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The WEB-Method

Three-Dimensional Linear Elasticity

As 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 0-9mm):

displaced flagstaff

deformed flagstaff, colored according to the maximum principal stress (unit: kN/cm2).

principal stress

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 web-splines and attained a relative accuracy of 0.4% in the maximum norm and 2e-5 in the L2-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.

cube classification

As second example, a circular table under gravital force is considered.


Again displacement and maximum principle stress were computed using web-splines 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.


K. Höllig, J. Hörner, A. Kopf: Web-spline Methods for Linear Elasticity. To appear in: Proceedings of the Fifth International Conference on Curves and Surfaces: Saint-Malo 2002.

See Publications for a complete list of WEB-publications.

Author: Jörg Hörner ; Last modification: 2004/03/02 15:26:14 UTC.

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