scholarly journals Multiple shooting method in stability analysis of non-prismatic multi-segment columns

2013 ◽  
Vol 12 (4) ◽  
pp. 225-232
Author(s):  
Ryszard Hołubowski ◽  
Andrzej Merena
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Shooting Method ◽  
High Efficiency ◽  
Variable Coefficients ◽  
Multiple Shooting ◽  
System Of Differential Equations ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Multiple Shooting Method

The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.

Energy absorption structures design of civil aircraft to improve crashworthiness

2014 ◽  
Vol 118 (1202) ◽  
pp. 383-398 ◽  
Author(s):  
Y. Ren ◽  
J. Xiang
Keyword(s):  
Finite Element Method ◽  
Energy Absorption ◽  
High Efficiency ◽  
Wave Beam ◽  
Sine Wave ◽  
Structure Design ◽  
Failure Model ◽  
The Finite Element Method ◽  
Civil Aircraft ◽  
Aircraft Crashworthiness

AbstractTo improve the crashworthiness of civil aircraft, the design concept of energy absorption structure for civil aircraft is investigated. Two typical different design principles could be identified. The first category includes Helicopter and Light fixed-wing Aircraft (HLA), and Transport, Mid-size and Commuter type Aircraft (TMCA) are classified into the second group. Frame, strut and bottom structure are the three kinds of energy absorption structure for TMCA. The strut layout of conventional civil aircraft is studied and some energy absorption devices are adopted. High efficiency energy absorption structures such as the foam and sine-wave beam are employed as the bottom structure for both of HLA and LMCA. The finite element method is used to analyse and design energy absorption structure in aircraft crashworthiness problem. Results show that the crashworthiness of civil aircraft could be largely improved by using proper strut layout and excellent energy absorption device. The stiffness combination of frame and strut should be considered to get better global aircraft deformation. Supporting platform and failure model are the two core problems of bottom energy absorption structure design. Foam and sine-wave beam under the lifted frame could improve the crashworthiness of civil aircraft.

Nonlinear Analysis of Rotor Systems Including a Bearing Clearance by the Multiple Shooting Method

2001 ◽  
Author(s):  
David Demailly ◽  
Fabrice Thouverez ◽  
Louis Jézéquel ◽  
Jérôme Bonini
Keyword(s):  
Contact Zone ◽  
Response Curve ◽  
Shooting Method ◽  
Simplified Model ◽  
Multiple Shooting ◽  
Frequency Response Curve ◽  
Rotor Systems ◽  
Transition Zones ◽  
Full Contact ◽  
Multiple Shooting Method

Abstract In this paper the Multiple Shooting Method is briefly exposed. This method is then applied to a simplified model of a rotor/stator system including a bearing with clearance under static and unbalance forces. With bearing having a small amount of clearance, it is pointed out that the orbits are no longer circular at certain frequencies as for linear systems. If the clearance is large, the frequency response curve can be divided into three zones: a non-contact zone, a zone with one or several gains and looses of contact per period and a full contact zone. For both cases we emphasize on the evolution of the orbits while passing through transition zones.

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