Variation Of Bending Stiffness Research Articles

Joints mechanical characteristics of prefabricated subway station considering bending stiffness difference

In prefabricated subway stations, the presence of joints leads to an uneven circumferential distribution of structural stiffness. However, there has been limited research focusing on the variability in bending stiffness of joints so far. Therefore, this paper proposes a theoretical framework to study deformation characteristics considering the differences in bending stiffness. This study aim to analyze the deformation characteristics of prefabricated structures, with a specific focus on the impact of variations in bending stiffness on the overall structural behavior. The research scope includes the calculation methods for the bending stiffness of joints, predicting maximum settlement of the top plate, and analyzing the influence of key parameters such as joint positions, geometric shapes, and dimensions, overburden density γ, lateral earth pressure coefficient λ, overburden thickness hf, and concrete density ρ on the joint bending stiffness. Results validate the reliability of the proposed method for calculating joint bending stiffness and demonstrate the key factors contributing to differences in bending stiffness.

Multi-point impact behavior and the relationship between CAI strength and DBIP of PMI foam sandwich structures

Sandwich structures are vulnerable to multi-point impacts, and such impacts can result in a reduction in residual strength even catastrophic accident. Therefore, the multi-point impact behaviors of PMI foam sandwich structure are investigated and studied using experimental and numerical coupled methods. Three impact energy levels and five Distances Between Impact Positions (DBIP) are considered in details, and representative impact characteristics are compared to reveal the association between Compression After Impact (CAI) strength and DBIP. Results indicate that the interference between the multi-point impact events has a dominant effect on CAI strength when DBIP is small, and the variation in bending stiffness induced by the boundary effect is the dominant factor affecting CAI strength when DBIP ranges from 20 mm to 60 mm. In addition, matrix damage represents the primary damage mode in multi-point impact, and the calculated ratio of energy absorbed by the top face sheet and honeycomb core, in relation to the total absorbed energy, serves as a clear indicator of the damage severity experienced by both components. This work is enlightening for the structural design of impact-resistant composites.

Programmable and Variable‐Stiffness Robotic Skins for Pneumatic Actuation

Pneumatic soft actuators possess relatively fast response, inherent high flexibility, and achieve extraordinary shape morphing under large deformations. Conventionally, the entire body of soft pneumatic robots needs to be designed for specific applications. Herein, a soft pneumatic actuator design with structured fabrics as actuator skins, which has high bending stiffness variation that can accomplish multiple tasks and different deformation modes in a single body, is proposed. By adjusting the structured skin, the developed soft actuator can be tailored to achieve various deformations. It is experimentally shown that the bending stiffness of the actuator can be adjusted from 108 to 5654 N m−1. The blocking force of the actuator in bending is comparable with that of conventional fabric‐reinforced pneumatic actuators, while the actuator skins are reusable and programmable. In application, the actuators are used to construct a bionic soft gripper with multiple degrees of freedom. By switching between three grasping modes, the gripper successfully fulfills a series of tasks including lifting weights up to 1 kg and grasping objects ranging from a grain of grape to a large iron basin. This work opens up an avenue for designing structured skins for pneumatic robots with programmable deformation modes and versatile functions.

Modeling of a two-degree-of-freedom fiber-reinforced soft pneumatic actuator

AbstractFiber winding reinforcement is widely used in soft robotic manipulators actuated by pressurized fluids. However, the specific effect of each type of winding on the bending motion of a tubular soft robotics manipulator with three chambers has not been explored widely. We present the development of precise finite element (FE) simulations and investigate the effect of helical fiber winding parameters on the bending motion of a two-degree-of-freedom manipulator with three internal chambers. We first show the development of an FE simulation that optimizes convergence and computational time and precisely matches the behavior of soft robots in practice. Compared to single-chamber robots, simulating three-chamber designs is more challenging due to the complex geometry. We then apply our FE model to simulate all the parameter variations. We show that for helical winding with a constant pitch, the closer the center of a chamber is to the intersection of the windings, the lower the bending stiffness of the chamber is. To minimize bending stiffness variation in different bending directions, the optimal angle between the center of the first chamber and the intersection of the two helical windings are 0° and 12°. Reducing the pitch of the helical windings or using other types of windings (i.e., ring winding or six helical winding) reduces the stiffness variation across different bending directions. The FE simulations are compared with experiments showing that the model can capture complex bending behaviors of the manipulator, even though the estimation tends to be less accurate at higher bending angles.

