensing coils, the parasitic twist of fibers would lead to the undesired elliptical birefringence in the fiber, which is the main cause of magnetically induced bias error for fiber optic gyroscope(FOG). For the purpose of suppressing the parasitic twist in the fiber coil, a polarization-maintaining solid core photonic crystal fiber (PCF) with non-centrosymmetric distribution of bending stiffness is proposed and investigated. The proposed PCF would bend towards a particular direction under the external forces, resulting in the consistency of birefringent axes arrangement, thus suppressing the nonreciprocal errors induced by both radial and axial components of the magentic field simultaneously. Dependence study of the fiber bending stiffness distribution on several key parameters is provided. The optical properties are also explored and compared with the previously studied PCF. Fiber coils fabricated with the proposed PCF are promising in reducing the magnetical sensitivity of FOG, thus making it possible for FOG to get rid of the thick magnetic shield, which is significant for the miniaturization of FOG.

Effect of body stiffness distribution on larval fish-like efficient undulatory swimming.

Energy-efficient propulsion is a critical design target for robotic swimmers. Although previous studies have pointed out the importance of nonuniform body bending stiffness distribution (k) in improving the undulatory swimming efficiency of adult fish-like robots in the inertial flow regime, whether such an elastic mechanism is beneficial in the intermediate flow regime remains elusive. Hence, we develop a class of untethered soft milliswimmers consisting of a magnetic composite head and a passive elastic body with different k These robots realize larval zebrafish-like undulatory swimming at the same scale. Investigations reveal that uniform k and high swimming frequency (60 to 100 Hz) are favorable to improve their efficiency. A shape memory polymer-based milliswimmer with tunable k on the fly confirms such findings. Such acquired knowledge can guide the design of energy-efficient leading edge-driven soft undulatory milliswimmers for future environmental and biomedical applications in the same flow regime.

Assessment of the bending stiffness distribution in large 2D RC plates and slabs like-structures based on spatially distributed strain data for structural health monitoring

The study proposes a new method to assess the bending stiffness distribution in plate- and slab- like reinforced concrete (RC) structures based on spatially distributed strain data. Specifically, the study aims to provide an adequate structural interpretation of the readings, which infers the structural health. It is especially relevant for RC structures, that are designed to be cracked during their service life. To meet this goal the study correlates damage induced by cracks and curvature computed from strains to analyze 2D RC structures characterised by directional strains, and moment redistribution. The study also considered the installation possibilities and the limited and thus averaged strain data. To exclusively correlate changes in curvatures, by means of curvature index factors, and residual bending stiffness distribution, the study proposed an iterative identification algorithm. The paper demonstrates the effectiveness of the algorithm by numerical simulations of strain measurements and considers the various limitations of the adopted strain measurements along large 2D RC structures. It is presented that the procedure succeeds in localising the damaged regions and provides less accurate, but still contributive, assessment of their severity. Thus, the proposed method can support engineers in decision making regarding the structural health of the structure.

Batch fabrication process of biomimetic wing with high flexibility of stiffness design for flapping-wing micro aerial vehicles

A lamination-based batch-fabrication process of biomimetic wing for flapping-wing micro aerial vehicles is presented. The key benefits of this process are:•One of the advantages of the process is high productivity; eight wings were successfully fabricated simultaneously in our experiment.•The wing fabricated with the reported process is made of soft polyimide and partially reinforced by a titanium layer. This configuration enables the flexible design of the bending stiffness distribution on the wing, which is the key specification for generating lift force.•The reinforcing material can be replaced with other metals or heat-resistant polymers, and the number of layers and layer thicknesses are also variable. This indicates that the reported process can be customized considerably to suit individual needs.

