Contemporary time integration model of atomic systems using a dynamic framework of finite element Lagrangian mechanics

2017 ◽  
Vol 193 ◽  
pp. 128-138 ◽  
Author(s):  
Ali Radhi ◽  
Kamran Behdinan
1985 ◽  
Vol 107 (2) ◽  
pp. 118-125 ◽  
Author(s):  
R. E. Harris ◽  
M. A. Dokainish ◽  
D. S. Weaver

A simplified finite element has been developed for modeling the added mass and inertial coupling arising when clusters of cylinders vibrate in a quiescent fluid. The element, which is based on two-dimensional potential flow theory, directly couples two adjacent beam elements representing portions of the adjacent cylindrical structures. The primary advantage of this approach over existing methods is that it does not require the discretization of the surrounding fluid and, therefore, is computationally much more efficient. The fundamental frequencies of tube bundles of various pitch ratios have been predicted using this method and compared with experimental data. Generally, the agreement is good, especially for the bandwidth of fluid coupled natural frequencies. The transient response of tube bundles is also examined using time integration of the finite element model. The beating phenomenon and time decay characteristics exhibited by the experimental bundles under single-tube excitation are well predicted and valuable insights are gained into the measurement of damping in tube bundles.


Author(s):  
Yiliu Weng ◽  
Lipeng Zheng

Engine fan blade-off (FBO) is an extreme event that could well place the flight safety at risk. When it happens, the engine will experience high-velocity impact at first, and then enter into a “high-power” stage due to huge unbalance before coming to a steady state called “windmilling”. The analytical process for FBO can be split into two phases, one for impact simulation and the other for obtaining the FBO load to pylon. Typically, explicit method with fine mesh finite elements is used in the first phase, and implicit method with coarse meshes is adopted in the second one. In most cases, the only connection between these two analyses may be the unbalance level caused by FBO. More structural responses other than the unbalance level due to fan blade impact are actually ignored in the succeeding implicit analysis. Attempts have been made by Boeing, GE and MSC to integrate these two processes by adding some features in MD Nastran. Yet the intermediate binary files created and the restricted input entries make the integration process quite inflexible. This paper introduces an explicit-implicit time integration approach for finite element analysis of engine load following an FBO event. The proposed method attempts to connect the two stages more closely, yet in a more flexible manner. In this approach, the engine structural response under FBO obtained from explicit analysis is transferred to the implicit analysis, together with the unbalance level caused by blade loss. The necessity of the approach is discussed, and sensitivity analysis is conducted to understand the factors that play significant roles in the approach. As the models for explicit and implicit analyses are different in mesh sizes and scales, the authors also develop a tool that can interpolate the load information and further, smooth it to fit calculation. Finally, the approach is tested on a full engine model to show its applicability and advantages over the traditional method for load evaluation of FBO event.


1981 ◽  
Vol 103 (4) ◽  
pp. 657-664 ◽  
Author(s):  
H. U. Akay ◽  
A. Ecer

Analysis of transonic flow through a cascade of airfoils is investigated using the finite element method. Development of a computational grid suitable for complex flow structures and different types of boundary conditions is presented. An efficient pseudo-time integration scheme is developed for the solution of equations. Modeling of the shock and the convergence characteristics of the developed scheme are discussed. Numerical results include a 45 deg staggered cascade of NACA 0012 airfoils with inlet flow Mach number of 0.8 and angles of attack 1, 0, and −1 deg.


2001 ◽  
Vol 123 (3) ◽  
pp. 310-317 ◽  
Author(s):  
Chang-New Chen

An integrated numerical technique for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM), which uses the differential quadrature (DQ) techniques to the finite element discretization, is used to analyze the static and dynamic nonlinear structural mechanics problems. Numerical time integration in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by the accelerated iteration schemes. The global secant relaxation-based accelerated constant stiffness and diagonal stiffness-based predictor-corrector equilibrium iterations which are efficient and reliable are used for the numerical computations. Sample problems are analyzed. Numerical results demonstrate the algorithm.