Inverse design and additive manufacturing of shape-morphing structures based on functionally graded composites

Shape-morphing structures possess the ability to change their shapes from one state to another, and therefore, offer great potential for a broad range of applications. A typical paradigm of morphing is transforming from an initial two-dimensional (2D) flat configuration into a three-dimensional (3D) target structure. One popular fabrication method for these structures involves programming cuts in specific locations of a thin sheet material (i.e. kirigami), forming a desired 3D shape upon application of external mechanical load. By adopting the non-linear beam equation, an inverse design strategy has been proposed to determine the 2D cutting patterns required to achieve an axisymmetric 3D target shape. Specifically, tailoring the localised variation of bending stiffness is the key requirement. In this paper, a novel inverse design strategy is proposed by modifying the bending stiffness via introducing distributed modulus in functionally graded composites (FGCs). To fabricate the FGC-based shape-morphing structures, we use a multi-material 3D printer to print graded composites with voxel-like building blocks. The longitudinal modulus of each cross-sectional slice can be controlled through the rule of mixtures according to the micro-mechanics model, hence matching the required modulus distribution along the elastic strip. Following the proposed framework, a diverse range of structures is obtained with different Gaussian curvatures in both numerical simulations and experiments. A very good agreement is achieved between the measured shapes of morphed structures and the targets. In addition, the compressive rigidity and specific energy absorption during compression of FGC-based hemi-ellipsoidal morphing structures with various aspect ratios were also examined numerically and validated against experiments. By conducting systematical numerical simulations, we also demonstrate the multifunctionality of the modulus-graded shape-morphing composites. For example, they are capable of blending the distinct advantages of two different materials, i.e. one with high thermal (but low electrical) conductivity, and the other is the other way around, to achieve combined effective properties in a single structure made by FGCs. This new inverse design framework provides an opportunity to create shape-morphing structures by utilising modulus-graded composite materials, which can be employed in a variety of applications involving multi-physical environments. Furthermore, this framework underscores the versatility of the approach, enabling precise control over material properties at a local level.

Design and analysis of a Contact-Aided Leaf Hinge (CALH) with continuous variable stiffness

This paper introduces a design method to realize the transition of variable stiffness from discrete to continuous through contact interaction. Based on this, a Contact-Aided Leaf Hinge (CALH) with passive variable stiffness is proposed, which consists of a flexible segment and a rigid part. As the deformation increases, the flexible segment contacts with the rigid part continuously, resulting in the variation of bending stiffness. The configuration, modeling and deformation process are illustrated in detail. Several examples of conic contact regions are analyzed through the chained pseudo-rigid-body model (CPRBM) and finite element analysis (FEA). Besides, physical prototypes are manufactured and experimental tests are performed to verify the feasibility of the design. Finally, some applications, parasitic motion and coupling effects are discussed. By further designing the dimensions and contact surface, the CALH can satisfy various requirements.

Laboratory measurements of the effects of interlaminar slip on vortex-induced vibrations of the unbonded umbilical

Laboratory tests were performed to investigate the influence of interlaminar slip on the vortex-induced vibrations (VIV) of the unbonded umbilicals. Two types of umbilical models with the same size were fabricated by using an acrylic tube enclosing seven-core spiral copper cable, in which the unbonded umbilical contains relative slip between its tube and cable, and the interior structure of the bonded one was fixed as a contrast. Both umbilical models under a same top tension were excited respectively in a flume with current velocity varying from 0.1 m/s to 0.7 m/s. Fiber Bragg Grating (FBG) sensors were employed to measure the VIV response in both cross-flow (CF) and in-line (IL) directions. Experimental results confirm that the unbonded umbilical is more susceptive to the reduced velocity in terms of displacement, frequency and trajectory, which is attributed to the nonlinear variation in bending stiffness resulting from the relative slip. Furthermore, the onset of lock-in region for the unbonded model occurs at a lower velocity than that for the bonded model, but with a similar width of lock-in region. Although VIV displacement in the mode transition is relatively small, the interlaminar slip still works due to the influence of its high frequency.

