Effect Of Initial Curvature Research Articles

Engineering static non-reciprocity in mechanical metamaterials

Non-reciprocity has recently been achieved in static fields by mechanical metamaterial that combines large non-linearity and asymmetric geometry. Novel devices are then designed to obtain one-way mechanical functionalities. Non-linearity is the fundamental part that regulates static non-reciprocity, but the influential path remains difficult to quantify. In this work, we employ the geometrically exact beam model to obtain the nonlinear deformation profile of mechanical metamaterials, and build nonlinear equations that govern the deformation behavior. A new two-step method is proposed to solve the nonlinear governing equations, which avoids Jacobi matrix singularity. We establish an accurate model that predicts the non-reciprocal mechanical behavior and verify its accuracy by finite element method. To gain further insight into non-linearity’s influences on mechanical non-reciprocity, we investigate mechanical metamaterials with curved beams, explore the effects of initial curvature on non-reciprocity, and engineer their non-reciprocity to obtain different non-reciprocal force–displacement responses. Our work offers beneficial vehicles to realize static direction-selective functionalities, contributing to shock absorption, vibration damping, and mechanical energy manipulation.

Design of High-Performance Triple-axis Cross Pivots

Abstract Cross-axis flexural pivots are increasingly implemented in mechanical systems due to their high precision and wide range of motion. However, designing high-performance pivots in terms of low axis drift, low rotational stiffness, and low values of maximum stress remains a challenging task. In fact, these features often behave antagonistically to each other. In this paper, the design of a novel family of high-performance cross-axis pivots is presented. The compliant joints are obtained by the composition of two crossing flexible elements with initially curved axis, and of one auxiliary flexure with straight axis. Two different arrangements, that depend on the constraints layout, are proposed. Chained beam constraint model and non-linear finite element analysis are implemented for the analysis of the kinetostatic response of the pivots. The effects of initial curvature and orientation of the flexures on axis drift, stiffness, and maximum stress, are investigated and reported in the form of design maps. A global performance index, that embodies the above-mentioned features and captures the overall kinetostatic behavior of the pivot is introduced. The design maps and the global index serve as key tools for the design procedure, giving insight into the antagonistic issue and leading to the determination of the best trade-off solutions that meet the application requirements. An experimental campaign is conducted to compare the performance improvement of triple-axis pivots with respect to a benchmark double-axis joint, and to validate the design method.

Design and testing of high-accuracy curved cross-axis flexural pivots with cable-driven actuation

The cross-axis flexural pivot proved to be a valid tool for replacing the traditional revolute joints in a variety of mechanical systems. However, the rotation axis drift limits its implementation in high-precision applications. This investigation presents a procedure for designing high-accuracy flexural pivots actuated by cable-driven systems. Kinetostatic simulations, resorting to finite element analysis and to chained beam constraint model, have been carried out to analyze the relations among the input and output parameters of the design. The effects of initial curvature on position accuracy, maximum stress, and actuation force have been investigated and several design maps have been generated to support the procedure in each step. The procedure has been applied to the design of high-accuracy pivots and an experimental campaign has been carried out to compare accuracy and kinetostatic performance of the curved configurations to the straight one.

Dynamic stability of slightly curved tensioned pipe conveying pressurized hot two phase fluid resting on non uniform foundation

The dynamic stability of slightly curved tensioned pipes conveying pressurized two phase fluid, under thermal loadings are investigated in this paper. Furthermore, these pipes are resting on nonuniform elastic foundations. The equation of motion of the system is derived using the extended Hamilton’s principle for open dynamic systems and considering the Euler–Bernoulli theory for slender beams. The free vibration and the effects of two phase fluid flow, geometric imperfections, thermal, tension and pressure on the pipe system resting on nonuniform foundations are investigated numerically. Three different boundary conditions (BC) are considered, namely simply-simply (SS) supported, simply-clamped (SC) supported and clamped-clamped (CC) supported. The numerical method of Finite Element was used on the partial differential equation. This method is used to accurately predict steady state natural frequency responses of a dynamical system through several numerical investigations. It was found that the stability of slightly curved pipes conveying two phase flow are significantly affected by the boundary condition. It is shown that the initial curvature term increases the critical velocities for all the nine modes considered, the increase is significant in the first and second critical velocities compared to the other modes. Initial curvature effect is more pronounced in simple supported ends. Further-more the influence of the fluid velocity, temperature, pressure and axial tension is analysed; the results show that the vibration frequency decreases when the fluid velocity, temperature, and pressure increase or the axial tension decreases, and the critical fluid velocity decreases when the temperature and pressure increase or the axial tension decreases. For the pipe on nonuniform foundation, an increased stiffness leads to an increased in the first critical velocity for all the BC. However, the pattern of the increment depends on the attachment parameter, initial curvature, and the vapour quality. Some of these results are completely absent in pipes conveying single flows.

