A 2D corotational formulation for dynamic analysis of flexible beams undergoing extremely large deformation

2020 ◽  
Author(s):  
Novi Andria ◽  
Lavi R. Zuhal ◽  
Leonardo Gunawan ◽  
Hari Muhammad
Keyword(s):  
Dynamic Analysis ◽  
Large Deformation ◽  
Flexible Beams ◽  
Corotational Formulation

Large Deformation Analysis and Experiments With Double Parallelogram Compliant Mechanisms

2018 ◽  
Author(s):  
Abhijit A. Tanksale ◽  
Prasanna S. Gandhi
Keyword(s):  
Large Deformation ◽  
High Precision ◽  
Large Deformations ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Vertical Plane ◽  
Coupled Analysis ◽  
Deformation Analysis ◽  
Flexible Beams ◽  
Straight Line

Compliant mechanisms are highly preferred in applications demanding motion with high precision. These mechanisms provide friction-less, backlash-free precise motion obtained through deformation of flexible members. The double parallelogram compliant mechanism (DPCM) is one the most important compliant mechanisms to obtain highly precise straight-line motion. DPCM when operated in horizontal plane yield high precision straight-line motion (even with large deformations) useful in several engineering applications. However, constraints such as space, dead loads, etc. may demand DPCMs to be used in the vertical plane. For DPCMs operating in a vertical plane, the axial load due to gravity causes tension and compression in flexible beams which get coupled to bending under large deformations. This ultimately affects the parasitic error of straight-line motion. This paper presents a coupled analysis, along with experimental validation, of DPCM operating in vertical plane considering gravity effects with large deformation.

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.

Dynamic Analysis of Soft Tissue considering Characteristic of Viscoelastic and Large Deformation

2002 ◽  
Vol 2002.40 (0) ◽  
pp. 33-34
Author(s):  
Izumi UENO ◽  
Takashi SAITO ◽  
Masaaki OKA ◽  
Atushi SAKUMA ◽  
Kimihiko NAKANO
Keyword(s):  
Soft Tissue ◽  
Dynamic Analysis ◽  
Large Deformation

Nonlinear Dynamic Analysis of Cantilever Beam Using POD Based Reduced Order Model

2015 ◽  
Vol 786 ◽  
pp. 398-403 ◽  
Author(s):  
Kulkarni Atul Shankar ◽  
Manoj Pandey
Keyword(s):  
Dynamic Analysis ◽  
Large Deformation ◽  
Cantilever Beam ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Numerical Technique ◽  
Nonlinear Dynamic Analysis ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order

In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

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