Handbook of Mechanical Stability in Engineering

Perelmuter, Anatoly V.; Slivker, Vladimir

doi:10.1142/8372

Cited by 13 publications

(12 citation statements)

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“…The inclination angle of the truss members is set to α = tan( w 0 /L) = 45°, giving a joint rotation of 90°. This value is below the stability limit 19 .…”

Section: Methodsmentioning

confidence: 81%

Integrated Design and Simulation of Tunable, Multi-State Structures Fabricated Monolithically with Multi-Material 3D Printing

Chen

Mueller

Shea

2017

Sci Rep

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Multi-material 3D printing has created new opportunities for fabricating deployable structures. We design reversible, deployable structures that are fabricated flat, have defined load bearing capacity, and multiple, predictable activated geometries. These structures are designed with a hierarchical framework where the proposed bistable actuator serves as the base building block. The actuator is designed to maximise its stroke length, with the expansion ratio approaching one when serially connected. The activation force of the actuator is parameterised through its joint material and joint length. Simulation and experimental results show that the bistability triggering force can be tuned between 0.5 and 5.0 N. Incorporating this bistable actuator, the first group of hierarchical designs demonstrate the deployment of space frame structures with a tetrahedron module consisting of three active edges, each containing four serially connected actuators. The second group shows the design of flat structures that assume either positive or negative Gaussian curvature once activated. By flipping the initial configuration of the unit actuators, structures such as a dome and an enclosure are demonstrated. A modified Dynamic Relaxation method is used to simulate all possible geometries of the hierarchical structures. Measured geometries differ by less than 5% compared to simulation results.

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“…The inclination angle of the truss members is set to α = tan( w 0 /L) = 45°, giving a joint rotation of 90°. This value is below the stability limit 19 .…”

Section: Methodsmentioning

confidence: 81%

Integrated Design and Simulation of Tunable, Multi-State Structures Fabricated Monolithically with Multi-Material 3D Printing

Chen

Mueller

Shea

2017

Sci Rep

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“…The second model, where the force was replaced with a mass known as the Willis-Stokes problem, was first formulated by Willis in 1849 [16] and subsequently solved analytically by Stokes [17]. By neglecting the beam's mass, Willis presented the fourth order partial differential equation, which represented the moving mass problem [22]. It was these early works that paved the way for more complex models of the train-bridge interaction and these eventually provided the design provisions that are available in the bridge design codes.…”

Section: Modelling Railway Bridge Dynamic Responsementioning

confidence: 99%

Dynamic Amplification of Railway Bridges under Varying Wagon Pass Frequencies

Rahman,

Imam,

Hajializadeh

2024

Infrastructures

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Train configurations give rise to a primary wagon pass forcing frequency and their multiples. When any one of these frequencies coincides with the natural frequency of vibration of the bridge, a resonant response can occur. This condition can amplify the dynamic response of the bridge, leading to increased levels of displacement, stresses and acceleration. Increased stress levels on critical bridge structural elements increases the rate at which fatigue damage accumulates. Increased bridge acceleration levels can affect passenger comfort, noise levels, and can also compromise train safety. For older bridges the effects of fatigue, and being able to predict the remaining life, has become a primary concern for bridge engineers. Better understanding of the sensitivity of fatigue damage to the characteristics of the passing train will lead to more accurate remaining life predictions and can also help to identify optimal train speeds for a given train–bridge configuration. In this paper, a mathematical model which enables the dynamic response of railway bridges to be assessed for different train configurations is presented. The model is based on the well established closed from solution of the Euler–Bernoulli Beam (EBB) model, for a series of moving loads, using the inverse Laplace–Carson transform. In this work the methodology is adapted to allow different train configurations to be easily implemented into the formulation in a generalised form. A generalised equation, which captures the primary wagon pass frequency for any train configuration, is developed and verified by presenting the results of the bridge response in the frequency domain. The model, and the accuracy of the equation for predicting the primary wagon pass frequency, is verified using independently obtained measured field train–bridge response data. The main emphasis of this work is to enable the practicing engineer, railway operators and bridge asset owners, to easily and efficiently make an initial assessment of dynamic amplification, and the optimal train speeds, for a given bridge and train configuration. This is visually presented in this work using a Campbell diagram, which shows dynamic amplification and compares this with those calculated based on the design code, across a range of train speeds. The diagram is able to identify train speeds at which a resonance response can occur, and the wagon pass frequency, or its multiples, which are causing the increased dynamic amplification. The model is implemented in Matlab and demonstrated by analysing a range of short- to medium-single span simply supported plate girder railway bridges, typically found on the UK railway network, using the standard BS-5400 train configurations. The model does not consider the effects of the train mass and suspension system as this would require a non-closed form numerical solution of the problem which is not practical for the purposes of an initial assessment of the train–bridge interaction problem.

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“…On account of the fact that the PWCPE structure is a system with multiple degrees of freedom, the minimum of total potential energy L ( θ , Δ) can be obtained with the aid of the Hessian matrix. If the matrix is positive definite, then the equilibrium mode of the structure does not intend to deviate to an adjacent equilibrium state—the Lagrange-Dirichlet theorem [ 20 ]. However, if the matrix is either negative definite or is not a sign definite, the equilibrium mode of the structure opts to deviate to an adjacent equilibrium mode—the first Lyapunov theorem [ 20 ].…”

Section: Prediction Of Fabric Wrinkling Based On An Instability Anmentioning

confidence: 99%

“…If the matrix is positive definite, then the equilibrium mode of the structure does not intend to deviate to an adjacent equilibrium state—the Lagrange-Dirichlet theorem [ 20 ]. However, if the matrix is either negative definite or is not a sign definite, the equilibrium mode of the structure opts to deviate to an adjacent equilibrium mode—the first Lyapunov theorem [ 20 ]. Hence, it is inferred that the instant at which the Hessian matrix of the structure changes its sign from positive definite to negative definite, may be considered as the onset of equilibrium mode deviation.…”

Section: Prediction Of Fabric Wrinkling Based On An Instability Anmentioning

confidence: 99%

A Mesoscopic Analytical Model to Predict the Onset of Wrinkling in Plain Woven Preforms under Bias Extension Shear Deformation

et al. 2017

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A mesoscopic analytical model of wrinkling of Plain-Woven Composite Preforms (PWCPs) under the bias extension test is presented, based on a new instability analysis. The analysis is aimed to facilitate a better understanding of the nature of wrinkle formation in woven fabrics caused by large in-plane shear, while it accounts for the effect of fabric and process parameters on the onset of wrinkling. To this end, the mechanism of wrinkle formation in PWCPs in mesoscale is simplified and an equivalent structure composed of bars and different types of springs is proposed, mimicking the behavior of a representative PWCP element at the post-locking state. The parameters of this equivalent structure are derived based on geometric and mechanical characteristics of the PWCP. The principle of minimum total potential energy is employed to formluate the model, and experimental validation is carried out to reveal the effectiveness of the derived wrinkling prediction equation.

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Handbook of Mechanical Stability in Engineering

Cited by 13 publications

References 0 publications

Integrated Design and Simulation of Tunable, Multi-State Structures Fabricated Monolithically with Multi-Material 3D Printing

Integrated Design and Simulation of Tunable, Multi-State Structures Fabricated Monolithically with Multi-Material 3D Printing

Dynamic Amplification of Railway Bridges under Varying Wagon Pass Frequencies

A Mesoscopic Analytical Model to Predict the Onset of Wrinkling in Plain Woven Preforms under Bias Extension Shear Deformation

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