Effect of initial curvature on soliton pair and breather pair in holographic medium

Formation of soliton pair in the holographic medium has been discussed in this paper. We have also shown, distinct types of coupled propagation in presence of finite initial curvature, including formation of rhythmic breather pair.

Free vibration analysis of curved lattice sandwich beams

In this paper, the effects of initial curvature and lattice core shape on the bending vibration of sandwich beams are investigated. The three-dimensional (3D) sandwich beam is simulated by combining a two-dimensional (2D) cross-sectional analysis with a one-dimensional (1D) nonlinear beam analysis. The sandwich beam is composed of two identical isotropic faces covering a lattice core. Four different lattice core structures are used to take into account the effect of core unit cell shape on the dynamic properties of the sandwich beam. The nonlinear governing equations of the sandwich beam are Discretized using a time-space scheme. Numerical results show that the lattice unit cell shape affects both in-plane and out of plane stiffness values and hence changes the dynamic behavior of the beam. Furthermore, it is observed that by changing the density ratio of the beam, modes veer away from each other at a specific value of density ratio for specific unit cell types. Moreover, the initial curvature of the beam is shown to affect the dynamics of the beam especially lower modes. Finally, it is obtained that the dynamics of the beam is different when it is initially curved or curved due to an applied end follower moment.

Finite beam element with 22 DOF for curved composite box girders considering torsion, distortion, and biaxial slip

Experimental and numerical study on the mechanical performance of curved steel–concrete composite box girders is reported in this research. First, this research establishes a theoretical model for curved composite girders with 11° of freedoms (DOFs) for each node. The DOFs include the longitudinal displacement, transverse displacement, deflection, torsion angle, warping angle, and interface biaxial slip between steel and concrete. Based on the virtual work theorem, the equilibrium function, the stiffness matrix, the node displacement matrix and the external load matrix are proposed for the curved composite girders using the FE spatial discretization. Second, the authors conduct an experimental program on three large-scale curved composite girders with various interface shear connectors and central angles. The comparison between the developed finite beam element, the elaborate FE model and the test results indicates the developed finite beam element has an adequate level of accuracy in predicting the deflection, the torsion angle and the axial strain distribution of test specimens. Third, based on the developed finite beam element model, the effect of initial curvature, number of diaphragms, and the interface connector stiffness on the curved composite girder is examined. The simulation results showed that the initial curvature significantly contributes to the displacement and stress of composite girders. Applying more diaphragms can notably reduce the distortion angle and distortion displacement. The interface shear connector stiffness has a significant influence on the curved composite girder. With the increasing shear connector stiffness, the displacement and stress of curved composite girders decrease notably. Based on the parametric analyses, it is recommended to limit the central angle of simply supported composite girder below 45°, to apply an adequate number of diaphragms, and to design curved composite girders as fully shear connection specimens.

A higher order geometrically nonlinear Cosserat‐shell model with initial curvature effects

AbstractUsing a geometrically motivated 8‐parameter ansatz through the thickness, we reduce a three‐dimensional shell‐like geometrically nonlinear Cosserat material to a fully two‐dimensional shell model. Curvature effects are fully taken into account. For elastic isotropic Cosserat materials, the integration through the thickness can be performed analytically and a generalized plane stress condition allows for a closed‐form expression of the thickness stretch and the nonsymmetric shift of the midsurface in bending. We obtain an explicit form of the elastic strain energy density for Cosserat shells, including terms up to order O(h5) in the shell thickness h. This energy density is expressed as a quadratic function of the nonlinear elastic shell strain tensor and the bending‐curvature tensor, with coefficients depending on the initial curvature of the shell.

