Conservative loads on shells (Q1825065)

Necessary and sufficient conditions for the body force and the surface force, applied to a thin shell of arbitrary shape, to be conservative are established. Assuming that each configuration of the shell can be represented by a generalized position vector \(q(\sigma_ 1,\sigma_ 2)\) defined on a closed region D in \(R^ 2\) and supposing that \(p(\sigma_ 1,\sigma_ 2)\) is a corresponding generalized load vector per unit area of D and that F(s) is a generalized edge vector per unit length of \(\partial D\), the condition that the combined loads p and F would be conservative is that the work W done by p and F together along any path, would depend only on the initial and final configuration of q and not on the path joining them. The case of hydrostatic pressure is examined in detail.