Modeling Large Deflections of Initially Curved Beams in Compliant Mechanisms Using Chained Beam Constraint Model

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Guangbo Hao ◽  
Weidong Zhu
Keyword(s):  
Cross Section ◽  
Compliant Mechanisms ◽  
Accurate Method ◽  
Curved Beams ◽  
Nonlinear Load ◽  
Circular Arc ◽  
Analysis And Design ◽  
Discretization Schemes ◽  
Uniform Cross Section ◽  
Constraint Model

Understanding and analyzing large and nonlinear deflections are the major challenges of designing compliant mechanisms. Initially, curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross section, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM), which is termed as the chained BCM (CBCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes. Compliant mechanisms utilizing initially curved beams of circular-arc, cosine and parabola shapes are modeled to demonstrate the effectiveness of CBCM for initially curved beams of various shapes. The method is also accurate enough to capture the relevant nonlinear load-deflection characteristics.

Modeling Large Deflections of Initially Curved Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model

2018 ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Guangbo Hao ◽  
Weidong Zhu
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Accurate Method ◽  
Curved Beam ◽  
Curved Beams ◽  
Nonlinear Load ◽  
Circular Arc ◽  
Analysis And Design ◽  
Discretization Schemes ◽  
Constraint Model

Understanding and analyzing large and nonlinear deflections is one of the major challenges of designing compliant mechanisms. Initially curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross-sections, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes. Compliant mechanisms utilizing initially curved beams of circular-arc, cosine and parabola shapes are modeled to demonstrate the effectiveness of CBCM for initially curved beams of various shapes. The method is also accurate enough to capture the relevant nonlinear load-deflection characteristics.

scholarly journals A modified pseudo-rigid-body modeling approach for compliant mechanisms with fixed-guided beam flexures

2017 ◽  
Vol 8 (2) ◽  
pp. 359-368 ◽  
Author(s):  
Pengbo Liu ◽  
Peng Yan
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Nonlinear Effects ◽  
Accurate Method ◽  
Element Analysis ◽  
Design And Optimization ◽  
Modeling Approach ◽  
The Finite Element Analysis ◽  
Constraint Model ◽  
Translational Mechanisms

Abstract. In the present paper, we investigate a modified pseudo-rigid-body (MPRB) modeling approach for compliant mechanisms with fixed-guided beam flexures by considering the nonlinear effects of center-shifting and load-stiffening. In particular, a fixed-guided compliant beam is modeled as a pair of fixed-free compliant beams jointed at the inflection point, where each fixed-free beam flexure is further modeled by a rigid link connected with an extension spring by a torsion spring, based on the beam constraint model (BCM). Meanwhile, the characteristic parameters of the proposed MPRB model are no longer constant values, but affected by the applied general tip load, especially the axial force. The developed MPRB modeling method is then applied to the analysis of three common compliant mechanisms (i.e. compound parallelogram mechanisms, bistable mechanisms and 1-DOF translational mechanisms), which is further verified by the finite element analysis (FEA) results. The proposed MPRB model provides a more accurate method to predict the performance characteristics such as deformation capability, stiffness variation, as well as error motions of complaint mechanisms with fixed-guided beam flexures, and offers a new look into the design and optimization of beam-based compliant mechanisms.

A Large-Deflection Annulus-Shape Flexure Hinge Based on Curved Beams

2008 ◽  
Author(s):  
Shanshan Zhao ◽  
Shusheng Bi ◽  
Jingjun Yu ◽  
Minglei Sun ◽  
Guanghua Zhong
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Accurate Method ◽  
Flexure Hinge ◽  
Curved Beam ◽  
Curved Beams ◽  
Element Analysis ◽  
Rigid Body Model ◽  
Compliant Joint ◽  
Design Tradeoffs

A curved flexure element such as an initially-curved beam can deflect largely and facilely. Using curved flexure elements in compliant mechanisms allows the mechanism to move a longer distance or undergo a larger rotation angle stroke than using conventional notch flexures. This paper presents a novel large-deflection annulus-shaped flexure hinge covering multiple curved-beam flexure elements. It has been shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in some improved performances of the flexure hinge. Additional fixed RCM characteristic of isosceles-trapezoidal flexure modules existed in this compliant joint further improve its accuracy. A master-motion pseudo-rigid-body model provides a simple and accurate method to analyze the force-deflection behavior of this new rotary flexure hinge. The accuracy of the model is verified by comparing outcomes to non-linear finite element analysis. The result shows the proposed rotary flexure hinge has a large stroke angle, a low axial and radial stiffness.

Large-Deflection Analysis of General Beams in Contact-Aided Compliant Mechanisms Using Chained Pseudo-Rigid-Body Model

2020 ◽  
Vol 12 (3) ◽  
Author(s):  
Mohui Jin ◽  
Zhou Yang ◽  
Collin Ynchausti ◽  
Benliang Zhu ◽  
Xianmin Zhang ◽  
...  
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Reaction Force ◽  
Curved Beams ◽  
Nonlinear Method ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Force Moment

Abstract The nonlinear analysis and design of contact-aided compliant mechanisms (CCMs) are challenging. This paper presents a nonlinear method for analyzing the deformation of general beams that contact rigid surfaces in CCMs. The large deflection of the general beam is modeled by using the chained pseudo-rigid-body model. A geometry constraint from the contact surface is developed to constrain the beam’s deformed configuration. The contact analysis problem is formulated based on the principle of minimum potential energy and solved using an optimization algorithm. Besides, a novel technique based on the principle of work and energy is proposed to calculate the reaction force/moment of displacement-loaded cases. Several analysis examples of the compliant mechanisms with straight or curved beams are used to verify the proposed method. The results show that the proposed method and technique can evaluate the deformation of beam-based CCMs and the reaction force/moment with acceptable accuracy, respectively.

scholarly journals Parametric optimization of the cross-section and shape of the longitudinal member in frontal impact

2019 ◽  
Vol 140 ◽  
pp. 02013
Author(s):  
Dmitry Bogdanov ◽  
Yury Boldyrev ◽  
Pavel Cvetkov ◽  
Oleg Klyavin ◽  
Ilya Davydov ◽  
...  
Keyword(s):  
Cross Section ◽  
Parametric Optimization ◽  
Numerical Procedure ◽  
Software Systems ◽  
Engineering Analysis ◽  
Frontal Impact ◽  
Mathematical Statement ◽  
Analysis And Design ◽  
Optimization Task ◽  
Python Programming

The article considers the problem of optimal design of car body elements (longitudinal members) according to the chosen criteria. Both the questions of formulation of the optimization task and individual problems of its solution are studied. The mathematical statement of the problem is considered. Thus, the most attention is given to consideration of realisation of used numerical procedure of optimization. The system of numerical calculations is based on the most widely spread software systems for engineering analysis and design. The developed scripts on Python programming language are briefly considered. Results of optimization of longitudinal members of the car are given.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

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