ON SOME VARIATIONAL FORMULATIONS FOR MINIMUM SURFACE

Abstract

An approach to resolving the minimum surface problem based on the total 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 respectively) independent systems of linear algebraic equations with symmetrical matrices in the banded form similar to global stiffness matrix of FEM assemblage. The efficiency of the approach is demonstrated by some 2D and 3D numerical tests. The formulation allows one to minimize the surface embodied into non-plane and plane, closed and non-closed contours. If a contour is closed and plane it allows to correct the triangle network distortion.