scholarly journals An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

2015 ◽  
Author(s):  
Marijn Nijenhuis ◽  
J. P. Meijaard ◽  
Just L. Herder ◽  
Shorya Awtar ◽  
Dannis M. Brouwer
Keyword(s):  
Three Dimensional ◽  
Beam Element ◽  
Element Analysis ◽  
Cross Sectional ◽  
Flexure Mechanism ◽  
Stiffness Properties ◽  
Spatial Beam ◽  
Discrete Nature ◽  
Stiffness Characteristics

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

scholarly journals An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Marijn Nijenhuis ◽  
J. P. Meijaard ◽  
Dhanushkodi Mariappan ◽  
Just L. Herder ◽  
Dannis M. Brouwer ◽  
...  
Keyword(s):  
Closed Form ◽  
Three Dimensional ◽  
Flexure Mechanism ◽  
Stiffness Properties ◽  
Spatial Beam ◽  
Bearing Stiffness ◽  
Stiffness Characteristics ◽  
Parametric Expression ◽  
Analytical Result ◽  
Analytical Expressions

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that govern its performance as a basic constituent of flexure mechanisms. This paper presents a new modeling approach for obtaining insight into the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear, and torsion deformation. The approach is based on the use of a discretized version of a finite (i.e., nonlinear) strain spatial beam formulation for extracting analytical expressions that describe deformation and stiffness characteristics of a flexure strip in a parametric format. This particular way of closed-form modeling exploits the inherent finite-element assumptions on interpolation and also lends itself for numeric implementation. As a validating case study, a closed-form parametric expression is derived for the lateral support stiffness of a flexure strip and a parallelogram flexure mechanism. This captures a combined torsion–bending dictated geometrically nonlinear effect that undermines the support bearing stiffness when the mechanism moves in the intended degree of freedom (DoF). The analytical result is verified by simulations and experimental measurements.

Nonlinear Constraint Model for Symmetric Three-Dimensional Beams

2010 ◽  
Author(s):  
Shiladitya Sen ◽  
Shorya Awtar
Keyword(s):  
Three Dimensional ◽  
Practical Interest ◽  
Nonlinear Constraint ◽  
Element Analysis ◽  
Flexure Mechanism ◽  
Spatial Beam ◽  
Non Linear ◽  
Simplifying Assumptions ◽  
Non Linear Load ◽  
Constraint Model

The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a slender, uniform and symmetric cross-section, spatial beam, which is one of the most basic flexure elements used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the non-linear load-displacement relations of the beam. Appropriate simplifying assumptions are made in deriving these relations so that relevant non-linear effects (load-stiffening, kinematic, and elastokinematic) are captured in a compact, closed-form, and parametric manner. The resulting spatial beam constraint model is shown to be accurate, using non-linear finite element analysis, within a load and displacement range of practical interest. The utility of this model lies in the physical and analytical insight that it offers into the constraint behavior of a spatial beam flexure, its use in 3D flexure mechanism geometries, and fundamental performance tradeoffs in flexure mechanism design.

scholarly journals Fabrication, Experiments, and Analysis of an LBM Additive-Manufactured Flexure Parallel Mechanism

Micromachines ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 572 ◽  
Author(s):  
Huaxian Wei ◽  
Li Wang ◽  
Xiaodong Niu ◽  
Jian Zhang ◽  
Alessandro Simeone
Keyword(s):  
Additive Manufacturing ◽  
Parallel Mechanism ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Element Analysis ◽  
Flexure Mechanism ◽  
Laser Beam Melting ◽  
Stiffness Characteristics ◽  
First Time

Additive manufacturing technology has advantages for realizing complex monolithic structures, providing huge potential for developing advanced flexure mechanisms for precision manipulation. However, the characteristics of flexure hinges fabricated by laser beam melting (LBM) additive manufacturing (AM) are currently little known. In this paper, the fabrication and characterization of a flexure parallel mechanism through the LBM process are reported for the first time to demonstrate the development of this technique. The geometrical accuracy of the additive-manufactured flexure mechanism was evaluated by three-dimensional scanning. The stiffness characteristics of the flexure mechanism were investigated through finite element analysis and experimental tests. The effective hinge thickness was determined based on the parameters study of the flexure parallel mechanism. The presented results highlight the promising outlook of LBM flexure parts for developing novel nanomanipulation platforms, while additional attention is required for material properties and manufacturing errors.

scholarly journals Experimental Investigations of Interactions between Sand Wave Movements, Flow Structure, and Individual Aquatic Plants in Natural Rivers: A Case Study of Potamogeton Pectinatus L.

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1166 ◽  
Author(s):  
Łukasz Przyborowski ◽  
Anna Łoboda ◽  
Robert Bialik
Keyword(s):  
Flow Velocity ◽  
Three Dimensional ◽  
Potamogeton Pectinatus ◽  
Sand Wave ◽  
Experimental Investigations ◽  
Cross Sectional ◽  
Bending Tests ◽  
Long Duration ◽  
Elevation Changes

Long-duration measurements were performed in two sandy bed rivers, and three-dimensional (3D) flow velocity and bottom elevation changes were measured in a vegetated area and in a clear region of a river. Detailed flow velocity profiles downstream and upstream of a single specimen of Potamogeton pectinatus L. were obtained and the bed morphology was assessed. Potamogeton plants gathered from each river were subjected to tensile and bending tests. The results show that the existence of the plants was influenced by both bottom and flow conditions, as the plants were located where water velocity was lower by 12% to 16% in comparison to clear region. The characteristics of the flow and sand forms depended on the cross-sectional arrangement of the river, e.g., dunes were approximately four times higher in the middle of the river than in vegetated regions near the bank. Furthermore, the studied hydrophytes were too sparse to affect water flow and had no discernible impact on the sand forms’ movements. The turbulent kinetic energy downstream of a single plant was reduced by approximately 25%. Additionally, the plants’ biomechanical characteristics and morphology were found to have adjusted to match the river conditions.

