
ThreeDimensional Linear ElasticityAs an example, the deformation of an aluminum flagstaff under gravitational force is determined. The flagstaff is attached to a vertical wall and is rotational symmetric with respect to a horizontal axis in its unstressed state. The rod is 4.00m long, the head has a diameter of 40cm. Stressfree state (shaded) and displacement with 30 fold magnification (range 09mm): deformed flagstaff, colored according to the maximum principal stress (unit: kN/cm^{2}). The problem was solved with the MIND software package. The displayed solution was computed with a grid width of 9cm. The resulting grid consisted of 50x5x5=1250 cubes. The weight function for the boundary condition was chosen as w(x,y,z)=x. For degree 2, the basis contained 498 websplines and attained a relative accuracy of 0.4% in the maximum norm and 2e5 in the L_{2}norm. The classification of some grid cubes is depicted in the following figure. Inner cubes are marked green, boundary cubes red, and outer cubes gray. As second example, a circular table under gravital force is considered.
Again displacement and maximum principle stress were computed using websplines of degree 2 on a grid consisting of 53x53x30 cubes. Stressfree state (shaded) and magnified displaced table colored according to the maximum principal stress: Please note, that grid lines are caused by visualization. In particular no radial basis has been used. LiteratureK. Höllig, J. Hörner, A. Kopf: Webspline Methods for Linear Elasticity. To appear in: Proceedings of the Fifth International Conference on Curves and Surfaces: SaintMalo 2002.See Publications for a complete list of WEBpublications.
Author: Jörg Hörner ; Last modification: 2004/03/02 15:26:14 UTC.
