An Improved Unified Solution for a Vibration Equation of Tension-Stiffening Beam Using Extended Rayleigh Energy Method

2019 ◽  
Author(s):  
Zhijun Yang ◽  
Ruiqi Li ◽  
Youdun Bai
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Energy Method ◽  
Physical Science ◽  
Element Analysis ◽  
Tension Stiffening ◽  
Design And Optimization ◽  
Micro Motion ◽  
Stiffening Effect ◽  
Good Agreement

Abstract The tension-stiffening effect is very important for physical science, which has been widely used in MEMS, sensors and micro-motion stages. The analytical solutions of the tension-stiffening beam are extremely significant, in consideration of the inefficiency of finite element analysis (FEA) for the design and optimization. Commonly, there are three typical types of boundary conditions for tension-stiffening (or stress-induced) beams, i.e., clamped-clamped, clamped-hinged, and hinged-hinged. But only the hinged-hinged beam has an analytical solution. Therefore, a method based on extended Rayleigh energy method is proposed in this paper to deduce the analytical solutions of three boundary conditions. The predictions are verified to be in good agreement with FEA and experiment results.

scholarly journals Output decoupling property of planar flexure-based compliant mechanisms with symmetric configuration

2016 ◽  
Vol 7 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Y. S. Du ◽  
T. M. Li ◽  
Y. Jiang ◽  
J. L. Zhang
Keyword(s):  
Analytical Model ◽  
Compliant Mechanisms ◽  
Element Analysis ◽  
Modeling Methods ◽  
Stiffness Modeling ◽  
Symmetric Configuration ◽  
Parallel Structures ◽  
The Matrix ◽  
Micro Motion ◽  
Good Agreement

Abstract. This paper presents the output decoupling property of planar flexure-based compliant mechanisms with symmetric configuration. Compliance/stiffness modeling methods for flexure serial structures and flexure parallel structures are first derived according to the matrix method. Analytical model of mechanisms with symmetric configuration is then developed to analyze the output decoupling property. The proposed analytical model shows that mechanisms are output decoupled when they are symmetry about two perpendicular axes or when they are composed of either three or an even number of identical fundamental forms distributed evenly around the center. Finally, output compliances of RRR and 4-RRR compliant micro-motion stages are derived from the analytical model and finite element analysis (FEA). The comparisons indicate that the results obtained from the proposed analytical model are in good agreement with those derived from FEA, which validates the proposed analytical model.

Polynomial Based Elasticity Solutions of Beams and their Numerical Validation: A Review

2011 ◽  
Vol 311-313 ◽  
pp. 2315-2321
Author(s):  
Sebin Jose ◽  
Sunil Bhat
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Stress Problem ◽  
Elasticity Solutions ◽  
Harmonic Equation ◽  
Complex Cases ◽  
Good Agreement

Solution of two-dimensional stress problem is reduced to integration of bi-harmonic equation[1].A polynomial is chosen as Airy’s stress function.Constants of the polynomial[2] are found by fulfilling the boundary conditions. Stress solutions are obtained from.The paper presents polynomial based stress solutions of beams for complex cases involving offset loads and other combinations with offset loads.The results are compared with those obtained from finite element analysis[3] and conventional methods.The results are in good agreement with each other.

Design and Optimization of Honeycomb Corrugated Chaff Forming Roller

2014 ◽  
Vol 597 ◽  
pp. 213-218
Author(s):  
Xiao Ping Yang ◽  
Bo Zhong ◽  
Chang Jie Luo
Keyword(s):  
Analysis Software ◽  
Forming Process ◽  
Element Analysis ◽  
Time Curve ◽  
Forming Quality ◽  
Design And Optimization ◽  
Number Of Teeth ◽  
Stress Contour ◽  
Forming Characteristics ◽  
Good Agreement

Abstract. By analyzing the material properties and forming characteristics of the 0.8mm length side hexagon honeycomb corrugated chaff , we studied forming roller’s design and optimization while making corrugated chaffs used forming method and focus on the influence of the chamfer of teeth top edge and number of teeth to forming quality at the corrugated chaff corner .We used finite element analysis software ANSYS / LS-DYNA to simulate the forming process of corrugated chaff , studied the stress contour and stress-time curve of typical element, found the optimal chamfer of teeth top edge and number of teeth, then we used the designed forming roller to verify the effect of chaff forming . By comparison experimental and simulation results,we found good agreement between the two, when the chamfer of teeth top edge dj = 0.08mm, number of teeth z = 40, the chaff has the best forming quality .

Finite element analysis for precision cold forging of helical gear using recurrent boundary conditions

1998 ◽  
Vol 212 (3) ◽  
pp. 231-240 ◽  
Author(s):  
Y B Park ◽  
D Y Yang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Helical Gear ◽  
Cold Forging ◽  
Rigid Plastic ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Good Agreement

In metal forming, there are problems with recurrent geometric characteristics without explicitly prescribed boundary conditions. In such problems, so-called recurrent boundary conditions must be introduced. In this paper, as a practical application of the proposed method, the precision cold forging of a helical gear (which is industrially useful and geometrically complicated) has been simulated by a three-dimensional rigid-plastic finite element method and compared with the experiment. The application of recurrent boundary conditions to helical gear forging analysis is proved to be effective and valid. The three-dimensional deformed pattern by the finite element analysis is shown, and the forging load is compared with the experimental load. The profiles of the free surface of the workpiece show good agreement between the computation and the experiment.

