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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[general, mechanics] (i.e., center-seeking) A rotating object is subjected to a continuous force that applies a change in direction irrespective of time. The rate of change in directional velocity (vector velocity) provides the angular acceleration, which is directly linked to the centripetal force changing the direction. The acceleration tied to the angular motion is defined by the angular velocity (ω) as a = v2/r = ω2r, where v is the tangential component of the motion of an object in a circular path. This acceleration is directed toward the center of the circular motion (m/s2) (see Figure A.23).
Fluid kinematics
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
where V denotes the tangential component of velocity along an element of the fluid. It is the Curl of the velocity field. The rate of rotation about the z-axis is the average of the two angles of rotation. It is also seen that the double integral in x-y plane can be reduced to a line integral along a closed curve. It is equal to the total strength of all vortex filaments that pass a closed curve. Circulation has the dimension L2T−1.
3D mixed finite elements for curved, flat piezoelectric structures
Published in International Journal of Smart and Nano Materials, 2019
Martin Meindlhumer, Astrid Pechstein
We assume to be a finite element mesh of the domain . The unit vector denotes the outer normal on element or domain boundaries or . In general on a (boundary) surface a vector field can be split into a normal component and a tangential component . A tensor field has a normal vector on a surface , which analogously can be split into a normal component and tangential component .
A novel material point method (MPM) based needle-tissue interaction model
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2021
Murong Li, Yong Lei, Dedong Gao, Yingda Hu, Xiong Zhang
MPM contact couples two material point objects based on particle to particle contact algorithm. As can be seen in Figure 3, when needle points and the tissue points are interpolated into the same mesh node, the node is to be detected as a contact node (See yellow pentagram). The interaction force is decomposed to the normal component (the radial direction perpendicular to the cross section of the needle body) and tangential component (opposite direction of the needle velocity). Figure 4 shows the normal vector and tangential vector of the needle surface. The vectors of tissue contact surface is just opposite with that of the needle’s.
Large deformation mixed finite elements for smart structures
Published in Mechanics of Advanced Materials and Structures, 2020
For some domain D, let denote its boundary. We denote the outward unit normal by . The normal and tangential component of a vector field are defined as and , respectively. For a tensor field σt we define the normal vector and use its normal and tangential components σnn and .