scholarly journals Discussion: “Numerical and Graphical Method of Solving Two-Dimensional Stress Problems” (Poritsky, H., Snively, H. D., and Wylie, Jr., C. R., 1939, ASME J. Appl. Mech., 6, pp. A63–A66)

1940 ◽  
Vol 7 (1) ◽  
pp. A39
Author(s):  
L. F. Richardson
Keyword(s):  
Graphical Method ◽  
Two Dimensional

A RAPID GRAPHICAL SOLUTION FOR THE AEROMAGNETIC ANOMALY OF THE TWO‐DIMENSIONAL TABULAR BODY

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 963-970 ◽  
Author(s):  
R. J. Bean
Keyword(s):  
Inclination Angle ◽  
Geomagnetic Field ◽  
Graphical Method ◽  
The Body ◽  
Two Dimensional ◽  
Half Maximum ◽  
Graphical Solution ◽  
Magnetization Direction ◽  
Maximum Slope ◽  
Magnetic Latitude

A graphical method of determining the depth and other parameters of two‐dimensional tabular bodies by analysis of aeromagnetic anomalies is outlined. The method uses the inflection and half maximum slope points of anomalies having either two flanks or a single high gradient. Ratios of distances between these points are used to obtain a solution. The problem is simplified by combining angles of dip, magnetization direction and the inclination of the geomagnetic field in the plane of the profile into an apparent inclination angle. By use of the graphs, the depth, width, and apparent inclination angle can be determined rapidly from only a few simple measurements, so the method is especially suited for rapid interpretation of large aeromagnetic surveys by use of the observed profiles. Graphs are also given for locating the center or edge of the block, and the product of the intensity of magnetization and the dip of the body can be obtained by utilizing the maximum slope of the anomaly. By use of alternate values of the apparent inclination angle, the method can be used for any direction of magnetization at any magnetic latitude.

Two-Dimensional Rigid-Body Collisions With Friction

1992 ◽  
Vol 59 (3) ◽  
pp. 635-642 ◽  
Author(s):  
Yu Wang ◽  
Matthew T. Mason
Keyword(s):  
Rigid Body ◽  
Graphical Method ◽  
Correct Identification ◽  
Two Dimensional ◽  
Contact Mode ◽  
New Class ◽  
Tangential Impact ◽  
Approach Velocity ◽  
Conservation Principles ◽  
Analytical Expressions

This paper presents an analysis of a two-dimensional rigid-body collision with dry friction. We use Routh’s graphical method to describe an impact process and to determine the frictional impulse. We classify the possible modes of impact, and derive analytical expressions for impulse, using both Poisson’s and Newton’s models of restitution. We also address a new class of impacts, tangential impact, with zero initial approach velocity. Some methods for rigid-body impact violate energy conservation principles, yielding solutions that increase system energy during an impact. To avoid such anomalies, we show that Poisson’s hypothesis should be used, rather than Newton’s law of restitution. In addition, correct identification of the contact mode of impact is essential.

On: “A rapid graphical method for the interpretation of the self‐potential anomaly over a two‐dimensional inclined sheet of finite depth extent” by H. V. Ram Babu and D. Atchuta Rao (GEOPHYSICS, 53, 1126–1128, August 1988).

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1215-1216 ◽  
Author(s):  
L. Eskola ◽  
H. Hongisto
Keyword(s):  
Graphical Method ◽  
Theoretical Models ◽  
Finite Depth ◽  
The Self ◽  
Inversion Method ◽  
Two Dimensional ◽  
Depth Extent ◽  
Self Potential ◽  
Graphical Algorithm ◽  
Inclined Sheet

Ram Babu and Atchuta Rao (1988a, b) presented a graphical algorithm for the interpretation of a self‐potential anomaly over a sheet. Ram Babu and Atchuta Rao (1988b) also presented an inversion method based on iterative optimization for the self‐potential anomalies caused by spherical, cylindrical, and sheetlike bodies. The theoretical models on which the algorithms are based are very simple: for the sphere, an electrostatic dipole; for the cylinder, a line dipole; and for the sheet two line poles, the negative one along the upper edge of the sheet and the positive one along its lower edge.

scholarly journals Stability of trusses by graphic statics

2021 ◽  
Vol 8 (6) ◽  
pp. 201970
Author(s):  
Allan McRobie ◽  
Cameron Millar ◽  
William F. Baker
Keyword(s):  
Axial Force ◽  
Graphical Representation ◽  
Graphical Method ◽  
Three Dimensional ◽  
Weighted Sum ◽  
Two Dimensional ◽  
Rotational Stiffness ◽  
Graphic Statics ◽  
Out Of Plane ◽  
Pinned Joints

This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell–Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the ‘product forces’ that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses.

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