Effect of Rotor Geometry on Bending Stiffness Variation

Bending stiffness variation (BSV) is a common problem causing vibration in large rotating machinery. BSV describes lateral bending stiffness and its variation as a function of the rotational angle. It has been observed that BSV causes excitation exactly twice per revolution, which leads to vibration problems, especially at half critical speed. BSV is caused by rotor geometry errors if the material is assumed to be homogeneous and linearly elastic. Therefore, the study investigated BSV with harmonic roundness components, which are commonly used in industry to describe the geometry of a rotor. Hence, the results are easily applicable in the industry. The research was conducted primarily by analytical means, but also static simulations and numeric calculations were used. The results clearly showed that when the effect of single harmonic roundness components in rotor cross-sections were observed, only the second component could produce BSV. However, when component pairs were studied, they produced BSV also without the second component. If the second component was included, the profile produced BSV the most aggressively. A generated arbitrary roundness profile, including components 3–50 with random phases and amplitudes, indicated that BSV occurs always twice per revolution despite different components in the profile. The results improve the possibilities of eliminating excessive BSV in the industry, when certain components and component pairs can be avoided.

Shell-Forming Stimulus-Active Hydrogel Composite Membranes: Concept and Modeling.

The swelling of active hydrogels combined with passive layers allows the design of shell-forming structures. A shell-like structure offers different properties than a flat structure, e.g., variations in bending stiffness across different directions. A drastic increase of the bending stiffness is favorable e.g., in rollable/flexible displays: in their unrolled form, they have to be stiff enough to resist bending due to dead weight. At the same time, they have to be flexible enough to be rolled-up. This can be achieved by shell-forming. In the current modeling and simulation work, we present a basic concept of combined active–passive composites and demonstrate how they form shells. As the example material class, we use hydrogels with isotropic swelling capabilities. We demonstrate how to model the combined mechanical behavior with the Temperature-Expansion-Model. Afterwards, we show numerical results obtained by Finite Element simulations. We conclude that the envisioned structure has a great potential for obtaining soft rollable sheets that can be stiffened by intrinsic activation.

Influence of Tooth Bending Stiffness Variation on Spur Gear Meshing

Influence of Tooth Bending Stiffness Variation on Spur Gear Meshing

Research on characteristic function for cable inverse analysis based on dynamic stiffness theory and its application

Parameter identification of cables in the operation period is a significant issue related to the state of serviceability and safety evaluation of cables. A generalized characteristic function is established based on the dynamic stiffness theory to identify cable parameters in the study. The characteristic function exhibits an analytical form. The function relatively fits actual engineering cables due to comprehensively considering cable bending stiffness, sag, inclination, etc., and thus it is a relatively accurate inverse-analysis model of cable parameters. The variation of bending stiffness and cable force with different geometric parameters and the influence of geometric parameters on the identification accuracy of the two parameters are investigated based on numerical analysis. And a parameter identification method based on the H-I ridges of inverse-analysis characteristic function is proposed. The proposed method identifies cable parameters using the multi-order frequencies of cables simultaneously, and the order of modal frequencies and the fundamental or lower-order frequency are not required in the application of the proposed method. Finally, the results of tension tests on two real cables with lengths of 20 m and 168 m verify the applicability of the inverse-analysis characteristic function and the parameter identification method proposed in the study.

Generalized spiral torsion spring energetic model

Torsional springs or coil springs are used to apply a torque and obtain a rotation of its shaft. They are usually manufactured with flat steel. Recommended maximum operating stresses in static applications are given as a percentage of tensile strength. These values could be consulted in an experimental table with an appropriate stress correction factor. An energetic model for torsional spiral springs is presented in this work. First of all a parametric study analyzes different variables which affect the spring performance. Main variables analyzed have been the length of the spring strip, strip thickness and height, housing diameter, shaft diameter, variation of bending stiffness and curvature along the length of the spring strip. Afterward, the analysis of energy storage in coil spring is carried out. There are two causes why energy storage is less than the maximum of the model developed. The first one is energy wasted in coil contact and in spring blocking and unblocking process. The second cause is that the torque applied to spin is less than the one which reached the yield strength in spring section. Both of them are quantified and incorporated in the model. At the end the energetic model is used to calculate the torque–angle turned curve, framework deformation and the spring-framework contact force. Model developed is validated with test on a monolithic fiberglass spiral spring.

