SIMPLIFIED CLOSED-FORM SOLUTION FOR THE DETERMINATION OF THE MOMENT-CURVATURE RESPONSE OF A CIRCULAR RC SECTION

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of Gambier, by constructing step by step an appropriate analytical technique. The developed procedure yields a general exact closed form solution of this equation, valid for specific values of the parameters involved and containing two arbitrary (free) parameters evaluated by the relevant initial conditions. We finally verify this technique by applying it to two specific sets of parameter values of the equation under consideration.

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Determination of Closed Form Solution for Acceptance Sampling Using ANN

Quality Assurance ◽

10.1080/10529410590930002 ◽

2005 ◽

Vol 11 (1) ◽

pp. 43-61 ◽

Cited By ~ 3

Author(s):

D. Vasudevan ◽

V. Selladurai ◽

P. Nagaraj

Keyword(s):

Closed Form ◽

Closed Form Solution ◽

Form Solution ◽

Acceptance Sampling

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On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

Journal of Lubrication Technology ◽

10.1115/1.3453205 ◽

1978 ◽

Vol 100 (3) ◽

pp. 442-444 ◽

Cited By ~ 2

Author(s):

B. C. Majumdar

Keyword(s):

Analytical Solution ◽

Pressure Distribution ◽

Closed Form ◽

Closed Form Solution ◽

Journal Bearings ◽

Form Solution ◽

Performance Characteristics ◽

Gas Bearing ◽

Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

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Determination of Eigenstresses from Curvature Data

MRS Proceedings ◽

10.1557/proc-276-221 ◽

1992 ◽

Vol 276 ◽

Cited By ~ 2

Author(s):

Mauro Ferrari ◽

Marie Weber

Keyword(s):

Structural Analysis ◽

Closed Form ◽

Mechanical Systems ◽

Closed Form Solution ◽

Form Solution ◽

Curvature Measurements

ABSTRACTCurvature measurements are generally employed in conjunction with elementary structural analysis to estimate deposition stresses in miniaturized electro-mechanical systems. In this paper the validity of this procedure is discussed by presenting a closed form solution for a bilayer subject to nonuniform intrinsic straining, and comparing the exact stress-curvature relations with the oft-used formulae of Stoney and Brenner-Senderoff.

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A Closed-Form Solution to the Crank Position Corresponding to the Maximum Velocity of the Slider in a Centric Slider-Crank Mechanism

Journal of Mechanical Design ◽

10.1115/1.2181997 ◽

2005 ◽

Vol 128 (3) ◽

pp. 654-656 ◽

Cited By ~ 4

Author(s):

W. J. Zhang ◽

Q. Li

Keyword(s):

Closed Form ◽

Classical Problem ◽

Closed Form Solution ◽

Maximum Velocity ◽

Form Solution ◽

Machine Design ◽

Rotary Engine ◽

Engine Systems ◽

Crank Mechanism

This paper revisits a classical problem in kinematics, specifically determination of the crank position corresponding to the maximum velocity of the slider in the centric slider-crank mechanism. This position is often critical in designing products constructed using the slider-crank mechanism, e.g., industrial sewing machinery, rotary engine systems, etc. In current literature, the numerical, graphical, or approximate closed-form solution to this problem is available. In this paper, an exact closed-form solution is derived. With this new closed-form solution, it is found that there exist significant errors in an approximate closed-form solution which can be found from many machine design text books for a practica1 use.

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Closed-Form Solution to the Noncoplanar P4P Problem for Uncalibrated Camera

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.145.6 ◽

2011 ◽

Vol 145 ◽

pp. 6-10

Author(s):

Yang Guo

Keyword(s):

Closed Form ◽

Affine Transformation ◽

Closed Form Solution ◽

Polynomial Equation ◽

Form Solution ◽

Potential Candidate ◽

Degree Polynomial ◽

Fast Determination ◽

Hand Eye Coordination

This paper presents a closed-form solution to determination of the position and orientation of a perspective camera with two unknown effective focal lengths for the noncoplanar perspective four point (P4P) problem. Given four noncoplanar 3D points and their correspondences in image coordinate, we convert perspective transformation to affine transformation, and formulate the problem using invariance to 3D affine transformation and arrive to a closed-form solution. We show how the noncoplanar P4P problem is cast into the problem of solving an eighth degree polynomial equation in one unknown. This result shows the noncoplanar P4P problem with two unknown effective focal lengths has at most 8 solutions. Last, we confirm the conclusion by an example. Although developed as part of landmark-guided navigation, the solution might well be used for landmark-based tracking problem, hand-eye coordination, and for fast determination of interior and exterior camera parameters. Because our method is based on closed-form solution, its speed makes it a potential candidate for solving above problems.

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Construct the closed-form solution of A-net of Petri nets by case study

Advances in Mechanical Engineering ◽

10.1177/1687814017691210 ◽

2017 ◽

Vol 9 (2) ◽

pp. 168781401769121 ◽

Cited By ~ 2

Author(s):

Daniel Yuh Chao ◽

Tsung Hsien Yu

Keyword(s):

Petri Nets ◽

Closed Form ◽

Closed Form Solution ◽

Form Solution ◽

Order System ◽

Deadlock Avoidance ◽

Prevention Policy ◽

Current State ◽

The Moment

After our researches on the effect of a non-sharing resource in a kth order which is the concept of customization manufacturing, in this article we extend the research on the closed-form solution of control-related states to the so-called A-net which has one top non-sharing circle subnet connected to the idle place of left process in a deficient kth order system and is the fundamental model of different productions sharing the same common parts in manufacturing. The formulas just are depended on the parameter k and states’ function of top non-sharing circle subnet for a subclass of nets with k sharing resources. By combining the concept of the partial deadlock avoidance/prevention policy, the moment to launch resource (controller) allocation based on the current state, and the construction of closed-form solution for deficient kth order system, it can realize the concept of dynamic non-sharing processes’ allocation.

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