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.

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 Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Kinematic Synthesis of Planar, Shape-Changing Compliant Mechanisms Using Pseudo-Rigid-Body Models

2012 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Flexible Beam ◽  
Beam Model ◽  
Flexible Beams ◽  
Multi Objective Genetic Algorithm ◽  
Optimization Loop

This paper presents a procedure using Pseudo-Rigid-Body Models (PRBMs) to synthesize partially compliant mechanisms capable of approximating a shape change defined by a set of morphing curves in different positions. To generate a single-piece compliant mechanism, flexural pivots and flexible beams are both utilized in the mechanism. New topologies defined by compliant mechanism matrices are enumerated by modifying the components that make up a single degree-of-freedom (DOF) rigid-body mechanism. Because of the introduction of the PRBM for flexural pivots and the simplified PRBM for flexible beams, torsional springs are attached at the characteristic pivots of the 1-DOF rigid-body mechanism in order to generate a corresponding pseudo-rigid-body mechanism. A multi-objective genetic algorithm is employed to find a group of viable compliant mechanisms in the form of candidate pseudo-rigid-body mechanisms that tradeoff minimizing shape matching error with minimizing actuator energy. Since the simplified beam model is not accurate, an optimization loop is established to find the position and shape of the flexible beam using a finite link beam model. The optimal flexible beams together with the pseudo-rigid-body mechanism define the solution mechanism. The procedure is demonstrated with an example in which a partially compliant mechanism approximating two closed-curve profiles is synthesized.

Dynamic Response Simulations of Flexible Beams Using the Energy Wave Scattering Method

2005 ◽  
Vol 219 (9) ◽  
pp. 859-868
Author(s):  
T Chen
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Dynamic Response ◽  
Wave Scattering ◽  
Experimental Results ◽  
Distributed Model ◽  
Flexible Beam ◽  
Scattering Method ◽  
Flexible Beams ◽  
Good Comparison

The dynamic response of a flexible beam is simulated using the energy wave scattering method. A new topology is demonstrated to model the flexible beam and it can distinguish the displacements contributed by kinetic energy and potential energy. Experiments are conducted using both a highly distributed model and a lumped-distributed model. Numerical procedures and examples are presented. The experimental results are compared with the simulated ones and a good comparison is shown.

Three-Dimensional Finite Element Modeling of Hard Turning Processes

Manufacturing ◽  
2003 ◽  
Author(s):  
T. D. Marusich ◽  
R. J. McDaniel ◽  
S. Usui ◽  
J. A. Fleischmann ◽  
T. R. Kurfess ◽  
...  
Keyword(s):  
Finite Element ◽  
Hard Turning ◽  
Metal Cutting ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Tool Material ◽  
Dimensional Accuracy ◽  
Element Model ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Hard turning processes promise affordable fabrication of machined components with high dimensional accuracy requirements. In an effort to achieve the desired economics a vast array of process variables must be considered including tool material, geometry, edge preparation, wear, speed and feed selection, while maintaining part quality. One method to reduce the number of necessary experiments is through accurate and reliable modeling. A three-dimensional finite element model is presented which includes fully adaptive unstructured mesh generation, tight thermo-mechanically coupling, deformable tool-chip-workpiece contact, interfacial heat transfer across the tool-chip boundary, momentum effects at high speeds and constitutive models appropriate for high strain rate, finite deformation analyses. The model is applied to nose turning of hardened steel workpieces, HRc 60. Metal cutting tests are performed, cutting forces collected, and validation comparison is made.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

Using Symplectic Schemes for Nonlinear Dynamic Analysis of Flexible Beams Undergoing Overall Motions

2010 ◽  
Vol 156-157 ◽  
pp. 854-861
Author(s):  
Jian Lian Cheng ◽  
Tie Shuan Zhao
Keyword(s):  
Nonlinear Dynamic Analysis ◽  
Elastic Strain Energy ◽  
Integration Scheme ◽  
Flexible Beam ◽  
Element Formulation ◽  
Flexible Beams ◽  
Flexible Bodies ◽  
Hamilton Equations ◽  
Flexible Beam System ◽  
Fidelity Model

In this paper, we developed a high-fidelity model to handle large overall motion of multi-flexible bodies. As a demonstration, the model is applied to a planar flexible beam system. An explicit expression of the kinetic energy is derived for the planar beams. The elastic strain energy is described via an accurate beam finite element formulation. The Hamilton equations are integrated by a symplectic integration scheme for enhanced accuracy and guaranteed numerical stability. The Hamilton and the corresponding Hamilton’s equations of beam vibration problems are formulated. It appears that the proposed symplectic finite elements are capable of providing accurate and robust simulation in the dynamic modeling of multi-flexible bodies systems with large overall motions.

