STATICAL NONLINEAR ANALYSIS OF SPHERICAL ASSEMBLIES UTILIZING PADE APPROXIMATION

Abstract

A new numerical technique for computing the displacement and internal force is presented and applied to the double-layer spherical model. This numerical approach takes into consideration the geometrical nonlinear response of the pin-jointed rigid systems. The presented method performs a practical way of employing the large deformation within the elastic limit for analyzing space structures. In the proposed technique the nonlinear geometrical response of the assembly is modeled and analyzed as a system of algebraic nonlinear equations. The Pade approximation method is conducted in the derivation to give a high rate of convergent ratio in solving the nonlinear equations. The result is validated using the nonlinear finite element software SAP2000 and the linear force method. The discrepancies between the proposed technique and SAP2000 analysis results for external nodal displacement difference and internal element force difference are computed and compared with the linear technique outcomes. The Euclidean norm index is also used to test the precision of calculated nonlinear nodal displacements. The findings showed more closeness to nonlinear SAP2000 results than the linear method.

Keywords

• geometric nonlinearity; nonlinear analysis; statical analysis; spherical; force method