Buckling Force For Deployable PantographicColumns

Abstract

The method of calculating the buckling load for a uniform pantographic column is presented. The deployable column is substituted with a simpler model a composite column consisting of links having infinite bending and finite axial stiffness. The links are connected by hinges and rotational springs. The parameters of the model are calculated based on the condition of stiffness equivalence of the two structures. The stiffness matrix of the axially loaded composite column is derived from the expression of potential energy under the condition of small lateral displacements. Some entries of the matrix are quadratic functions of the load. The solution of the nonlinear eigenvalue problem gives the buckling load. A number of different columns are analyzed. The results show that for constant height and constant degree of deployment the buckling load increases as the number of pantographic units in the column grows. The buckling load decreases as a particular column deploys. Certain conclusions are made concerning the applicability of the procedure.