Experimental study and theoretical analysis of glulam-concrete composite beams connected with ductile shear connectors

Ductile shear connectors are often applied in timber-concrete composite beams. The relative interface slip of such kind of composite beams will affect the mechanical performance of the composite beams and result in structural nonlinearity. Gamma method which adopts effective bending stiffness to reflect semi-rigid connection is recommended in Eurocode 5. The effective bending stiffness is irrelevant to external loads and calculation points of the composite beam. However, actual bending stiffness distribution along the beam is variable due to that shear connectors are subjected to different shear force. In order to verify the accuracy of gamma method, four-point bending tests of a total of three glulam-concrete composite beams with lag screw connectors and one pure glulam beam were conducted in this article. The failure mode, bearing capacity, and load–deflection relationship were investigated in the experiment. Meanwhile, push-out tests of composite beams were also conducted for determination of the force–displacement relationship of ductile shear connectors. Then, numerical simulation using beam-truss model was established for investigation on the mechanism of composite beams. Finally, theoretical analysis of composite beams considering the effect of interface slip was also presented. Comparing results from gamma method with the presented method, it is shown that both methods can calculate deflection at serviceability limit state with high precision. However, non-uniform distribution of actual bending stiffness cannot be reflected by gamma method.

Bending strength and failure of single-layer and double-layer sandwich structure with graded truss core

The influence of the gradient of a sandwich structure with graded truss core on bending behavior are investigated in this paper. The single-layer and double-layer composite sandwich structures are formed by alternating width of core bars and stiffening plate. Three different types of sandwich structure with graded truss core are designed and manufactured. The gradient of a sandwich structure is characterized by introducing a gradient ratio g. A continuum damage model based on Hashin criteria is developed to predict the strength of these structures. The results from three-point bending tests are used to verify the FE model. Good agreements can be achieved between experimental and numerical results. The numerical model is subsequently used to investigate the influence of gradient ratio g on bending strength, stiffness and damage distribution of these sandwich structures. The results indicate that the gradient ratio g can prominently influence the failure mode of the double-layer sandwich structure. An appropriate gradient ratio g of truss core can promote the sandwich structure with higher strength and stiffness. The stiffening plate can significantly enhance the strength and stiffness of the double-layer sandwich structure.

Rayleigh-Ritz method-based analysis of dry coupled horizontal-torsional-warping vibration of rectelliptic open-section containership bare-hulls

The coupled horizontal-torsional-warping vibration of a thin-walled open-section 7800 TEU container ship bare-hull, modelled as a non-uniform girder, is analysed by the efficient energy-based Rayleigh-Ritz method, in order to generate the dry asymmetric vibration frequencies. Since the centre of gravity is within the hull and the shear centre is below the keel, the horizontal and torsional modes of vibration are highly coupled. An open section is also prone to warping. In a novel attempt, the bare-hull geometry is generated mathematically, using section-wise closed-form semi super-ellipses (Lame’s curves). The main dimensions, weight distributions, and fineness ratios are preserved, and closed-form expressions of sectional properties become available in the process. The hull has arbitrarily (non-mathematically) varying mass, bending stiffness, warping stiffness, and shear stiffness distributions along the length. The non-uniform beam modeshape in horizontal/torsional vibration is assumed to be a weighted sum of the uniform beam horizontal/torsional modeshapes. Several benchmark cases of simpler geometry have been analysed first, for both torsion-warping vibration, and coupled horizontal-torsional-warping vibration. Pontoon approximation of the containership has been analysed and validated. Subsequently, the coupled dry vibration frequencies are obtained for the open deck non-uniform girder, and compared with published results.

Springing Responses Analysis and Segmented Model Test on a 550,000 Dead Weight Tonnage Ore Carrier

In hydroelastic model tests, segmented ship models are usually used to make sure that the model scale and the full size ship satisfy the similarity law of structural natural frequency and distribution of ship bending stiffness. However, springing barely occurs in those tests because the natural frequency of segmented ship models is too high for the regular waves required to be generated in a tank. In order to investigate the springing effect, three sets of backbone of variable cross section are adopted in the test. One set of backbones satisfies the similarity law of natural frequency, and two extra sets of low stiffness backbones are used so that the springing effect can appear and be measured. Experimental results show that the springing occurs when the wave encounter frequency coincides with the first elastic natural frequency of the ship, or with half or one-third of it. A good agreement has also been obtained between the experimental and the numerical results by a three-dimensional (3D) hydroelasticity method. Based on these results, the contribution of the springing responses to the fatigue damage of the ship is estimated and analyzed.

