Finite element method for developing arbitrary surfaces to flattened forms
In this paper the principle for developing 3D mesh of flat triangles on arbitrary surfaces to its closest flattened 2D mesh is proposed. Such principle is proved equivalent to the condition that the finite element method (FEM) residual forces of the 2D-mesh member structure are equal to zero. The incremental FEM method and iterative procedures are derived for eliminating such residual forces. For developable 3D mesh of flat triangles, the method of this paper will give the accurate flattened 2D mesh, and for non-developable 3D mesh, this paper can lead to the closest flattened 2D mesh. The obtained 2D mesh can also be taken as the flattened form of the curved surface, which is described by the 3D mesh of flat triangles. Numerical examples show that the method of this paper has stable convergence and high efficiency.
finite member element method surface development incremental method