Helical wire stress analysis of unbonded flexible riser under irregular response

A helical wire is a critical component of an unbonded flexible riser prone to fatigue failure. The helical wire has been the focus of much research work in recent years because of the complex multilayer construction of the flexible riser. The present study establishes an analytical model for the axisymmetric and bending analyses of an unbonded flexible riser. The interlayer contact under axisymmetric loads in this model is modeled by setting radial dummy springs between adjacent layers. The contact pressure is constant during the bending response and applied to determine the slipping friction force per unit helical wire. The model tracks the axial stress around the angular position at each time step to calculate the axial force gradient, then compares the axial force gradient with the slipping friction force to judge the helical wire slipping region, which would be applied to determine the bending stiffness for the next time step. The proposed model is verified against the experimental data in the literature. The bending moment–curvature relationship under irregular response is also qualitatively discussed. The stress at the critical point of the helical wire is investigated based on the model by considering the local flexure. The results indicate that the present model can well simulate the bending stiffness variation during irregular response, which has significant effect on the stress of helical wire.

Application of linear buckling sensitivity analysis to economic design of cylindrical steel silos composed of corrugated sheets and columns

Abstract The paper deals with global stability of steel cylindrical silos composed of corrugated walls and vertical columns with loads imposed by a bulk solid following Eurocode 1. The optimum silo design with respect to the steel weight was based on a sensitivity analysis method. The changes of silo column profiles at each design step were performed by means of influence lines for the buckling load factor due to the unit column bending stiffness variation. The corrugated walls were simulated as an equivalent orthotropic shell and vertical thin-walled columns as beam elements. The results were compared with the Eurocode 3 approach and verified by FE results of linear buckling and non-linear analyses with geometric non-linearity carried out with the commercial finite element code ABAQUS for a 3D shell model of a perfect silo. The proposed procedure allowed for a rational silo design with an economic material use. Some recommendations for the silo optimum design were elaborated.

Experimental Study of Dynamic Bending Stiffness of ACSR Overhead Conductors

Aeolian vibrations of transmission-line conductors may cause fretting fatigue failure at or near the location of clamped devices. At these locations, the bending stiffness variation of the conductor has a large influence on its deformed shape and, hence, on its fatigue mechanics. Variable bending stiffness models could be integrated in nonlinear finite-element programs to obtain better mechanical behavior predictions. However, there is very little data available in the literature to validate such numerical models. The objective of this paper is to present experimental data for the deformed shape of two types of ACSR conductors undergoing vibrations. The tests were performed on a 5.83-m test bench for various tensions, displacement amplitudes, and frequencies. The displacement amplitude was measured at the vibration anti-node and at five locations near the square-faced bushing. The results suggest a large stiffness variation near the bushing. This experimental study provides valuable data to compare with a numerical model of a vibrating conductor that includes variable bending stiffness.

Time History Modeling of Vibrations on Overhead Conductors With Variable Bending Stiffness

Although bending stiffness of cables is small, it has a large influence on the deformed shape near constraints. A practical application where it is important is for the prediction of the deflection curve of transmission-line conductors during aeolian vibrations. These vortex-induced vibrations may cause fretting fatigue failure at or near the location of clamped devices. The objective of this paper is to model with a nonlinear time history finite-element analysis the deformed shape of conductors during aeolian vibrations using available bending stiffness models. The deformed shape obtained numerically is compared to laboratory measurements available in the literature. It was found that theoretical bending stiffness models can be used to predict the deformed shape of cables near the clamps. However, the results obtained with variable bending stiffness are not significantly more accurate than those for a constant bending stiffness equal to half of the maximum theoretical bending stiffness. In general, the variation of bending stiffness found experimentally is less important than the prediction of nonlinear models. The dynamic nonlinear numerical method presented here remains a powerful tool for the prediction of the deformed shape of vibrating conductors.

