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.

scholarly journals Modeling of Flexible Beam Networks and Morphing Structures by Geometrically Exact Discrete Beams

2020 ◽  
Vol 87 (8) ◽  
Author(s):  
Claire Lestringant ◽  
Dennis M. Kochmann
Keyword(s):  
Constitutive Models ◽  
Discrete Differential Geometry ◽  
Flexible Beam ◽  
Flexible Beams ◽  
Shape Morphing ◽  
Large Rotations ◽  
Dimensional Finite Element ◽  
Slender Beams ◽  
Efficient Alternative ◽  
Reconfigurable Structures

Abstract We demonstrate how a geometrically exact formulation of discrete slender beams can be generalized for the efficient simulation of complex networks of flexible beams by introducing rigid connections through special junction elements. The numerical framework, which is based on discrete differential geometry of framed curves in a time-discrete setting for time- and history-dependent constitutive models, is applicable to elastic and inelastic beams undergoing large rotations with and without natural curvature and actuation. Especially, the latter two aspects make our approach a versatile and efficient alternative to higher-dimensional finite element techniques frequently used, e.g., for the simulation of active, shape-morphing, and reconfigurable structures, as demonstrated by a suite of examples.

Self-Locking Satellite Boom With Flexure-Mode Joints

1997 ◽  
Vol 50 (11S) ◽  
pp. S225-S231 ◽  
Author(s):  
W. Szyszkowski ◽  
K. Fielden ◽  
D. W. Johnson
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Large Deflection ◽  
Cylindrical Shells ◽  
Experimental Results ◽  
Large Deflections ◽  
Large Rotations

Dynamic analysis, numerical simulation, and experimental results of the deployment of a self-locking lightweight satellite boom are presented. The joints that connect the two segments of the boom are made of flexible semi-cylindrical shells. During the deployment, the shells undergo large deflections and large rotations, up to π radians. The boom is to be launched in the folded configuration and then deployed from a rotating satellite. In the straight configuration, after locking the joints, the boom should be stiff enough to precisely position a heavy sensor in a required location. Several models of the boom are considered for analysis. In order to optimize the sensor trajectory and the locking sequence, a model that includes stiffness of the joints but neglects flexibility of the links is developed. The joints, which are prone to instabilities and snap-through behavior, are analyzed using large deflection quasistatic approach. Finally, nonlinear dynamics FEA is performed to simulate the deployment of the complete boom. The simulation is compared with experimental results obtained from the preliminary tests.

scholarly journals Static and dynamic analysis of homogeneous Micropolar-Cosserat panels

2021 ◽  
pp. 1-53
Author(s):  
S. K. Singh ◽  
A. Banerjee ◽  
R. K. Varma ◽  
S. Adhikari ◽  
S. Das
Keyword(s):  
Dynamic Analysis ◽  
Static And Dynamic Analysis

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

Static and dynamic analysis of a gradient-elastic bar in tension

2002 ◽  
Vol 72 (6-7) ◽  
pp. 483-497 ◽  
Author(s):  
K. G. Tsepoura ◽  
S. Papargyri-Beskou ◽  
D. Polyzos ◽  
D. E. Beskos
Keyword(s):  
Dynamic Analysis ◽  
Static And Dynamic Analysis ◽  
Elastic Bar
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