Large Deflection Modeling of Cross-spring Pivots Based on Comprehensive Elliptic Integral Solution

2014 ◽  
Vol 50 (11) ◽  
pp. 80 ◽  
Author(s):  
Aimei ZHANG
Keyword(s):  
Large Deflection ◽  
Elliptic Integral ◽  
Integral Solution

An Elliptic Integral Solution to the Multiple Inflections Large Deflection Beams in Compliant Mechanisms

2014 ◽  
Vol 971-973 ◽  
pp. 349-352 ◽  
Author(s):  
Jiang Yong Song
Keyword(s):  
Euler Equations ◽  
Inflection Point ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Accurate Method ◽  
Integral Solution ◽  
Large Deflections ◽  
Cantilever Beams ◽  
Inflection Points

In this paper, a solution based on the elliptic integrals is proposed for solving multiples inflection points large deflection. Application of the Bernoulli Euler equations of compliant mechanisms with large deflection equation of beam is obtained ,there is no inflection point and inflection points in two cases respectively. The elliptic integral solution which is the most accurate method at present for analyzing large deflections of cantilever beams in compliant mechanisms.

A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Cantilever Beams in Compliant Mechanisms

2012 ◽  
Author(s):  
Aimei Zhang ◽  
Guimin Chen
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Accurate Method ◽  
Integral Solution ◽  
Large Deflections ◽  
Cantilever Beams ◽  
Complex Modes ◽  
Inflection Points ◽  
Moment Load

The elliptic integral solution is often considered as the most accurate method for analyzing large deflections of cantilever beams in compliant mechanisms. In this paper, by explicitly including the number of inflection points (m) and the sign of the end-moment load (SM) in the derivation, a comprehensive solution based on the elliptic integrals is proposed for solving the large deflection problems. The comprehensive solution is capable of solving large deflections of cantilever beams subject to any kind of load cases and of any kind of deflected modes. A few deflected configurations of complex modes solved by the comprehensive solution are presented and discussed. The use of the comprehensive solution in analyzing compliant mechanisms is also demonstrated by a few case studies.

A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms

2013 ◽  
Vol 5 (2) ◽  
Author(s):  
Aimei Zhang ◽  
Guimin Chen
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Accurate Method ◽  
Integral Solution ◽  
Large Deflections ◽  
Complex Modes ◽  
Inflection Points ◽  
Moment Load ◽  
Thin Beams

The elliptic integral solution is often considered to be the most accurate method for analyzing large deflections of thin beams in compliant mechanisms. In this paper, a comprehensive solution based on the elliptic integrals is proposed for solving large deflection problems. By explicitly incorporating the number of inflection points and the sign of the end-moment load in the derivation, the comprehensive solution is capable of solving large deflections of thin beams with multiple inflection points and subject to any kinds of load cases. The comprehensive solution also extends the elliptic integral solutions to be suitable for any beam end angle. Deflected configurations of complex modes solved by the comprehensive solution are presented and discussed. The use of the comprehensive solution in analyzing compliant mechanisms is also demonstrated by examples.

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

1995 ◽  
Vol 117 (1) ◽  
pp. 156-165 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha
Keyword(s):  
Closed Form ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Cantilever Beams ◽  
Simple Method ◽  
Body Angle ◽  
Analysis And Design ◽  
Integral Solutions

Geometric nonlinearities often complicate the analysis of systems containing large-deflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closed-form elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms.

scholarly journals Natural Frequency Analysis of Two Nonlinear Panels Coupled with a Cavity Using the Approximate Elliptic Integral Solution and the Method of Harmonic Residual Minimization

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Y. Y. Lee
Keyword(s):  
Natural Frequency ◽  
Frequency Analysis ◽  
Elliptic Integral ◽  
Integral Solution ◽  
Acoustic Problem ◽  
Nonlinear Structural ◽  
Homogeneous Wave ◽  
Flexible Panels ◽  
Natural Frequency Analysis ◽  
Residual Minimization

