Torsion in bars of polygonal profile, with allowance for stress-function characteristics

1968 ◽  
Vol 4 (8) ◽  
pp. 88-94 ◽  
Author(s):  
I. V. Goncharyuk ◽  
V. L. Rvachev ◽  
L. I. Shklyarov
Keyword(s):  
Stress Function ◽  
Polygonal Profile

scholarly journals Data-driven graph drawing techniques with applications for conveyor systems

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Simone Göttlich ◽  
Sven Spieckermann ◽  
Stephan Stauber ◽  
Andrea Storck
Keyword(s):  
Real World ◽  
Connected Graph ◽  
Stress Function ◽  
Graph Drawing ◽  
Point Of View ◽  
Data Driven ◽  
Challenging Problem ◽  
Conveyor System ◽  
System Graph ◽  
Real World Problems

AbstractThe visualization of conveyor systems in the sense of a connected graph is a challenging problem. Starting from communication data provided by the IT system, graph drawing techniques are applied to generate an appealing layout of the conveyor system. From a mathematical point of view, the key idea is to use the concept of stress majorization to minimize a stress function over the positions of the nodes in the graph. Different to the already existing literature, we have to take care of special features inspired by the real-world problems.

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

A MOISTURE STRESS INDEX FOR WHEAT BY MEANS OF A MODULATED SOIL MOISTURE BUDGET

1968 ◽  
Vol 48 (5) ◽  
pp. 535-544 ◽  
Author(s):  
A. R. Mack ◽  
W. S. Ferguson
Keyword(s):  
Soil Moisture ◽  
Stress Function ◽  
Potential Evapotranspiration ◽  
Moisture Stress ◽  
Moisture Distribution ◽  
Stress Index ◽  
Wheat Crop ◽  
Moisture Budget ◽  
Dough Stage ◽  
Soil Moisture Budget

Actual evapotranspiration (AE), soil moisture distribution, and moisture stress for a wheat crop (PE-AE) were estimated by the modulated soil moisture budget of Holmes and Robertson. The estimated soil moisture was reasonably well correlated with soil moisture measured weekly by means of gypsum blocks. Wheat yields from experimental plots in the corresponding area were related more closely to the moisture stress function (PE-AE: r = − 0.83), than to the seasonal precipitation (r = 0.62), the potential evapotranspiration (PE) or the evapotranspiration ratio (AE/PE). Regression analyses showed that the grain yields were reduced by an average of 156 (±sb = 40) kg/ha per cm of moisture stress from emergence to harvest, or by 311 and 69 kg/ha per cm of stress, from the fifth-leaf to the soft-dough stage and from the soft-dough stage to maturity, respectively. The moisture stress function may be used to characterize the soil–plant–atmosphere environment for the growing season of a crop. Precipitation and evapotranspiration data are presented annually for three standardized growing periods at Brandon from 1921 to 1963.

Zero Gravity Validation of Smart Aperture Antennas

1999 ◽  
Author(s):  
Hwan-Sik Yoon ◽  
Gregory Washington
Keyword(s):  
Spherical Shell ◽  
Analytical Model ◽  
Stress Function ◽  
Spherical Shape ◽  
Element Model ◽  
Shallow Spherical Shell ◽  
Zero Gravity ◽  
Governing Equations ◽  
Homogeneous Solutions ◽  
Calculated Stress

Abstract In this study, a smart aperture antenna of spherical shape is modeled and experimentally verified. The antenna is modeled as a shallow spherical shell with a small hole at the apex for mounting. Starting from five governing equations of the shallow spherical shell, two governing equations are derived in terms of a stress function and the axial deflection using Reissner’s approach. As actuators, four PZT strip actuators are attached along the meridians separated by 90 degrees respectively. The forces developed by the actuators are considered as distributed pressure loads on the shell surface instead of being applied as boundary conditions like previous studies. This new way of applying the actuation force necessitates solving for the particular solutions in addition to the homogeneous solutions for the governing equations. The amount of deflections is evaluated from the calculated stress function and the axial deflection. In addition to the analytical model, a finite element model is developed to verify the analytical model on the various surface positions of the reflector. Finally, an actual working model of the reflector is built and tested in a zero gravity environment, and the results of the theoretical model are verified by comparing them to the experimental data.

Graphical-Numerical Solution of Problems of Saint-Venant Torsion and Bending

1953 ◽  
Vol 20 (3) ◽  
pp. 321-326
Author(s):  
B. A. Boley
Keyword(s):  
Cross Section ◽  
Stress Function ◽  
Arbitrary Cross Section ◽  
Successive Approximations ◽  
Shear Stresses ◽  
Shearing Stress ◽  
First Approximation ◽  
Difference Form ◽  
Bending Of Beams

Abstract A simple successive-approximations procedure for the solution of the problems of Saint-Venant torsion and bending of beams of arbitrary cross section is presented. The shear stresses in a cross section of the beam are first calculated from the formulas valid for thin-walled sections, on the basis of an assumed set of lines of shearing stress. From these a first approximation to the stress function of either the torsion or the bending problem is found. The second approximation to the stress function is then obtained from the governing equation of the problem, expressed in finite-difference form; this in turn allows the determination of an improved set of lines of shearing stress, and hence of the shearing stress itself. The procedure can be repeated until the results of two successive steps are sufficiently close. Applications are presented for a beam cross section for which the exact solutions are known, and it is shown that no further difficulties arise in applications to more complicated shapes.

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