An evaluation of simplified techniques for estimating three-dimensional undrained ground movements due to tunnelling in soft soils

1992 ◽  
Vol 29 (1) ◽  
pp. 39-52 ◽  
Author(s):  
R. K. Rowe ◽  
K. M. Lee
Keyword(s):  
Plane Strain ◽  
Deformation Behaviour ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Cumulative Probability ◽  
Element Analysis ◽  
Cross Sectional ◽  
Soft Soils ◽  
Longitudinal Plane ◽  
Stress Changes

A number of simplified approaches have been used by various researchers to estimate the three-dimensional stress changes and ground deformations due to shallow tunnels in soft soils. The effectiveness of these simplified analyses, such as (i) axisymmetric analysis, (ii) longitudinal plane strain analysis, and (iii) empirical cumulative probability distribution approach, has been examined by comparison of results with those from a full three-dimensional elastoplastic finite-element analysis. For tunnels located at shallow depths, axisymmetric analyses are generally found to be unable to predict the correct magnitude of displacement around a tunnel heading. However, the trend of the three-dimensional deformation behaviour near the tunnel heading can be reasonably approximated by the average of the normalized displacement curves predicted by the two axisymmetric assumptions as described in this paper. The three-dimensional distribution of the displacement near the ground surface, on the other hand, can be approximately predicted by the cumulative probability approach, provided that the three empirical parameters required by the equations are reasonably estimated. In this paper, these parameters were estimated from the result of a two-dimensional plane strain cross-sectional analysis. Finally, it was found that modelling of three-dimensional deformations by a longitudinal plane strain analysis did not give good results for the cases examined. Key words : tunnelling, soft ground, analysis.

Elastic Averaging in Flexure Mechanisms: A Three-Beam Parallelogram Flexure Case Study

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Shorya Awtar ◽  
Kevin Shimotsu ◽  
Shiladitya Sen
Keyword(s):  
Improve Performance ◽  
Mathematical Basis ◽  
Element Analysis ◽  
Redundant Constraints ◽  
Flexure Mechanism ◽  
Design Paradigm ◽  
Constraint Model ◽  
Effective Use ◽  
Exact Constraint

Redundant constraints are generally avoided in mechanism design because they can lead to binding or loss in expected mobility. However, in certain distributed-compliance flexure mechanism geometries, this problem is mitigated by the phenomenon of elastic averaging. Elastic averaging is a design paradigm that, in contrast with exact constraint design principles, makes deliberate and effective use of redundant constraints to improve performance and robustness. The principle of elastic averaging and its advantages are illustrated in this paper by means of a three-beam parallelogram flexure mechanism, which represents an overconstrained geometry. In a lumped-compliance configuration, this mechanism is prone to binding in the presence of nominal manufacturing and assembly errors. However, with an increasing degree of distributed-compliance, the mechanism is shown to become more tolerant to such geometric imperfections. The nonlinear elastokinematic effect in the constituent beams is shown to play an important role in analytically predicting the consequences of overconstraint and provides a mathematical basis for elastic averaging. A generalized beam constraint model is used for these predictions so that varying degrees of distributed compliance are captured using a single geometric parameter. The closed-form analytical results are validated against finite element analysis, as well as experimental measurements.

A super-convergent thin-walled 3D beam element for analysis of laminated composite structures with arbitrary cross-section

2021 ◽  
pp. 1-23
Author(s):  
M. Talele ◽  
M. van Tooren ◽  
A. Elham
Keyword(s):  
Cross Sections ◽  
Composite Structures ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Beam Element ◽  
Arbitrary Cross Section ◽  
Beam Model ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Abstract An efficient, fully coupled beam model is developed to analyse laminated composite thin-walled structures with arbitrary cross-sections. The Euler–Lagrangian equations are derived from the kinematic relationships for a One-Dimensional (1D) beam representing Three-Dimensional (3D) deformations that take into account the cross-sectional stiffness of the composite structure. The formulation of the cross-sectional stiffness includes all the deformation effects and related elastic couplings. To circumvent the problem of shear locking, exact solutions to the approximating Partial Differential Equations (PDEs) are obtained symbolically instead of by numerical integration. The developed locking-free composite beam element results in an exact stiffness matrix and has super-convergent characteristics. The beam model is tested for different types of layup, and the results are validated by comparison with experimental results from literature.

The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports

1969 ◽  
Vol 91 (4) ◽  
pp. 1105-1113 ◽  
Author(s):  
E. J. Gunter ◽  
P. R. Trumpler
Keyword(s):  
Internal Friction ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Analog Computer ◽  
Three Dimensional Model ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Internal Rotor

This paper evaluates the stability of the single mass rotor with internal friction on damped, anisotropic supports. The paper shows under what conditions the rotor stability may be improved by an undamped support with anisotropic stiffness properties. A three dimensional model is presented to show the influence of rotor and support stiffness characteristics on stability. Curves are also presented on how support damping may also improve or even reduce rotor stability. An analog computer solution of the governing equations of motion is presented showing the shaft transient motion for various speed ranges, and also plots of the rotor steady state motion are given for various speeds up to and including the stability threshold. The analysis is used to explain many of the experimental observations of B. L. Newkirk concerning stability due to internal rotor friction.

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