Chained Beam-Constraint-Model (CBCM): A Powerful Tool for Modeling Large and Complicated Deflections of Flexible Beams in Compliant Mechanisms

2014 ◽  
Author(s):  
Fulei Ma ◽  
Guimin Chen
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Research Community ◽  
The Other ◽  
New Method ◽  
Flexible Beam ◽  
Large Deflections ◽  
Flexible Beams ◽  
Constraint Model

Modeling large deflections has been one of the most fundamental problems in the research community of compliant mechanisms. Although many methods are available, there still exists a need for a method that is simple, accurate, and can be applied to a vast variety of large deflection problems. Based on the beam constraint model (BCM), we propose a new method for modeling large deflections called chained BCM (CBCM), which divides a flexible beam into a few elements and models each element by BCM. It is demonstrated that CBCM is capable of modeling various large and complicated deflections of flexible beams in compliant mechanisms. In general, CBCM obtains accurate results with no more than 6 BCM elements, thus is more efficient than most of the other discretization-based methods.

On the Understanding of Non-Stationary VIV of Slender Beams

2010 ◽  
Author(s):  
Carl M. Larsen ◽  
Jie Wu ◽  
Halvor Lie
Keyword(s):  
Empirical Model ◽  
Large Scale ◽  
Peak Frequency ◽  
Flexible Beam ◽  
Response Process ◽  
Discrete Response ◽  
Proposed Model ◽  
Slender Beams ◽  
Competing Response ◽  
Large Scale Tests

VIV of slender beams at high mode order will appear as a non-stationary response process. Amplitudes, dominating frequency and mode composition are seen to vary in time, but so far we do not have a complete understanding of this process. One approach is to attempt to understand and model the physical mechanism behind the observed behaviour, but an alterative is to establish a simplified model that can be used for fatigue calculations. The purpose of the present paper is to compare the dominant response frequencies that have been observed in large scale tests of a flexible beam to the discrete response frequencies that are predicted by an empirical model for prediction of VIV. Use of wavelet and modal analyses on experimental data makes it possible to describe the time variation of the peak frequency, and hence also the relative period of time this frequency falls into discrete frequency bins. An empirical model is also proposed for calculation of relative duration of competing response frequencies. The observed frequencies can hence be compared to the results from the proposed model. The conclusion is that the model identifies the domination response frequencies with satisfactory accuracy. The range of calculated discrete response frequencies is larger than for the discrete peak frequencies identified from the experiments. But the observed response process has a broader frequency band than the variation of the peaks. Hence, the results from the analysis seem to agree well with observations. Further analyses are, however, still needed in order to verify the proposed model.

Numerical Assessment of the Boundary Layer Effect Predicted by the Shear Flexible Beam Theory with the Sixth-Order Differential Equations

2011 ◽  
Vol 105-107 ◽  
pp. 1705-1711
Author(s):  
Xiao Dan Wang ◽  
Guang Yu Shi
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Beam Theory ◽  
Sixth Order ◽  
Flexible Beam ◽  
Element Analysis ◽  
Flexible Beams ◽  
Displacement Boundary ◽  
Numerical Assessment ◽  
Layer Effect

The analytical solutions of shear flexible beams with displacement boundary conditions are derived by using the new sixth-order differential equation beam theory presented by Shi and Voyiadjis (ASME J. Appl. Mech., Vol. 78, 021019, 2011), in which the boundary layer effects are included. The accuracy of the boundary layer effects predicted by the new sixth-order beam theory is evaluated by the finite element analysis in this study. The numerical results show that the new sixth-order beam theory is capable of taking account of the displacement boundary conditions of shear deformable beams and predicting good results of the boundary layer effects induced by the displacement boundaries and the continuity constraints.

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