Chemisorption-Induced Resonance Frequency Shift of a Microcantilever

The autonomy and property of atoms/molecules adsorbed on the surface of a microcantilever can be probed by measuring its resonance frequency shift due to adsorption. The resonance frequency change of a cantilever induced by chemisorption is theoretically studied. Oxygen chemisorbed on the Si(100) surface is taken as a representative example. We demonstrate that the resonant response of the cantilever is mainly determined by the chemisorption-induced bending stiffness variation, which depends on the bond configurations formed by the adsorbed atoms and substrate atoms. This study is helpful for optimal design of microcantilever-based sensors for various applications.

Adsorption-induced resonance frequency shift in Timoshenko microbeams

This paper adopts a sandwich-beam model with two surface layers of finite thickness to investigate the resonance frequency shift of moderately thick microbeams due to atom/molecule adsorption in presence of surface effects. Timoshenko beam theory is employed to take into account the effects of shear deformation and rotary inertia. It is found that, in addition to surface effects, the resonance frequency could perceptively depend on adsorption-induced mass and bending stiffness variation of the microbeam which in turn depend on the adatom category and the substrate material. Adsorption and surface effects on the first three modes of vibrations are also studied, and comparisons are made with the results obtained on the basis of Euler–Bernoulli beam theory. This study is of interest for the optimal design of micro- and nanobeam-based sensors.

Variation in the mechanical properties of flight feathers of the blackcapSylvia atricapillain relation to migration

Migration causes temporal and energetic constraints during plumage development, which can compromise feather structure and function. In turn, given the importance of a good quality of flight feathers in migratory movements, selection may have favoured the synthesis of feathers with better mechanical properties than expected from a feather production constrained by migration necessities. However, no study has assessed whether migratory behaviour affects the relationship between the mechanical properties of feathers and their structural characteristics. We analysed bending stiffness (a feather mechanical property which is relevant to birds’ flight), rachis width and mass (two main determinants of variation in bending stiffness) of wing and tail feathers in migratory and sedentary blackcapsSylvia atricapilla. Migratory blackcaps produced feathers with a narrower rachis in both wing and tail, but their feathers were not significantly lighter; in addition, bending stiffness was higher in migratory blackcaps than in sedentary blackcaps. Such unexpected result for bending stiffness remained when we statistically controlled for individual variation in rachis width and feather mass, which suggests the existence of specific mechanisms that help migratory blackcaps to improve the mechanical behaviour of their feathers under migration constraints.

Optimization of Variable-Stiffness Panels for Maximum Buckling Load Using Lamination Parameters

With the large-scale adoption of advanced fiber placement technology in industry, it has become possible to fully exploit the anisotropy of composite materials through the use of fiber steering. By steering the composite fibers in curvilinear paths, spatial variation of stiffness can be induced resulting in beneficial load and stiffness distribution patterns. One especially relevant area in which fiber steering has proved its effectiveness is in improving buckling loads of composite panels. Previous research used predefined forms of fiber angle variations and the coefficients of these analytic expressions were used as design variables. Alternatively, the local ply angles were used as design variables directly. In this paper, a framework is developed to treat the most general approach that considers the largest possible design space. The use of lamination parameters efficiently defines stiffness variation over a structural domain with the minimum number of variables. A conservative reciprocal approximation scheme is introduced. The inverse buckling factor is expanded linearly in terms of the in-plane stiffness and in terms of the inverse bending stiffness. The new approximation scheme is convex in lamination parameter space. Numerical results demonstrate improvements in excess of 100% in buckling loads of variable-stiffness panels compared to the optimum constant stiffness designs. Buckling load improvements are attributed primarily to in-plane load redistribution, which is confirmed both by the prebuckling stress distribution as well as by comparing the performance of designs optimized with variation of both in-plane and bending stiffness to those optimized with only bending stiffness variation. A tradeoff study between in-plane stiffness and buckling performance is also presented and shows the benefits of variable-stiffness design in enlarging the design possibilities of composite panels.