Effect of initial curvature in uniform flexures on position accuracy

Position accuracy is a prerequisite for compliant mechanisms, especially in micro-scale applications. Generally, this feature depends on the flexures ability to imitate the revolute joints of the pseudo-rigid body model. In case of flexible elements, the center of the relative rotation varies its position during the deflections, affecting the position accuracy. In this paper, the role played by the initial curvature is investigated, in case of uniform primitive flexures. Analytical expressions are derived to evaluate the shift of the rotation axis with respect to the flexure centroid. An example shows the performance of four flexures with different curvatures, evaluated by comparing the rotation axis shift and the position error.

Probability analysis of double layer barrel vaults considering the effect of initial curvature and length imperfections simultaneously

Load carrying capacity of reticulated space structures majorly depend on the structures’ imperfections. Imperfections in initial curvature, length, and residual stress of members are all innately random and can affect the load-bearing capacity of the members and consequently that of the structure. The present study investigated the effect of the probability distribution of initial curvature imperfection and lack of fit of members on the load-bearing capacity of double-layer barrel vault space structures with different types of support. A random number was first assigned to each member using gamma and normal distributions for initial curvature and member length imperfections, respectively. Afterwards, the ultimate bearing capacity and the collapse behavior of the structure was determined using nonlinear finite-element analysis in OpenSees software and finally structures reliability was acquired. The results demonstrate that the collapse behavior of doable-layer barrel vault space structures is sensitive to the random distribution of initial imperfections.

Stability Analysis of Columns with Imperfection

In this paper, geometrically exact fully intrinsic equations and variational asymptotic beam sections are used to study the buckling and postbuckling of a column under self-weight. Initial curvature effects both generalized one-dimensional beam equations and the cross-sectional stiffness properties. The effects of initial curvature have been studied on buckling and postbuckling in this paper. This problem is a valuable test case for the utility of the fully intrinsic equations and variational asymptotic beam sections.

Isogeometric analysis for the dynamic problem of curved structures including warping effects

ABSTRACTCurved beam structures have been used in many civil, mechanical, aircraft, and aerospace constructions. The analysis is mainly based on solid and plate models due to the fact that traditional curved beam elements do not include nonuniform warping effects, especially in the dynamic analysis. In this article, independent warping parameters have been taken into account and the initial curvature effect is considered. Curved beam’s behavior becomes more complex, even for dead loading, due to the coupling between axial force, bending moments, and torque that curvature produces. In addition to these, the Isogeometric tools (b-splines or NURBS), either integrated in the Finite Element Method or in a Boundary Element–based Method called Analog Equation Method, have been employed in this contribution for the dynamic analysis of horizontally curved beams of open or closed (box-shaped) cross sections. Free vibration characteristics and responses of the stress resultants and displacements to moving loading have been studied.

Stability analysis of an embedded single-walled carbon nanotube with small initial curvature based on nonlocal theory

ABSTRACTMany experimental observations have shown that most nanostructures, such as carbon nanotubes, are often characterized by a certain degree of waviness along their axial direction. This geometrical imperfection has profound effects on the mechanical behavior of carbon nanotubes. In the present work, stability of a slightly curved carbon nanotube under lateral loading is investigated based on Eringen's nonlocal elasticity theory. Euler Bernoulli and Timoshenko beam theories are employed to obtain equilibrium equations. Winkler-Pasternak elastic foundation is used to approximate the effect of matrix. Effects of initial curvature, nonlocal parameter, beam length, and elastic foundation parameters on initiation of critical conditions are investigated.

Effects of initial curvature on coiled tubing buckling behavior and axial load transfer in a horizontal well

This paper builds an analytical model to describe the comprehensive buckling behavior of coiled tubing (CT) with initial curvature in a horizontal well. The new buckling equation and contact force considering the effect of initial curvature is built on the basis of beam-column theory. With the new contact force expression, the work done by lateral friction can be obtained, thus the total potential energy of CT with initial curvature can be calculated. By use of the principle of virtual work and energy conservation, the critical sinusoidal and helical buckling load can be obtained. Moreover, the effect of initial curvature on axial load transfer is also calculated by a new axial load equation. The calculation results indicate that initial curvature has a strong influence on buckling loads and a CT with initial curvature is less efficient for axial load transfer compared to a straight CT. To verify the proposed model, the results of this paper are compared to experimental results, which support the proposed solutions.

