Stiffness Matrix Method for Nonlinear Analysis of Plane Frames

Abstract

In this paper, geometric nonlinear analysis of plane frames was performed by the stiffness matrix method using stability functions. At first, the argument of the stability functions was set as 0.01. The stiffness matrix of the frame has been assembled, as well as the nodal load vector of the frame. The boundary conditions (support restraint and windbracing restraint) were introduced for the reduction of this matrix and the nodal load vector. At this stage, the determinant of the reduced stiffness matrix and the reduced nodal displacement vector are calculated. The argument of the stability functions is incremented by 0.01 and the operations are repeated until the determinant of the reduced stiffness matrix changes sign. The argument of the iteration preceding the sign change of the determinant and corresponding to its positive value is taken and refined by a process described in the paper. The buckling loads of the frame members are determined at this stage. Windbracing and the increase of supports stiffness increase the value of the critical load (less sensitivity to the phenomena of elastic instability) and have been identified as factors of stability.