A simple and effective solution of the elastica problem

2008 ◽  
Vol 222 (12) ◽  
pp. 2513-2516 ◽  
Author(s):  
L F Campanile ◽  
A Hasse
Keyword(s):  
Effective Solution ◽  
Element Analysis ◽  
Solution Approach ◽  
Closed Form Solutions ◽  
Design And Optimization ◽  
Linear Finite Element ◽  
Leaf Springs ◽  
Special Cases ◽  
Standard Solution ◽  
Bending Behaviour

The bending behaviour of thin stripes and leaf springs, in the presence of large deflections, is ruled by the so-called Bernoulli—Euler equation. The standard solution approach of this problem (‘elastica’) is represented by the non-linear finite-element analysis. In some special cases, closed-form solutions are available, which involve elliptic integrals and functions. In this article, an alternative method is presented based on the discretization of the deformed beam into circular-arc segments. The method is fast and simple to implement, and therefore suits well for the design and optimization of compliant kinematics.

Specimen positioning effect on microshear test: Non-linear finite element analysis

2012 ◽  
Vol 28 ◽  
pp. e15-e16
Author(s):  
L.H.A. Raposo ◽  
L.C.M. Dantas ◽  
T.A. Xavier ◽  
A.G. Pereira ◽  
A. Versluis ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Element Analysis ◽  
Linear Finite Element ◽  
Non Linear

Limit Loads for Laterally Loaded I-Section Beams With Consideration of Shear

2003 ◽  
Vol 47 (02) ◽  
pp. 83-91
Author(s):  
L. Belenkiy ◽  
Y. Raskin
Keyword(s):  
Physical Model ◽  
Limit Load ◽  
Nonlinear Finite Element ◽  
Shear Forces ◽  
Element Analysis ◽  
Limit Loads ◽  
Closed Form Solutions ◽  
Engineering Technique ◽  
Laterally Loaded ◽  
The Web

The paper examines an effect of shear forces on limit load for I-section beams carrying later alloads. The problem is solve don the basis of a physical model, which enables one to take into account the effect of a resistance of beam flanges to the plastic shears train in the web of the beam. The physical model for the evaluation of limit loads was veriŽed using nonlinear finite element analysis. An engineering technique for the calculation of limit loads for shiphull beams subjected to large shear forces was developed using this model. As illustrative examples, the paper shows the application of the proposed technique to obtain closed-form solutions for the prediction of limit loads.

Spring constants of filament-wound composite circular rings

2001 ◽  
Vol 215 (2) ◽  
pp. 211-226 ◽  
Author(s):  
P C Tse ◽  
S R Reid ◽  
S P Ng
Keyword(s):  
Three Dimensional ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Composite Ring ◽  
Filament Wound ◽  
Dimensional Finite Element ◽  
Filament Wound Composite ◽  
Circular Rings ◽  
Three Dimensional Finite Element ◽  
Wound Composite

Closed-form solutions from complementary strain energy are derived for the spring stiffnesses of mid-surface symmetric, filament-wound, composite circular rings under unidirectional loading. A three-dimensional finite element analysis (FEA) including the effects of transverse shear has also been applied to study the problem. Four > 45° and four > 75° E-glass/epoxy composite rings of odd numbers of covers were tested. Comparisons of the results obtained from the two methods with experimental data are made and the results are found to be in good agreement. The FEA prediction of stiffness is always higher than the theoretical result. The relationships between the spring stiffnesses and the winding angles and geometry of the filament-wound composite ring are considered and discussed.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

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