The nonlinear structural acoustic problem considered in this study is the nonlinear natural frequency analysis of flexible double panels using the elliptic integral solution method. There are very limited studies for this nonlinear structural-acoustic problem, although many nonlinear plate or linear double panel problems have been tackled and solved. A multistructural/acoustic modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibrations of the flexible panels and acoustic pressure induced within the air gap. One is the von Karman’s plate equation and the other is the homogeneous wave equation. The results obtained from the proposed method approach are verified with those from a numerical method. The effects of vibration amplitude, gap width, aspect ratio, the numbers of acoustic modes and harmonic terms, and so forth on the resonant frequencies of the in-phase and out of phase modes are examined.

scholarly journals Predicting Nonlinear Stiffness, Motion Range, and Load-Bearing Capability of Leaf-Type Isosceles-Trapezoidal Flexural Pivot Using Comprehensive Elliptic Integral Solution

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Aimei Zhang ◽  
Yanjie Gou ◽  
Xihui Yang
Keyword(s):  
Elliptic Integral ◽  
Integral Solution ◽  
Leaf Spring ◽  
Nonlinear Stiffness ◽  
Load Bearing ◽  
Large Rotation ◽  
Leaf Type ◽  
Proposed Model ◽  
Motion Range ◽  
Stiffness Characteristics

A leaf-type isosceles-trapezoidal flexural (LITF) pivot consists of two leaf springs that are situated in the same plane and intersect at a virtual center of motion outside the pivot. The LITF pivot offers many advantages, including large rotation range and monolithic structure. Each leaf spring of a LITF pivot subject to end loads is deflected into an S-shaped configuration carrying one or two inflection points, which is quite difficult to model. The kinetostatic characteristics of the LITF pivot are precisely modeled using the comprehensive elliptic integral solution for the large-deflection problem derived in our previous work, and the strength-checking method is further presented. Two cases are employed to verify the accuracy of the model. The deflected shapes and nonlinear stiffness characteristics within the range of the yield strength are discussed. The load-bearing capability and motion range of the pivot are proposed. The nonlinear finite element results validate the effectiveness and accuracy of the proposed model for LITF pivots.

Nonlinear Mechanics of Interlocking Cantilevers

2017 ◽  
Vol 84 (12) ◽  
Author(s):  
Joseph J. Brown ◽  
Ryan C. Mettler ◽  
Omkar D. Supekar ◽  
Victor M. Bright
Keyword(s):  
Large Deflection ◽  
Elliptic Integral ◽  
Contact Point ◽  
Reaction Force ◽  
Insertion Force ◽  
Element Analysis ◽  
Fast Analysis ◽  
Analysis And Design ◽  
Physical Measurements ◽  
Compliant Systems

The use of large-deflection springs, tabs, and other compliant systems to provide integral attachment, joining, and retention is well established and may be found throughout nature and the designed world. Such systems present a challenge for mechanical analysis due to the interaction of contact mechanics with large-deflection analysis. Interlocking structures experience a variable reaction force that depends on the cantilever angle at the contact point. This paper develops the mathematical analysis of interlocking cantilevers and provides verification with finite element analysis and physical measurements. Motivated by new opportunities for nanoscale compliant systems based on ultrathin films and two-dimensional (2D) materials, we created a nondimensional analysis of retention tab systems. This analysis uses iterative and elliptic integral solutions to the moment–curvature elastica of a suspended cantilever and can be scaled to large-deflection cantilevers of any size for which continuum mechanics applies. We find that when a compliant structure is bent backward during loading, overlap increases with load, until a force maximum is reached. In a force-limited scenario, surpassing this maximum would result in snap-through motion. By using angled cantilever restraint systems, the magnitude of insertion force relative to retention force can vary by 50× or more. The mathematical theory developed in this paper provides a basis for fast analysis and design of compliant retention systems, and expands the application of elliptic integrals for nonlinear problems.

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

1992 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Closed Form ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Cantilever Beams ◽  
Simple Method ◽  
Body Angle ◽  
Analysis And Design ◽  
Integral Solutions

Abstract Geometric nonlinearities often complicate the analysis of systems containing large-deflection members. The time and resources required to develop closed-form or numerical solutions nave inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter, called the pseudo-rigid-body angle. The approximations are accurate to within 0.5% of the closed-form elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms.

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