In this paper, we analyse an approximation of general thin shell problems where the middle surface is approached by flat triangular facets, whereas the displacement field is approximated by triangles of type (1) for the membrane components and by reduced H.C.T. triangles for the bending component. In this second part of the paper, we define a sixth degree of freedom:the rotation around the normal. This introduces a “small” perturbation but has the advantage to make the implementation easier: indeed, the connection between two adjacent facets is simply realized by imposing the continuity of the displacement and rotation vectors at the vertices of the triangulation. We prove the “pseudo-convergence” of this method for sufficiently shallow shells; then we propose a new expression of the bending terms upon each facet for which the approximation method is unconditionally convergent, for arbitrary thin
展开▼
