The Finite Strip-Element Method

Huan-ding, Wang; Zhang, Jinsheng

doi:10.1007/978-4-431-68042-0_21

Cited by 9 publications

(10 citation statements)

References 1 publication

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“…It is thus obvious that [13,14,16,18] both the average acceleration method ( = 1/4, = 1/2) and the constant acceleration method ( = 1/2, = 1) meet the unconditionally stable condition, while the linear acceleration method ( = 1/6, = 1/2) and the central difference method ( = 0, = 1/2) are the conditionally stable method. In general, the accuracy of Newmark method depends on the time interval, the physical parameters of the system, and the loading condition.…”

Section: Algorithmic Damping Of the Newmark Methodmentioning

confidence: 99%

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Study on the Damping of the Discontinuous Deformation Analysis Based on Two‐Block Model

Feng

Jiang

et al. 2017

Mathematical Problems in Engineering

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The deformation and failure of rock mass is a process of energy dissipation; the damping of DDA is a very important and basic problem. The correctness and effectiveness of DDA rely on the appropriate values of the numeric controlling parameters like time interval, spring stiffness, and assumed maximum displacement ratio 2 , and the contact using the penalty method is the core content of DDA. A mechanical model of two contact blocks loaded with the normal force acting along one side of block boundary is established to study the DDA damping problem, which involves the contact and eliminates the influence of some numeric control parameters (e.g., 2 ). Based on the Newmark method and the theory of DDA, the motion equations of two-block system can be established, and then the relationship of some numeric control parameters and the influence of damping can be obtained. The algorithmic damping increases with the increasing of time interval. Given a very small time interval, the spring stiffness may have no obvious effect on the algorithmic damping. The numerical results reveal that the essence of time interval influencing the openclose iteration is the fact that the algorithmic damping is mainly controlled by time interval.

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Section: Algorithmic Damping Of the Newmark Methodmentioning

confidence: 99%

“…A direct time-integration scheme is used for solving (4), in which the acceleration and the velocity within each time step are taken as the following equations of the Newmark assumption [18]:…”

Section: Equations Of Motion Of the Block Systemmentioning

confidence: 99%

Study on the Damping of the Discontinuous Deformation Analysis Based on Two‐Block Model

Feng

Jiang

et al. 2017

Mathematical Problems in Engineering

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“…For the FEM, special treatments and complex modifications are necessary to deal with problems of this kind, such as the arc-length method and co-rotational coordinate approach [27]. However, in the MFEM, particles are assumed to be rigid, and thus rigid body motion of particles can be removed naturally in the process of solving the pure displacement of contact points using the rigid body kinematics.…”

Section: Mdem For Modelling Geometric Nonlinearitymentioning

confidence: 99%

Member Discrete Element Method for Static and Dynamic Responses Analysis of Steel Frames with Semi-Rigid Joints

2017

Applied Sciences

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Featured Application: The MDEM can naturally deal with strong nonlinearity and discontinuity. A unified computational framework is applied for static and dynamic analyses. The method is an effective tool to investigate complex behaviors of steel frames with semi-rigid connections.Abstract: In this paper, a simple and effective numerical approach is presented on the basis of the Member Discrete Element Method (MDEM) to investigate static and dynamic responses of steel frames with semi-rigid joints. In the MDEM, structures are discretized into a set of finite rigid particles. The motion equation of each particle is solved by the central difference method and two adjacent arbitrarily particles are connected by the contact constitutive model. The above characteristics means that the MDEM is able to naturally handle structural geometric nonlinearity and fracture. Meanwhile, the computational framework of static analysis is consistent with that of dynamic analysis, except the determination of damping. A virtual spring element with two particles but without actual mass and length is used to simulate the mechanical behaviors of semi-rigid joints. The spring element is not directly involved in the calculation, but is employed only to modify the stiffness coefficients of contact elements at the semi-rigid connections. Based on the above-mentioned concept, the modified formula of the contact element stiffness with consideration of semi-rigid connections is deduced. The Richard-Abbort four-parameter model and independent hardening model are further introduced accordingly to accurately capture the nonlinearity and hysteresis performance of semi-rigid connections. Finally, the numerical approach proposed is verified by complex behaviors of steel frames with semi-rigid connections such as geometric nonlinearity, snap-through buckling, dynamic responses and fracture. The comparison of static and dynamic responses obtained using the modified MDEM and those of the published studies illustrates that the modified MDEM can simulate the mechanical behaviors of semi-rigid connections simply and directly, and can accurately effectively capture the linear and nonlinear behaviors of semi-rigid connections under static and dynamic loading. Some conclusions, as expected, are drawn that structural bearing capacity under static loading will be overestimated if semi-rigid connections are ignored; when the frequency of dynamic load applied is close to structural fundamental frequency, hysteresis damping of nonlinear semi-rigid connections can cause energy dissipation compared to rigid and linear semi-rigid connections, thus avoiding the occurrence of resonance. Additionally, fracture analysis also indicates that semi-rigid steel frames possess more anti-collapse capacity than that with rigid steel frames.

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“…The procedure to handle the influence of the shear deflection is as follows: the beam deflection is divided into two parts which are caused by bending and shear, respectively, and the two kinds of deflections are subsequently analyzed with the classical beam theory separately, and thereafter, the desired consequence could be obtained through the superposition of the two results. The stiffness and mass matrices of the nth (n = 1, 2) Timoshenko beam element and the deducing process could be found in Wang 16 , Doyle 17 , Pilkey, 18 and Du et al 19 m e is the mass of the element per unit length. I me and J me are the diametral and polar mass moments of inertia of the element per unit length, respectively.…”

Section: Timoshenko Beam Elementmentioning

confidence: 99%

Dynamic modeling of double-helical gear with Timoshenko beam theory and experiment verification

Dong

Wang

Lin

et al. 2016

Advances in Mechanical Engineering

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In the dynamic study of the double-helical gear transmission, the coupling shaft in the middle of the two helical gears is difficult to be handled accurately. In this article, the coupling shaft is treated as the Timoshenko beam elements and is synthesized with the lumped-mass method of the two helical gear pairs. Then, the numerical integration method is used to solve the amplitude-frequency responses and dynamic factors under diverse operating conditions. A gear vibration test rig of closed power circuit is developed for in-depth experimental measurements and model validation. After comparing the theoretical data with the practical results, the following conclusions are drawn: (1) the dynamic model with the Timoshenko beam element is quite appropriate and reliable in the dynamic analysis of double-helical gear transmission and is of great theoretical value in the accurate dynamic research of the double-helical gear transmission. (2) In both theoretical analysis and experimental measurements, the dynamic factors of gear pair diminish with the increase in the input torque and augment with the increase in the input speed. (3) The deviation ratio of the theoretical data and the experimental results decrease with the increase in the input torque, reaching the minimum at the highest input speed.

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The Finite Strip-Element Method

Cited by 9 publications

References 1 publication

Study on the Damping of the Discontinuous Deformation Analysis Based on Two‐Block Model

Study on the Damping of the Discontinuous Deformation Analysis Based on Two‐Block Model

Member Discrete Element Method for Static and Dynamic Responses Analysis of Steel Frames with Semi-Rigid Joints

Dynamic modeling of double-helical gear with Timoshenko beam theory and experiment verification

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