Dynamic Analysis of Flexible Beams Undergoing Overall Motion Employing Linear Strain Measures

AIAA Journal ◽  
2002 ◽  
Vol 40 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Seok Seo ◽  
Hong Hee Yoo
Keyword(s):  
Dynamic Analysis ◽  
Linear Strain ◽  
Flexible Beams ◽  
Strain Measures

Finite Element Formulation for Dynamic Analysis of Planar Flexible Beams With Finite Rotations

1993 ◽  
Author(s):  
M. Iura
Keyword(s):  
Dynamic Analysis ◽  
Strain Energy ◽  
Inertial Frame ◽  
Nonlinear Dynamic Analysis ◽  
Small Strain ◽  
Special Technique ◽  
Element Formulation ◽  
Rotating Frame ◽  
Flexible Beams ◽  
Finite Rotations

Abstract An efficient formulation for dynamic analysis of planar Timoshenko’s beam with finite rotations is presented. Both an inertial frame and a rotating frame are introduced to simplify computational manipulation. The kinetic energy of the system is obtained by using the inertial frame so that it takes a quadratic uncoupled form. The rotating frame together with the small strain assumption is employed to derive the strain energy of the system. Since the exact solutions for linear static theory of Timoshenko’s beam are employed to obtain the strain energy, the present stiffness operator is free from the shear locking without using any special technique. Nonlinear effects appear only in the transformation of displacement components between global and local coordinates. This results in a drastic simplification of nonlinear dynamic analysis of flexible beams. Numerical examples, including a planar mechanism, demonstrate the accuracy and efficiency of the present formulation.

Kinematic and dynamic analysis of compliant mechanisms considering both lateral and axial deformations of flexural beams

2018 ◽  
Vol 233 (3) ◽  
pp. 1007-1020 ◽  
Author(s):  
Yue-Qing Yu ◽  
Peng Zhou ◽  
Qi-Ping Xu
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Dynamic Model ◽  
Compliant Mechanisms ◽  
Dynamic Responses ◽  
Flexible Beams ◽  
Rigid Body Dynamic ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Dynamic

The kinematic and dynamic analysis of compliant mechanisms is investigated comprehensively in this work. Based on the pseudo-rigid-body model, a new PR model is proposed to simulate both the lateral and axial deformations of flexural beams in compliant mechanisms. An optimization for the characteristic factors and a linear regression for the stiffness coefficients of PR pseudo-rigid-body model are presented. Compared with the 1R and 2R pseudo-rigid-body model, the advantage of the PR model is well illustrated. The dynamic modeling of flexible beams in compliant mechanisms is then developed based on the PR pseudo-rigid-body model. The dynamic equation of a PR pseudo-rigid-body dynamic model is derived and the dynamic responses are then presented. The kinematic and dynamic analysis of a compliant slider-crank mechanism is presented by the 1R, 2R and PR model, respectively. The effectiveness of pseudo-rigid-body models and the superiorities of the PR pseudo-rigid-body model and PR pseudo-rigid-body dynamic model are shown clearly in the numerical example.

STATIC AND DYNAMIC ANALYSIS OF FLEXIBLE BEAMS: A CONSISTENT UPDATED LAGRANGIAN FORMULATION

1997 ◽  
Vol 21 (2) ◽  
pp. 141-177 ◽  
Author(s):  
K. Behdinan ◽  
M.C. Stylianou ◽  
B. Tabarrok
Keyword(s):  
Dynamic Analysis ◽  
Large Deflections ◽  
Flexible Beams ◽  
Static And Dynamic Analysis ◽  
Small Strains ◽  
Large Rotations ◽  
Slender Beams ◽  
Updated Lagrangian Formulation ◽  
Updated Lagrangian ◽  
Rotational Method

A study of static and dynamic analysis of slender beams undergoing large deflections is undertaken here. the Euler-Bernoulli hypothesis is employed and the beam deforms with large rotations but small strains. Initially the static analysis, using the consistent updated Lagrangian techniques which accounts for full non-linearity of the beam is undertaken and is then extended to dynamic analysis. Several examples illustrating the implementation and the performance of the proposed formulation are included and a comparison with results obtained by the co-rotational method is provided.

Co-rotational dynamic analysis of flexible beams

1998 ◽  
Vol 154 (3-4) ◽  
pp. 151-161 ◽  
Author(s):  
K. Behdinan ◽  
M.C. Stylianou ◽  
B. Tabarrok
Keyword(s):  
Dynamic Analysis ◽  
Flexible Beams ◽  
Rotational Dynamic

scholarly journals Numerical Effectiveness of Different Formulations of the Rigid Finite Element Method

2014 ◽  
Vol 19 (3) ◽  
pp. 475-485
Author(s):  
I. Adamiec-Wójcik ◽  
Ł. Drąg ◽  
S. Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Benchmark Problem ◽  
Flexible Beams ◽  
New Approach ◽  
Constraint Equations ◽  
Rigid Finite Element Method ◽  
Alternative Approach ◽  
Element Method

Abstract The paper presents an application of different formulations of the rigid finite element method (RFEM) to dynamic analysis of flexible beams. We discuss numerical effectiveness of the classical RFEM and an alternative approach in which continuity of displacements is preserved by means of constraint equations. The analysis is carried out for a benchmark problem of the spin-up motion in planar and spatial cases. Torsion is omitted for numerical simulations and two cases of the new approach are considered. The results obtained by means of these methods are compared with the results obtained using a nonlinear two-node superelement

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