ON SOME VARIATIONAL FORMULATIONS FOR MINIMUM SURFACE

An approach to resolving the minimum surface problem based on the tota l energy balance of the nodal system is represented in this work. The approach leads to design of two or three (for 2D or 3D problems respec tively) independent systems of linear algebraic equations with symmetr ical matrices in the banded form similar to global stiffness matrix of FEM assemblage. The efficiency of the approach is demonstrated by som e 2D and 3D numerical tests. The formulation allows one to minimize th e surface embodied into non-plane and plane, closed and non-closed con tours. If a contour is closed and plane it allows to correct the trian gle network distortion.