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Kinetics of a Rigid Body
Published in M Rashad Islam, A K M Monayem H Mazumder, Mahbub Ahmed, Engineering Dynamics, 2022
M Rashad Islam, A K M Monayem H Mazumder, Mahbub Ahmed
If a rigid body rotates around an axis, the moment of inertia of that body with respect to that axis means the summation of the product of square of distance from the axis and the mass of each of the particles of the body. Mathematically, the mass moment of inertia can be expressed in the following way: I=∫r2dm
Finite Element Method
Published in M.S. Rahman, M.B. Can Ülker, Modeling and Computing for Geotechnical Engineering, 2018
Here kinematic admissibility requires that: (i) the elements must not violate compatibility, and(ii) boundary conditions have to be satisfied. For the virtual displacement to be kinematically admissible, x + δx should be a kinematically admissible displacement as well. While a rigid body only translates and rotates, a deformable body experiences shape and dimension changes. If we choose virtual displacements that are not just rigid body displacements, the virtual work done will not be zero. For example, if we consider the spring of length, L, given below (Figure 10.4-13), and apply a small elongation, dx, to the spring, the force F will do work, dW=Fdx $$ dW = ~Fdx $$
Introduction to Linkages
Published in Keith L. Richards, Design Engineer's Sourcebook, 2017
A kinematic link or bar is a rigid body or assembly which constitutes the parts of a mechanism and is the smallest element of the mechanism that transmits motion to other links. A rigid body is one which does not deform or change shape due to the application of a force. In a mechanism, three types of links, rigid link, flexible link and fluid link, are the most widely used.
MFS fading regularization method for the identification of boundary conditions from partial elastic displacement field data
Published in European Journal of Computational Mechanics, 2018
L. Caillé, J-L. Hanus, F. Delvare, N. Michaux-Leblond
A rigid body motion is the composition of a translation and a rotation. Characterizing the rigid body translation by its two components and and the rigid body rotation by the angle , the components and of the displacement can be written as follows: