Stability of explicit subcycling time integration with linear interpolation for first-order finite element semidiscretizations

1998 ◽  
Vol 151 (3-4) ◽  
pp. 311-324 ◽  
Author(s):  
Patrick Smolinski ◽  
Yi-Sheng Wu
1991 ◽  
Vol 3 (1) ◽  
pp. 235-253 ◽  
Author(s):  
L. D. Philipp ◽  
Q. H. Nguyen ◽  
D. D. Derkacht ◽  
D. J. Lynch ◽  
A. Mahmood

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohammad H. Jabbari ◽  
Parviz Ghadimi ◽  
Ali Masoudi ◽  
Mohammad R. Baradaran

Using one-dimensional Beji & Nadaoka extended Boussinesq equation, a numerical study of solitary waves over submerged breakwaters has been conducted. Two different obstacles of rectangular as well as circular geometries over the seabed inside a channel have been considered in view of solitary waves passing by. Since these bars possess sharp vertical edges, they cannot directly be modeled by Boussinesq equations. Thus, sharply sloped lines over a short span have replaced the vertical sides, and the interactions of waves including reflection, transmission, and dispersion over the seabed with circular and rectangular shapes during the propagation have been investigated. In this numerical simulation, finite element scheme has been used for spatial discretization. Linear elements along with linear interpolation functions have been utilized for velocity components and the water surface elevation. For time integration, a fourth-order Adams-Bashforth-Moulton predictor-corrector method has been applied. Results indicate that neglecting the vertical edges and ignoring the vortex shedding would have minimal effect on the propagating waves and reflected waves with weak nonlinearity.


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.


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