1985 ◽  
Vol 107 (1) ◽  
pp. 13-18 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton

Capabilities for the analysis of combined viscous and plastic behavior have been added to an existing finite element computer program for two-dimensional elastic-plastic calculations. This program (PAPSTB) has been formulated for elastic-plastic stress and deformation analyses of two-dimensional and axisymmetric structures. It has the ability to model large strains and large deformations of elastic-perfectly plastic, multi-linear hardening, or power-hardening materials. The program is based on incremental plasticity theory with a von Mises yield criterion. Time dependent behavior has been introduced into the PAPSTB program by adding a viscous strain increment to the elastic and plastic strain increment to form the total strain increment. The viscous calculations presently employ a power-law relationship between the viscous strain rate and the effective stress. The finite element code can be easily modified to handle more complex viscous models. The Newmark method for time integration is used, i.e., an input parameter is included which enables the user to vary the time domain approximation between forward (explicit) and backward (implicit) difference. Automatic time stepping is used to provide for stability in the viscous calculations. It is controlled by an input parameter related to the ratio of the current viscous strain increment to the total strain. The viscoplastic capabilities of the PAPSTB program are verified using the axisymmetric problem of an internally pressurized, thick-walled cylinder. The transient viscoplastic case is analyzed to demonstrate that the elastic-perfectly plastic solution is obtained as a steady-state condition is approached. The influence of varying the time integration parameter for transient viscoplastic calculations is demonstrated. In addition, the effects of time step on solution accuracy are investigated by means of the automatic time stepping algorithm in the program. The approach is then applied to a simple forging problem of cylinder upsetting.


Author(s):  
Tamer M. Wasfy ◽  
Michael J. Leamy

A time-accurate explicit time-integration finite element code is used to simulate the dynamic response of tires including tire/pavement and tire/rim frictional contact. Eight-node brick elements, which do not exhibit locking or spurious modes, are used to model the tire’s rubber. Those elements enable use of one element through the thickness for modeling the tire. The bead, tread and ply are modeled using truss or beam elements along the tire circumference and meridian directions with appropriate stiffness and damping properties. The tire wheel is modeled as a rigid cylinder. Normal contact between the tire and the wheel and between the tire and the pavement is modeled using the penalty technique. Friction is modeled using an asperity-based approximate Coulomb friction model.


2019 ◽  
Vol 16 (07) ◽  
pp. 1850106 ◽  
Author(s):  
Prakasha Chigahalli Ramegowda ◽  
Daisuke Ishihara ◽  
Tomoya Niho ◽  
Tomoyoshi Horie

This work presents multiphysics numerical analysis of piezoelectric actuators realized using the finite element method (FEM) and their performances to analyze the structure-electric interaction in three-dimensional (3D) piezoelectric continua. Here, we choose the piezoelectric bimorph actuator without the metal shim and with the metal shim as low-frequency problems and a surface acoustic wave device as a high-frequency problem. More attention is given to low-frequency problems because in our application micro air vehicle’s wings are actuated by piezoelectric bimorph actuators at low frequency. We employed the Newmark’s time integration and the central difference time integration to study the dynamic response of piezoelectric actuators. Monolithic coupling, noniterative partitioned coupling and partitioned iterative coupling schemes are presented. In partitioned iterative coupling schemes, the block Jacobi and the block Gauss–Seidel methods are employed. Resonance characteristics are very important in micro-electro-mechanical system (MEMS) applications. Therefore, using our proposed coupled algorithms, the resonance characteristics of bimorph actuator is analyzed. Comparison of the accuracy and computational efficiency of the proposed numerical finite element coupled algorithms have been carried out for 3D structure–electric interaction problems of a piezoelectric actuator. The numerical results obtained by the proposed algorithms are in good agreement with the theoretical solutions.


Geophysics ◽  
2021 ◽  
pp. 1-43
Author(s):  
Qingtao Sun ◽  
Runren Zhang ◽  
Yunyun Hu

To facilitate the modeling of time-domain controlled-source electromagnetic survey, we propose an efficient finite-element method with weighted Laguerre polynomials, which shows a much lower computational complexity than conventional time integration methods. The proposed method allows sampling the field at arbitrary time steps and also its accuracy is determined by the number of polynomials, instead of the time sampling interval. Analysis is given regarding the optimization of the polynomial number to be used and the criterion of selecting the time scale factor. Two numerical examples in marine and land survey environments are included to demonstrate the superiority of the proposed method over the existing backward Euler time integration method. The proposed method is expected to facilitate the modeling of transient electromagnetic surveys in the geophysical regime.


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