Stiffening Effect of Motor Core Webs for Torsional Rotordynamics

2012 ◽  
Author(s):  
Chris D. Kulhanek ◽  
Stephen M. James ◽  
Justin R. Hollingsworth
Keyword(s):  
Torsional Stiffness ◽  
Poor Agreement ◽  
Motor Shaft ◽  
Element Analysis ◽  
Resonance Frequencies ◽  
Cooling Air Flow ◽  
Cooling Air ◽  
Sufficient Space ◽  
Stiffening Effect ◽  
Good Agreement

Longitudinal webs or spider bars are often placed mid-span of a motor shaft and are primarily used to support the windings or rotor laminations while allowing sufficient space for cooling air flow. When subject to a torque, the radial webs experience a loading configuration that includes bending and torsion while the base shaft experiences pure torsion. A webbed cross-section has a higher torsional stiffness as compared to the torsional stiffness of just the circular portion of the shaft section. This influences the torsional critical speeds and can become important for torsional systems that operate with minimal separation margins from resonance frequencies. This work presents various approaches to calculate the stiffening effect. The approaches include empirical and analytical methods described by Nestorides and API 684. An additional method uses a solid model of the motor core and a commercial Finite Element Analysis (FEA) solver to predict steady-state deflection under a torsional load. This in turn allows for a torsional stiffness calculation. Motor core configurations with various shaft diameters, number of spider bars, and spider bar geometries are considered. Good agreement is shown between the FEA results and the Griffith and Taylor method described by Nestorides. The other methods considered, including the calculation method described in API 684, show generally poor agreement with the FEA torsional stiffness results for the webbed shaft geometries studied.

Design and Optimization of a Spatial Hybrid Motion System

2010 ◽  
Author(s):  
P. R. Ouyang ◽  
Steven Cargnello
Keyword(s):  
Optimization Design ◽  
Design Principle ◽  
Compliant Mechanism ◽  
Dynamic Performance ◽  
Parallel Architecture ◽  
Element Analysis ◽  
Design And Optimization ◽  
Motion System ◽  
Micro Motion ◽  
Hybrid Motion

In this paper, a spatial hybrid motion system is developed that integrates two types of motions through one compliant mechanism: a macro motion driven by a DC servomotor and a micro motion driven by a PZT actuator. A unique feature of the developed hybrid motion system is the elimination of interaction between the macro motion and micro motion. Three issues are addressed in this study: (1) the design principle and implementation of the hybrid motion system; (2) the kinematic analysis and dynamic analysis; and (3) the optimization design of the hybrid motion system. For the micro motion, the five-bar topology of a mechanical amplifier is used to increase amplifying ratio and improve dynamic performance of the system. Finite element analysis results verify the design principle of the parallel architecture for the hybrid motion system.

scholarly journals Computational consistency of the material models and boundary conditions for finite element analyses on cantilever beams

2018 ◽  
Vol 10 (6) ◽  
pp. 168781401878002 ◽  
Author(s):  
Wei-chen Lee ◽  
Chen-hao Zhang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Material Model ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Material Models ◽  
The Finite Element Analysis ◽  
Selection Of ◽  
Good Agreement

The objective of this research was to investigate the effects of material models, element types, and boundary conditions on the consistency of finite element analysis. Two cantilever beams were used; one made of stainless steel SUS301 3/4H and the other made of polymer polyoxymethylene. The load–deflection curves of the two cantilever beams obtained by experiments were compared to those obtained by finite element analysis, where the material models—including bilinear, trilinear, and multi-linear—were used. Four element types—beam, plane stress, shell, and solid—were also employed with the material models to obtain the simulated load–deflection curves of the cantilever beams. It was found that bilinear material models had the stiffest behavior due to their overestimated yield strength. In addition, by applying a finite displacement to simulate the grip of the cantilever beams, the discrepancy between the simulated permanent set and the experimental set could be reduced from 80% to 5%. To sum up, both the selection of the material model and the setup of the boundary conditions are critical for obtaining good agreement between the finite element analysis results and the experimental data.

scholarly journals Analysis of Functionally Graded Timoshenko Beams by Using Peridynamics

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Boundary Conditions ◽  
Lagrange Equation ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Governing Equations ◽  
Element Analysis ◽  
Free Boundary Conditions ◽  
Support Roller ◽  
Roller Support ◽  
Good Agreement

Abstract In this study, a new peridynamic formulation is presented for functionally graded Timoshenko beams. The governing equations of the peridynamic formulation are obtained by utilising Euler-Lagrange equation and Taylor’s expansion. The proposed formulation is validated by considering a Timoshenko beam subjected to different boundary conditions including pinned support-roller support, clamped-roller support and clamped-free boundary conditions. Results from peridynamics are compared against finite element analysis results. A very good agreement is obtained for transverse displacements, rotations and axial displacements along the beam.

scholarly journals Solving partial differential equations in deformed grids by estimating local average gradients with planes

2021 ◽  
Vol 2090 (1) ◽  
pp. 012069
Author(s):  
Aarne Pohjonen
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Physical Science ◽  
Partial Differential ◽  
Average Gradient ◽  
Initial And Boundary Conditions ◽  
Local Average

Abstract For constructing physical science based models in irregular numerical grids, an easy-to-implement method for solving partial differential equations has been developed and its accuracy has been evaluated by comparison to analytical solutions that are available for simple initial and boundary conditions. The method is based on approximating the local average gradients of a field by fitting equation of plane to the field quantities at neighbouring grid positions and then calculating an estimate for the local average gradient from the plane equations. The results, comparison to analytical solutions, and accuracy are presented for 2-dimensional cases.

Computer Modeling of a Tire under Cornering Loads

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves
Keyword(s):  
Finite Element Analysis ◽  
Geometric Approach ◽  
Lateral Force ◽  
Slip Angle ◽  
Element Analysis ◽  
Pressure Distributions ◽  
Slip Effects ◽  
Improved Accuracy ◽  
Nonlinear Geometric ◽  
Good Agreement

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

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