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Integrating fields
Published in A.V. Durrant, Vectors in Physics and Engineering, 2019
A plane curve is described by an equation relating x and y, for example, the parabola path in Fig 6.7 is described by y = x2. More generally a path of integration may be a curve in three dimensions (such as the helix shown in Fig 6.13). Such curves are best described by introducing a single variable t called the parameter of the curve. The cartesian coordinates of a point on the curve can then be expressed in terms of t.
Plate-Bending Theory
Published in Ansel C. Ugural, Plates and Shells, 2017
The curvature (equal to the reciprocal of the radius of curvature) of a plane curve is defined as the rate of change of the slope angle of the curve with respect to distance along the curve. Because of assumption 1 of Section 3.3, the square of a slope may be regarded as negligible, and the partial derivatives of Equations 3.3a represent the curvatures of the plate. Therefore, the curvatures κ (kappa) at the midsurface in planes parallel to the xz, yz, and xy planes are, respectively, 1rx=∂∂x(∂w∂x)=κx1ry=∂∂y(∂w∂y)=κy1rxy=∂∂x(∂w∂y)=κxy where κxy=κyx.
A new method of multi-scale fracture identification in tight gas sandstone reservoir
Published in Geosystem Engineering, 2019
Tao Wu, Yuezhi Wang, Bin Fu, Peng Wu
The curvature of a plane curve describes the rotational rate of the tangent at a particular point and is closely related to the second derivative of the curve defining the surface which indicates to what extent the curve deviates from the straight line (see Equation 1). The more bent the surface is, the larger will be the curvature which reflects a high probability of fractures existence.