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.

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.

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.

Parametric Deflection Approximations for Initially Curved, Large-Deflection Beams in Compliant Mechanisms

1996 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Curved Beam ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Fundamental Type ◽  
Applied Forces ◽  
Flexible Member

Abstract The analysis of systems containing highly flexible members is made difficult by the nonlineararities caused by large deflections of the flexible members. The analysis and design of many such systems may be simplified by using pseudo-rigid-body approximations in modeling the flexible members. The pseudo-rigid-body model represents flexible members as rigid links, joined at pin joints with torsional springs. Appropriate values for link lengths and torsional spring stiffnesses are determined such that the deflection path and force-deflection relationships are modeled accurately. Pseudo-rigid-body approximations have been developed for initially straight beams with externally applied forces at the beam end. This work develops approximations for another fundamental type of flexible member, the initially curved beam with applied force at the beam end. This type of flexible member is commonly used in compliant mechanisms. An example of the use of the resulting pseudo-rigid-body approximations in compliant mechanisms is included.

Stresses in Curved Beams of Noncircular Center Line

1960 ◽  
Vol 27 (3) ◽  
pp. 445-454
Author(s):  
M. M. Abbassi
Keyword(s):  
Cross Sections ◽  
Plane Curve ◽  
The Body ◽  
Curved Beam ◽  
Center Line ◽  
Curved Beams ◽  
Concentrated Load ◽  
Initial Curvature

The paper deals with the general case of a curved beam whose center line is a plane curve not necessarily circular. The body-stress equations and the compatibility equations for stresses in their general form are found for the chosen system of co-ordinates and put in their simplest form. Solutions for the equations with the aim of finding the stresses when the beam is subjected to a torque and to a bending out of its plane of initial curvature are obtained for both elliptic and circular cross sections of the beam. The case of a concentrated load at one end perpendicular to the plane of initial curvature is also considered.

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.

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.

Random Vibration Suppression of Non-Uniform Curved Beams Using Optimal Tuned Mass Damper

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Vibration Suppression ◽  
Transportation Systems ◽  
Structural Vibration ◽  
Element Formulation ◽  
Curved Beam ◽  
Curved Beams ◽  
Tuned Mass Dampers ◽  
Analysis And Design ◽  
Structural Design Optimization ◽  
Beam Type

Beam type structures have many applications in mechanical, aerospace and civil engineering fields. Due to low damping and recent trend for light weight design (especially for aerospace vehicles and transportation systems), these structures may easily vibrate in their low natural frequencies which may subsequently lead to failure of structure. Thus vibration control of these structures is a very important task which should be considered in preliminary structural design optimization. One of the engineering concerns is to design non-uniform beam type structures with changing geometry. In this study, the structural vibration analysis and design of a curved beam with attached tuned mass dampers under random excitations are presented. The finite element formulation of the curved beam with attached tuned mass dampers has been derived and combined with Sequential Quadratic Programming optimization algorithm to find optimal design variables in tuned mass dampers to minimize the vibration. Illustrative examples are provided to demonstrate the methodology.

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.

Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Stiffness ◽  
Model Concept ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Joints

Abstract Compliant mechanisms gain some or all of their mobility from the flexibility of their members rather than from rigid-body joints only. More efficient and usable analysis and design techniques are needed before the advantages of compliant mechanisms can be fully utilized. In an earlier work, a pseudo-rigid-body model concept, corresponding to an end-loaded geometrically nonlinear, large-deflection beam, was developed to help fulfill this need. In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed. The result is a simplified method of modeling the force/deflection relationships of large-deflection members in compliant mechanisms. Flexible segments which maintain a constant end angle are discussed, and an example mechanism is analyzed. The resulting models are valuable in the visualization of the motion of large-deflection systems, as well as the quick and efficient evaluation and optimization of compliant mechanism designs.

Earthquake response of linear-elastic arch-frames using exact curved beam formulations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Baran Bozyigit
Keyword(s):  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Opening Angle ◽  
Earthquake Response ◽  
Response Analysis ◽  
Curved Beam ◽  
Curved Beams ◽  
Base Shear ◽  
Content Type

PurposeThis study aims to obtain earthquake responses of linear-elastic multi-span arch-frames by using exact curved beam formulations. For this purpose, the dynamic stiffness method (DSM) which uses exact mode shapes is applied to a three-span arch-frame considering axial extensibility, shear deformation and rotational inertia for both columns and curved beams. Using exact free vibration properties obtained from the DSM approach, the arch-frame model is simplified into an equivalent single degree of freedom (SDOF) system to perform earthquake response analysis.Design/methodology/approachThe dynamic stiffness formulations of curved beams for free vibrations are validated by using the experimental data in the literature. The free vibrations of the arch-frame model are investigated for various span lengths, opening angle and column dimensions to observe their effects on the dynamic behaviour. The calculated natural frequencies via the DSM are presented in comparison with the results of the finite element method (FEM). The mode shapes are presented. The earthquake responses are calculated from the modal equation by using Runge-Kutta algorithm.FindingsThe displacement, base shear, acceleration and internal force time-histories that are obtained from the proposed approach are compared to the results of the finite element approach where a very good agreement is observed. For various span length, opening angle and column dimension values, the displacement and base shear time-histories of the arch-frame are presented. The results show that the proposed approach can be used as an effective tool to calculate earthquake responses of frame structures having curved beam elements.Originality/valueThe earthquake response of arch-frames consisting of curved beams and straight columns using exact formulations is obtained for the first time according to the best of the author’s knowledge. The DSM, which uses exact mode shapes and provides accurate free vibration analysis results considering each structural members as one element, is applied. The complicated structural system is simplified into an equivalent SDOF system using exact mode shapes obtained from the DSM and earthquake responses are calculated by solving the modal equation. The proposed approach is an important alternative to classical FEM for earthquake response analysis of frame structures having curved members.

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