Self-sensing and quantitative assessment of prestressed concrete structures based on distributed long-gauge fiber Bragg grating sensors

Quantitative assessment of strengthened concrete structures using self-sensing fiber-reinforced polymer sheets is presented in this article. First, strain distribution along the height of a structure induced by pre-tension force (initiate state) is theoretically estimated. Second, the procedure for parameter estimation of prestressed fiber-reinforced polymer–strengthened structures under external load using measured and pre-tension force–induced strain is established, and nonlinearity caused by random cracks is considered in the method. Both local parameters (neutral axis position, bending stiffness distribution, strain distribution along the cross section, etc.) and global parameter (deflection) of structures can be accurately estimated by measured long-gauge strain responses. Finally, both prestressed fiber–reinforced polymer–strengthened and reinforced concrete beams installed with long-gauge fiber Bragg grating sensors have been experimentally investigated to prove the effectiveness of this method. Experimental results indicate that the estimated neutral axis height and local bending stiffness can reflect initiation of random cracks and deterioration process of structures under increasing external load. Meanwhile, the estimated strain along the beam height and deflection at mid-span agree well with the measured ones, which further verifies the accuracy of the estimated neutral axis position affected by randomly appeared cracks. Hence, the method can be utilized for assessment and maintenance of fiber-reinforced polymer–strengthened structures.

Nonlinear parameter identification of timber-concrete composite beams using long-gauge fiber optic sensors

A novel method for nonlinear parameter identification of partially composite beams using long-gauge strain responses is proposed in this paper. Firstly, theoretical analysis shows that neutral axis position of timber beam and concrete slab can be estimated by measured long-gauge strain and material properties. Then, distribution of curvature, bending stiffness, deflection and interface slip can be determined by identified neutral axis position. Secondly, timber-concrete composite beams connected by ductile connectors with different degree of composite action are designed to verify the presented method. Experimental results show that the estimated parameters (neutral axis position, bending stiffness and interface slip) can clearly reflect and quantify the deterioration process of partially composite beams. Meanwhile, both global and local responses can be predicted by long-gauge strain sensors. The predicted responses (deflection at mid-span and strain along the beam height) agree well with the test results when partially composite action is considered, the errors will be unacceptable without considering partially composite action. Hence, the presented method can be utilized for better understanding of mechanical properties of partially composite beams and performance assessment of existing composite structures.

Application and Optimization of Stiffness Abruption Structures for Pressure Sensors with High Sensitivity and Anti-Overload Ability.

The influence of diaphragm bending stiffness distribution on the stress concentration characteristics of a pressure sensing chip had been analyzed and discussed systematically. According to the analysis, a novel peninsula-island-based diaphragm structure was presented and applied to two differenet diaphragm shapes as sensing chips for pressure sensors. By well-designed bending stiffness distribution of the diaphragm, the elastic potential energy induced by diaphragm deformation was concentrated above the gap position, which remarkably increased the sensitivity of the sensing chip. An optimization method and the distribution pattern of the peninsula-island based diaphragm structure were also discussed. Two kinds of sensing chips combined with the peninsula-island structures distributing along the side edge and diagonal directions of rectangular diaphragm were fabricated and analyzed. By bonding the sensing chips with anti-overload glass bases, these two sensing chips were demonstrated by testing to achieve not only high sensitivity, but also good anti-overload ability. The experimental results showed that the proposed structures had the potential to measure ultra-low absolute pressures with high sensitivity and good anti-overload ability in an atmospheric environment.