A Conical Beam Finite Element for Rotor Dynamics Analysis

The development of finite element formulations for use in rotor dynamics analysis has been the subject of many recent publications. These works have included the effects of rotatory inertia, gyroscopic moments, axial load, internal damping, and shear deformation. However, for most closed-form solutions, the element geometry has been limited to a cylindrical cross-section. This paper extends these previous works by developing a closed-form expression including all of the above effects in a linearly tapered conical cross-section element. Results are also given comparing the formulation to previously published examples, to stepped cylinder representations of conical geometry, and to a general purpose finite element elasticity solution. The elimination of numerical integration in the generation of the element matrices, and the ability of the element to represent both conical and cylindrical geometries, make this formulation particularly suited for use in rotor dynamic analysis computer programs.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.856.147 ◽

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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Closed-Form Expression for Temperature in a Semi-Infinite Solid Due to a Fast Moving Surface Heat Source

Journal of Tribology ◽

10.1115/1.2920699 ◽

1991 ◽

Vol 113 (4) ◽

pp. 828-831 ◽

Cited By ~ 2

Author(s):

J. A. Tichy

Keyword(s):

Heat Source ◽

Closed Form ◽

Frictional Contact ◽

Closed Form Expression ◽

Moving Heat Source ◽

Convolution Integral ◽

Form Expression ◽

Exponential Integral ◽

Surface Conditions ◽

Closed Form Solutions

In the thermal analysis of an asperity on a sliding surface in frictional contact with an opposing surface, conditions are often idealized as a moving heat source. The solution to this problem at arbitrary Pe´cle´t number in terms of a singular integral is well known. In this study, closed-form solutions are found in terms of the exponential integral for high Pe´cle´t number. Fortunately, the closed-form solutions are accurate at Pe´cle´t number of order one. While several restrictions are necessary, the closed-form expressions offer considerable numerical savings relative to evaluations of the convolution integral.

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Elastic–plastic deformation and residual stresses in helical springs

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-04-2019-0085 ◽

2019 ◽

Vol 16 (3) ◽

pp. 448-475

Author(s):

Vladimir Kobelev

Keyword(s):

Residual Stresses ◽

Closed Form ◽

Cross Section ◽

Circular Cross Section ◽

Content Type ◽

Closed Form Solutions ◽

Helical Springs ◽

First Case ◽

Setting Process ◽

The Wire

Purpose The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs. Design/methodology/approach For helical compression or tension springs, a spring wire is twisted. In the first case, the torsion of the straight bar with the circular cross-section is investigated, and, for derivations, the StVenant’s hypothesis is presumed. Analogously, for the torsion helical springs, the wire is in the state of flexure. In the second case, the bending of the straight bar with the rectangular cross-section is studied and the method is based on Bernoulli’s hypothesis. Findings For both cases (compression/tension of torsion helical spring), the closed-form solutions are based on the hyperbolic and on the Ramberg–Osgood material laws. Research limitations/implications The method is based on the deformational formulation of plasticity theory and common kinematic hypotheses. Practical implications The advantage of the discovered closed-form solutions is their applicability for the calculation of spring length or spring twist angle loss and residual stresses on the wire after the pre-setting process without the necessity of complicated finite-element solutions. Social implications The formulas are intended for practical evaluation of necessary parameters for optimal pre-setting processes of compression and torsion helical springs. Originality/value Because of the discovery of closed-form solutions and analytical formulas for the pre-setting process, the numerical analysis is not necessary. The analytical solution facilitates the proper evaluation of the plastic flow in torsion, compression and bending springs and improves the manufacturing of industrial components.

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An Intelligent System for Spur Gear Design and Analysis

Volume 2A: 27th Design Automation Conference ◽

10.1115/detc2001/dac-21037 ◽

2001 ◽

Author(s):

El-Sayed Aziz ◽

C. Chassapis

Keyword(s):

Finite Element ◽

Closed Form ◽

Intelligent System ◽

Tooth Profile ◽

Hertzian Contact ◽

Design Parameters ◽

Analysis Model ◽

Closed Form Solutions ◽

Gear Teeth ◽

Gear Design

Abstract A methodology for the analysis of load distribution and contact stress on gear teeth, which utilizes a combination of closed form solutions and two-dimensional finite element methods, within a constraint-based knowledge-based environment, is presented. Once the design parameters are specified, the complete process of generating the analysis model, starting from the determination of the coordinates of the tooth profile, the creation of a sector of the mating gear teeth, automatic mesh generation, boundary conditions and loading, is totally automated and transparent to the designer. The effects of non-standard geometry, load sharing on the contact zone, friction and root stresses are easily included in the model. The Finite Element Method (FEM) based results compare favorably with those obtained from closed form solutions (AGMA equations and classical Hertzian contact solution). The advantage of the approach rests in the ability to modify any of the gear design parameters such as diametral pitch, tooth profile modification etc., in an automated manner along with obtaining a better estimation of the risks of failure of the gear design on hand. The procedure may be easily extended to other types of gearing systems.

