GEOMETRICALLY NONLINEAR FE FORMULATIONS FOR THE MACRO-ELEMENT UNIPLET OF FOLDABLE STRUCTURES

Introduction　　 Pantographic foldable structure works on theprinciple of a pantograph1,2 ] . A structure of thistype may be referred to as“pantograph structure”,or simply“p- structure”. The basic unit for the p-structure is a componentso- called duplet3 ] ,orpan-tograph unit4] ,Scissor- Like Element ( SLE) 5] ,asshown in Fig.1 .A pantograph unitconsists of twocoplanar straightbars called uniplet,which are ca-pable of rotating about the intermediate pivot,re-ferred to as a scissor h…

GEOMETRICALLY NONLINEAR FE FORMULATIONS FOR THE MACRO-ELEMENT UNIPLET OF FOLDABLE STRUCTURES

Geometrically nonlinear stiffness matrix due to large displacement small strain was firstly formulated explicitly for the basic components of pantographic foldable structures,namely, the uniplet, derived from a three node beam element.The formulation of the uniplet stiffness matrix is based on the precise nonlinear finite element theory and the displacement harmonized and internal force constraints are applied directly to the deformation modes of the three node beam element. The formulations were derived in general form, and can be simplified for particular foldable structures, such as flat, cylindrical and spherical structures.Finally, two examples were presented to illustrate the applications of the stiffness matrix evolved.