A Benchmark Study on Crushing and Cutting of Plated Structures

A benchmark study on several closed-form solutions for the mean crushing strength and the cutting resistance of plated structures during collision or grounding is carried out by comparing theoretical solutions with experimental data. Based on expressions which have been derived for unstiffened structures, an extension of the methods is proposed for longitudinally and/or transversely stiffened structures. Dynamic effects on the crushing and cutting response are discussed, and applicability of the quasistatic formulations to analyze the crushing and cutting damage of the structure in the dynamic situations is investigated.

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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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Variation Analysis of Position, Velocity, and Acceleration of Two-Dimensional Mechanisms by the Direct Linearization Method

Volume 5: 35th Design Automation Conference, Parts A and B ◽

10.1115/detc2009-86236 ◽

2009 ◽

Cited By ~ 1

Author(s):

Robert C. Leishman ◽

Kenneth W. Chase

Keyword(s):

Closed Form ◽

Process Variations ◽

Linearization Method ◽

Analysis Tool ◽

Large Set ◽

Computationally Efficient ◽

Closed Form Solutions ◽

Direct Linearization ◽

The Mean ◽

Kinematic Performance

Velocity and acceleration analysis is an important tool for predicting the motion of mechanisms. The results, however, may be inaccurate when applied to manufactured products, due to the process variations which occur in production. Small changes in dimensions can accumulate and propagate in an assembly, which may cause significant variation in critical kinematic performance parameters. A new statistical analysis tool is presented for predicting the effects of variation on mechanism kinematic performance. It is based on the Direct Linearization Method developed for static assemblies. The solution is closed form, and may be applied to 2-D, open or closed, multi-loop mechanisms, employing common kinematic joints. It is also shown how form, orientation, and position variations may be included in the analysis to analyze variations that occur in kinematic joints. Closed form solutions eliminate the need of generating a large set of random assemblies, and analyzing them one-by one, to determine the expected range of critical variables. Only two assemblies are analyzed to characterize the entire population. The first determines the performance of the mean, or average assembly, and the second estimates the range of variation about the mean. The system is computationally efficient and well suited for design iteration.

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On Quasi-Static Crushing of a Stiffened Square Tube

Journal of Ship Research ◽

10.5957/jsr.1996.40.3.258 ◽

1996 ◽

Vol 40 (03) ◽

pp. 258-267 ◽

Cited By ~ 1

Author(s):

Jeom Kee Paik ◽

Jang Young Chung ◽

Min Sung Chun

Keyword(s):

Experimental Data ◽

Plate Thickness ◽

Simple Expression ◽

Stiffened Plates ◽

Stiffened Plate ◽

Simple Analytical Expression ◽

Crushing Strength ◽

Axial Crushing ◽

The Mean ◽

Thin Walled

The aims of this study are to obtain experimental data on the crushing of stiffened square tubes, and to develop a simple analytical expression for predicting the mean crushing strength of stiffened plates making up a plated structure. A series of axial crushing tests in a quasistatic condition was carried out on thin-walled square tubes which were composed of four identical panels. Specimens with longitudinal and/or transverse stiffeners, including unstiffened specimens, were tested, varying dimensions of plate and stiffener. The effective crushing length and the mean crushing strength of the test specimens were investigated. It was concluded that a longitudinally stiffened plate could reasonably be replaced by an unstiffened plate with equivalent plate thickness. Based on this approach, a simple expression for the effective crushing length and the mean crushing strength of stiffened plates was derived.

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Alternative closed-form solutions for the mean rate of exceedance of structural limit states

Earthquake Engineering & Structural Dynamics ◽

10.1002/eqe.2300 ◽

2013 ◽

Vol 42 (12) ◽

pp. 1827-1845 ◽

Cited By ~ 7

Author(s):

Xavier Romão ◽

Raimundo Delgado ◽

Aníbal Costa

Keyword(s):

Closed Form ◽

Limit States ◽

Closed Form Solutions ◽

The Mean

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Generalized Reference Basis Model Updating in Structural Dynamics

Volume 1B: 16th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc97/vib-4151 ◽

1997 ◽

Author(s):

Rachel Kenigsbuch ◽

Yoram Halevi

Keyword(s):

Experimental Data ◽

Closed Form ◽

Prior Knowledge ◽

Structural Dynamics ◽

Optimization Problem ◽

Model Updating ◽

Optimization Criterion ◽

Constrained Optimization Problem ◽

Closed Form Solutions ◽

Insight Into

Abstract The paper considers the problem of updating an analytical model from experimental data. The approach that is taken is the reference basis, where some of the parameters are considered to be completely accurate while the others are updated by solving a constrained optimization problem. The main results of this paper are closed form solutions to these problems with general weighting matrices in the optimization criterion. These are generalizations of several model reference updating problems that were solved and reported in the literature. The importance of this generalization is the ability to incorporate prior knowledge regarding the accuracy of the model in specified areas into the method. Another aspect of this work is the investigation of geometrical interpretation of the results which provides insight into the mechanism of the updating process. The advantages of the new updating schemes are demonstrated by means of examples.

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Modeling Variation Propagation Through a Manufacturing Process

Volume 3a: 8th Design for Manufacturing Conference ◽

10.1115/detc2003/dfm-48149 ◽

2003 ◽

Author(s):

Daniel Kern ◽

Anna Thornton

Keyword(s):

Standard Deviation ◽

Closed Form ◽

Manufacturing Process ◽

Dimensional Change ◽

New Method ◽

Closed Form Solutions ◽

Effective Manner ◽

Variation Propagation ◽

The Mean ◽

High Level

Companies are under increased pressure to manufacture products that have a high level of quality. Manufacturing products with a high level of quality in a cost-effective manner requires the products to be designed so that they can be manufactured with an acceptable level of variation. Creating a new design that can be produced with the necessary level of variation has historically been a very challenging problem. A new method for calculating the effect a manufacturing process has on the mean and standard deviation of a distribution is presented. This new method is founded on the concept of characterizing a manufacturing process with two math functions called DeltaP and SigmaP. DeltaP and SigmaP represent the theory of Process Imparted Dimensional Change and Process Imparted Variation. Using these functions, closed-form solutions for the mean and standard deviation of a distribution exiting a manufacturing process can be calculated. The authors present the background of the theory as well as the derivation of the closed form solutions for the output mean and standard deviation from a generic manufacturing process. The derivation is followed by a simple example to demonstrate the method.

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The Lure of the Mean Axes

Journal of Applied Mechanics ◽

10.1115/1.2338060 ◽

2006 ◽

Vol 74 (3) ◽

pp. 497-504 ◽

Cited By ~ 19

Author(s):

Leonard Meirovitch ◽

Ilhan Tuzcu

Keyword(s):

Closed Form ◽

Analytical Solutions ◽

Numerical Solutions ◽

Equations Of Motion ◽

Space Structures ◽

Aerodynamic Forces ◽

State Equations ◽

Flexible Bodies ◽

Closed Form Solutions ◽

The Mean

A variety of aerospace structures, such as missiles, spacecraft, aircraft, and helicopters, can be modeled as unrestrained flexible bodies. The state equations of motion of such systems tend to be quite involved. Because some of these formulations were carried out decades ago when computers were inadequate, the emphasis was on analytical solutions. This, in turn, prompted some investigators to simplify the formulations beyond all reasons, a practice continuing to this date. In particular, the concept of mean axes has often been used without regard to the negative implications. The allure of the mean axes lies in the fact that in some cases they can help decouple the system inertially. Whereas in the case of some space structures this may mean complete decoupling, in the case of missiles, aircraft, and helicopters the systems remain coupled through the aerodynamic forces. In fact, in the latter case the use of mean axes only complicates matters. With the development of powerful computers and software capable of producing numerical solutions to very complex problems, such as MATLAB and MATHEMATICA, there is no compelling reason to insist on closed-form solutions, particularly when undue simplifications can lead to erroneous results.

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