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Using quadratic shape functions, we reduce approximation errors inherent to methods based on linear finite elements.
The presented second-order MPM uses a special set of piecewise quadratic shape functions to circumvent the well-known issue of producing zero nodal mass contributions.
Based on this theory, a finite element formulation and a user-defined quadrilateral serendipity element with quadratic shape functions and nine degrees of freedom (DOFs) is presented.
Second, the boundary contour method formulations are obtained by introducing quadratic shape functions and Green's functions [Ding, H.J., Jiang, A.M., 2004.
In contrast, for UPN and LPN, approximately one third of the curves had a distinct positively oriented quadratic shape, one third suggested a piecewise linear pattern with a breakpoint at roughly 25% MVC, and one third could fit both profiles.
The present paper describes the results of the experimental investigation of the damping system consisting of a steel plate of quadratic shape (wedge) covered on one side by a strip of absorbing layer.
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Models were estimated with three to seven groups and linear or quadratic shapes using adiposity z scores at eight time points.
Since we expect the curve to consist of two very smooth pieces, joined at a more rapidly changing junction point where the breast meets the surrounding torso, this modest increase in flexibility over simple linear or quadratic shapes is appealing and the suitability of this choice has been endorsed by repeated effective use over a wide variety of breast curves of this type.
For EKS and SIL ecotypes, the functional relationship between percent cover and historic MAP was characterized as quadratic in shape (P < 0.0001 in each case).
Two-photon absorption results in a non-linear energy distribution that is radially dependent perpendicular to the axis of propagation and dependent on distance from the focal point along the axis of propagation; the energy distribution is quadratic in shape in both of these directions [ 5, 6].
The patterns noticed were: linear (positive or negative slopes) or quadratic (positive/convex shaped or negative/concave shaped curves).
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