On 11/23/22 02:07, Deepika Kushwah wrote:
I understood that dealii software uses the weak form to solve any kind of
problem.
But my question is that in step 8 the weak form for elasticity is for a
general case or it is specifically for the plane strain case?
Deepika:
the introduction of step-8 contains this note, which I believe is the best
description of what equation the program is solving:
As written, the equations above are generally considered to be the right
description for the displacement of three-dimensional objects if the
displacement is small and we can assume that Hooke's law is valid. In that
case, the indices i,j,k,l above all run over the set {1,2,3} (or, in the C++
source, over {0,1,2}). However, as is, the program runs in 2d, and while the
equations above also make mathematical sense in that case, they would only
describe a truly two-dimensional solid. In particular, they are not the
appropriate description of an x−y cross-section of a body infinite in the z
direction; this is in contrast to many other two-dimensional equations that
can be obtained by assuming that the body has infinite extent in z-direction
and that the solution function does not depend on the z coordinate. On the
other hand, there are equations for two-dimensional models of elasticity; see
for example the Wikipedia article on plane strain, antiplane shear and plan
stress.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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