NEW VARIATIONAL FORMULATIONS FOR MINIMAL-SURFACES

Using curvilinear co-ordinates of the surface, a functional is developed for the classical formulation for minimum surfaces and is then utilized to obtain a complementary formulation. Unlike the classical formulation in Cartesian co-ordinates, these two formulations are applicable to multi-valued surfaces and give upper and lower bounds to the exact solution when used in an approximate analysis, e.g. finite elements. By means of Lagrange multipliers, a constraint on enclosed volume is incorporated into the basic functional.