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A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration. The distance between any two particles changes if and only if deformation has occurred. If displacement occurs without deformation, then it is a rigid-body displacement.
The compatibility conditions in linear elasticity are obtained by observing that there are six strain-displacement relations that are functions of only three unknown displacements. This suggests that the three displacements may be removed from the system of equations without loss of information.
If vectors u and v have direction cosines (α u, β u, γ u) and (α v, β v, γ v) respectively, with an angle θ between them, their units vectors are ^ = + + (+ +) = + + ^ = + + (+ +) = + +. Taking the dot product of these two unit vectors yield, ^ ^ = + + = , where θ is the angle between the two unit vectors, and is also the angle between u and v.
The system stiffness matrix K is square since the vectors R and r have the same size. In addition, it is symmetric because k m {\displaystyle \mathbf {k} ^{m}} is symmetric. Once the supports' constraints are accounted for in (2), the nodal displacements are found by solving the system of linear equations (2), symbolically:
In other words, it is the displacement or translation that maps the origin to P: [1] r = O P → . {\displaystyle \mathbf {r} ={\overrightarrow {OP}}.} The term position vector is used mostly in the fields of differential geometry , mechanics and occasionally vector calculus .
When n / g screw operations have been performed, the displacement will be m / g , which since it is a whole number means one has moved to an equivalent point in the lattice, while carrying out a rotation by 360° / g . So 4 2, 6 2 and 6 4 create two-fold rotation axes, while 6 3 creates a three-fold axis.
cannot be written as the exterior product of two vectors. A bivector that can be written as the exterior product of two vectors is simple. In two and three dimensions all bivectors are simple, but not in four or more dimensions; in four dimensions every bivector is the sum of at most two exterior products.
Displacement is the shift in location when an object in motion changes from one position to another. [2] For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).