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

2013 ◽  
Vol 42 (12) ◽  
pp. 1827-1845 ◽  
Author(s):  
Xavier Romão ◽  
Raimundo Delgado ◽  
Aníbal Costa
Keyword(s):  
Closed Form ◽  
Limit States ◽  
Closed Form Solutions ◽  
The Mean

A Benchmark Study on Crushing and Cutting of Plated Structures

1997 ◽  
Vol 41 (02) ◽  
pp. 147-160
Author(s):  
Jeom Kee Paik ◽  
Tomasz Wierzbicki
Keyword(s):  
Experimental Data ◽  
Closed Form ◽  
Dynamic Effects ◽  
Crushing Strength ◽  
Closed Form Solutions ◽  
Cutting Resistance ◽  
Benchmark Study ◽  
Stiffened Structures ◽  
The Mean

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.

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

2009 ◽  
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.

Modeling Variation Propagation Through a Manufacturing Process

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.

The Lure of the Mean Axes

2006 ◽  
Vol 74 (3) ◽  
pp. 497-504 ◽  
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.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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