Spatial Finite Element Analysis for Dynamic Response of Curved Thin-Walled Box Girder Bridges

According to the flexural and torsional characteristics of curved thin-walled box girder with the effect of initial curvature, 7 basic displacements of curved box girder are determined. And then the strain-displacement calculation correlations were established. Under the curvilinear coordinate system, a three-noded curved girder finite element which has 7 degrees of freedom per node for the vibration characteristic and dynamic response analysis of curved box girder is constructed. The shape functions are used as the interpolation functions of variable curvature and variable height to accommodate to the variation of curvature and section height. A MATLAB numerical analysis program has been implemented.

Effect of initial tool-plate curvature on snap-through load of unsymmetric laminated cross-ply bistable composites

In this study, the effect of the initial curvature of a tool plate on the snap-through load of square cross-ply bistable composites was analyzed. The snap-through load is a function of the cured curvature and residual moment. In the curing process, both these physical quantities are affected by the initial tool-plate curvature. As a result, the snap-through load can also be changed by adjusting the initial tool-plate curvature. Then, for evaluating its effect on the snap-through load, a snap-through process was simulated by minimizing the total potential energy of the bistable composites through the Rayleigh–Ritz approximation method. The simulation results show that the snap-through load changes linearly with the initial tool-plate curvature. The simulation results are compared with those obtained experimentally and by a finite element analysis (FEA) in order to verify the pre-identified effect of the initial tool-plate curvature.

Investigations on Vibration and Buckling of Carbon Nanotubes with Small Initial Curvature by Nonlocal Elasticity Theory

Many experimental observations have shown that in most nanostructures such as nanocomposites, carbon nanotubes (CNTs) are often characterized by a certain degree of waviness along their axial dimension. This geometrical imperfection has a profound effect on the mechanical behavior of CNTs. In the present work, the effects of initial curvature, shear deformation and influence of surrounding medium that are modeled as Winkler-Pasternak elastic foundation on behavior of slightly curved carbon nanotubes are investigated. It is shown that the initial curvature has an important role on mechanical behavior of curved carbon nanotubes. To capture the small size effects, nonlocal elasticity theory is implemented. Timoshenko beam theory (TBT) is used to model the behavior of CNTs and the governing equations are solved analytically. The effects of initial height and shear deformation on vibration frequencies and buckling loads are studied. It is found that these effects considerably contribute to mechanical behavior of nanostructures and cannot be ignored.

Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery

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

Elastic Stability of Circular Arches with the Open Thin-walled Monosym-metric Section Considering the Prebuckling Deformation

The effect of prebuckling in-plane deformations on the elastic flexural-torsional buckling of arches is studied in this paper. Nonlinear strain-displacement relations considering initial curvature effects and higher order prebuckling de-formation terms with curvature in deriving process are substituted into the second variation of the total potential to obtain the buckling energy equation. The analytical solutions for the flexural-torsional buckling moment of arches in uniform bending, containing the effects of the prebuckling deformation, are proposed. Also, the influence of the higher order prebuckling deformation terms with the curvature effects is investigated according to the ratio of the minor axis flexural stiffness to the major axis flexural stiffness.

Nonlinear dynamics of curved IPMC actuators undergoing electrically driven large deformations

The nonlinear dynamics of curved ionic polymer–metal composite (IPMC) actuators having large tip displacement and periodical jumping locomotion was investigated experimentally. Through snap-through phenomena, the actuator generates much larger tip displacement and shows abrupt jumps in the transitions of upswings and downswings with low input energy. Two curved IPMC cantilever actuators having two different constant curvatures of 0.01 mm−1 and 0.02 mm−1 were fabricated through thermal treatment from flat IPMCs, simultaneously with no residual stress. As-fabricated IPMC actuators were tested to evaluate the effect of initial curvature under static and dynamic electrical excitations. Unlike the case of the flat IPMC actuator, asymmetric characteristics in step and harmonic responses were investigated in the curved IPMC actuators. Also, at relatively higher input voltage, snap-through phenomena were observed with much larger transverse displacements and periodical abrupt jumps of the instant speed. This revealed jumping movements between the multiple equilibrium points. The results show that optimum curvatures for better bending performance of curved cantilever IPMCs exist and that this snap-through mechanism could be applied to IPMC actuators by considering their soft and flexible properties and the geometric structures.