On Some Boundary Value Problems for the Equation nabla \cdot (F(|nabla w|)nabla w) = 0
A method based on the use of a reciprocal theorem and dual functions in the strain plane (γ x, γ y), where γ x = partial w/partial x, γ y = partial w/partial y is used to deduce solutions of the equation nabla \cdot (F(|nabla w|)nabla w) = 0 for various boundary value problems. The method is applied, in principle, to general (F(|nabla w|) and specific examples, previously treated by other methods (e.g. F(|nabla w|) = |nabla w|N), are worked out in detail as a check on the method.
Proceedings of the Royal Society of London Series A
- Pub Date:
- February 1995