Numerical Analysis of Thin-Walled Structure Finite Displacements

The behavior of the structure thin-walled elements upon finite displacements is described in terms of the boundary value problem for non-linear differential equations. The dependence of the mechanical system state vector $$\mathop {\rm{X}}\limits^ \to$$ on external effect vector $$\mathop {\rm{Q}}\limits^ \to$$ may be very complicated. Thus Fig.I shows the relation between deflection W_o in the vertex of the gently sloping spherical shell and load parameter q [1]. To obtain the solution of such problems numerical methods are usually used.