An elastic approach for developing non-developable sheets

Surface development origins from the cloth-making and computer graphics without consideration of the thickness, involving nonlinear optimization and constraints. Moreover the research of surface development mainly focuses on the planar development. In this paper, the development of the non-developable sheet to planar, singly-curved and doubly-curved surface patterns is investigated. An optimal developing algorithm is formulated to minimize the strain energy required for the deformation of the sheet, in which an orthogonal curvilinear coordinate system is used for three target patterns to simplify the constraints for the developing process, resulting in an unconstrained quadratic optimization. Both shell element and solid element are utilized in the finite element analysis. Similar developed results are obtained for planar and spherical patterns by using these two types of elements. But for the cylindrical pattern, the solid element model gives more accurate result due to no contribution of the shell element to the translation of the rotational freedom.