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Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed–fixed boundary condition

Composites Part B Engineering ◽

10.1016/j.compositesb.2013.10.077 ◽

2014 ◽

Vol 58 ◽

pp. 361-370 ◽

Cited By ~ 62

Author(s):

Korak Sarkar ◽

Ranjan Ganguli

Keyword(s):

Boundary Condition ◽

Closed Form ◽

Cross Section ◽

Functionally Graded ◽

Timoshenko Beams ◽

Fixed Boundary ◽

Closed Form Solutions ◽

Uniform Cross Section ◽

Fixed Boundary Condition

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Corner-Filleted Flexure Hinges

Journal of Mechanical Design ◽

10.1115/1.1372190 ◽

2000 ◽

Vol 123 (3) ◽

pp. 346-352 ◽

Cited By ~ 217

Author(s):

Nicolae Lobontiu ◽

Jeffrey S. N. Paine ◽

Ephrahim Garcia ◽

Michael Goldfarb

Keyword(s):

Finite Element ◽

Closed Form ◽

Finite Element Simulation ◽

Analytical Approach ◽

Flexure Hinge ◽

Closed Form Solutions ◽

Flexure Hinges ◽

Element Simulation ◽

Model Predictions ◽

The Right

The paper presents an analytical approach to corner-filleted flexure hinges. Closed- form solutions are derived for the in-plane compliance factors. It is demonstrated that the corner-filleted flexure hinge spans a domain delimited by the simple beam and the right circular flexure hinge. A comparison that is made with the right circular flexure hinges indicates that the corner-filleted flexures are more bending-compliant and induce lower stresses but are less precise in rotation. The finite element simulation and experimental results confirmed the model predictions.

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Closed-Form Approximate Formulas for Torsional Analysis of Hollow Tubes with Straight and Circular Edges

Journal of Mechanics ◽

10.1017/s1727719100002884 ◽

2009 ◽

Vol 25 (4) ◽

pp. 401-409 ◽

Cited By ~ 7

Author(s):

A. Doostfatemeh ◽

M. R. Hematiyan ◽

S. Arghavan

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Closed Form ◽

Cross Section ◽

Stress Function ◽

Analytical Formulas ◽

The Cross ◽

Torsional Analysis ◽

Approximate Formulas ◽

Element Method

ABSTRACTSome analytical formulas are presented for torsional analysis of homogeneous hollow tubes. The cross section is supposed to consist of straight and circular segments. Thicknesses of segments of the cross section can be different. The problem is formulated in terms of Prandtl's stress function. The derived approximate formulas are so simple that computations can be carried out by a simple calculator. Several examples are presented to validate the formulation. The accuracy of formulas is verified by accurate finite element method solutions. It is seen that the error of the formulation is small and the formulas can be used for analysis of thin to moderately thick-walled hollow tubes.

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Torsion of Composite Elastic Bars of Arbitrary Cross Section

Journal of Engineering for Industry ◽

10.1115/1.3604661 ◽

1968 ◽

Vol 90 (3) ◽

pp. 435-440 ◽

Cited By ~ 1

Author(s):

E. M. Sparrow ◽

H. S. Yu

Keyword(s):

Exact Solution ◽

Closed Form ◽

Elastic Properties ◽

Cross Section ◽

Excellent Agreement ◽

Solution Method ◽

Circular Cross Section ◽

High Accuracy ◽

Arbitrary Cross Section ◽

Closed Form Solutions

A method of analysis is presented for determining closed-form solutions for torsion of inhomogeneous prismatic bars of arbitrary cross section, the inhomogeneity stemming from the layering of materials of different elastic properties. It is demonstrated that the solution method is very easy to apply and provides results of high accuracy. As an application, solutions are obtained for the torsion of a bar of circular cross section consisting of two materials separated by a plane interface. The results are compared with those of various limiting cases and excellent agreement is found to exist. Among the limiting cases, an exact solution was derived by Green’s functions for the problem in which the interface between the materials coincides with a diameter of the circular cross section.

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