An Algorithm for Reducing the Size of Finite Element Closed-Form Source Code Files

2009 ◽  
Author(s):  
Sara McCaslin ◽  
Kent Lawrence
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Source Code ◽  
Simple Algorithm ◽  
Higher Order ◽  
Error Estimator ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Large Source

Closed-form solutions, as opposed to numerically integrated solutions, can now be obtained for many problems in engineering. In the area of finite element analysis, researchers have been able to demonstrate the efficiency of closed-form solutions when compared to numerical integration for elements such as straight-sided triangular [1] and tetrahedral elements [2, 3]. With higher order elements, however, the length of the resulting expressions is excessive. When these expressions are to be implemented in finite element applications as source code files, large source code files can be generated, resulting in line length/ line continuation limit issues with the compiler. This paper discusses a simple algorithm for the reduction of large source code files in which duplicate terms are replaced through the use of an adaptive dictionary. The importance of this algorithm lies in its ability to produce manageable source code files that can be used to improve efficiency in the element generation step of higher order finite element analysis. The algorithm is applied to Fortran files developed for the implementation of closed-form element stiffness and error estimator expressions for straight-sided tetrahedral finite elements through the fourth order. Reductions in individual source code file size by as much as 83% are demonstrated.

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.

scholarly journals Closed-form solutions of hole distortion for use in deep-hole drilling measurements of residual stress in orthotropic plates

2016 ◽  
Vol 52 (2) ◽  
pp. 77-82 ◽  
Author(s):  
Carlos Garza ◽  
Anton Shterenlikht ◽  
Martyn J Pavier ◽  
David J Smith
Keyword(s):  
Residual Stress ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Hole Drilling ◽  
Shear Stresses ◽  
Deep Hole ◽  
Element Analysis ◽  
Deep Hole Drilling ◽  
Closed Form Solutions

The measurement of residual stress using the deep-hole drilling method relies on the evaluation of the distortion of a hole in a plate under the action of far-field direct and shear stresses. While closed-form solutions exist for the isotropic materials, in previous work for orthotropic materials, finite element analysis has been used to find the distortion. In this technical note, Lekhnitskii’s analysis is used to find closed-form solutions for the distortion of a circular hole in an orthotropic plate. The results are compared with those of finite element analysis for a range of material properties with excellent agreement.

An Improved Method for Designing Flexure-Based Nonlinear Springs

2012 ◽  
Author(s):  
Qiaoling Meng ◽  
Giovanni Berselli ◽  
Rocco Vertechy ◽  
Vincenzo Parenti Castelli
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Compliant Mechanisms ◽  
Empirical Equations ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Nonlinear Springs ◽  
Aspect Ratios ◽  
Analytical Relations ◽  
Flexural Hinges

Monolithic Flexure-based Compliant Mechanisms (MFCM) can functionally act as nonlinear springs by providing a desired load-displacement profile at one point on their structure. Once the MFCM topology is chosen, these particular springs can be conveniently synthesized by resorting to the well-known Pseudo-Rigid-Body approximation, whose accuracy strongly depends on the modeling precision of the flexures’ principal compliance. For various types of flexures, closed-form solutions have been proposed which express the compliance factors as functions of the flexure dimensions. Nonetheless, the reliability of these analytical relations is limited to slender, beam-like, hinges undergoing small deflections. In order to overcome such limitations, this paper provides empirical equations, derived from finite element analysis, that can be used for the optimal design of circular, elliptical, and corner-filleted flexural hinges with general aspect ratios on the basis of both principal compliance and maximum bearable stress. As a case study, a nonlinear spring conceived as a four-bar linkage MFCM is synthesized and simulated by means of finite element analysis. Numerical results confirm that the aforementioned empirical equations outperform their analytical counterparts when modeling thick cross-section hinges undergoing large deflections.

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