Chapter 3 - Second-order elastic analysis by the newton-raphson method

Abstract

This chapter introduces the second-order elastic analysis of framed structures using the Newton-Raphson method. Bifurcation analysis is based on a mathematical idealization that the structure deforms only in the loaded directions until the bifurcation load is reached. As a result, the element stiffness is only a function of force in the structural members and other basic material and geometrical properties before loaded. All structures contain a certain degree of initial imperfection and the loads are not perfectly concentric so that deflections, however small, occur in directions other than the loading plane. The increase or decrease of load can be monitored by the sign of the determinant of the tangent stiffness matrix. In the iterative process, a deflection increment due to the unbalanced force is added to the nodal coordinates of the structure to correct the structural geometry in response to the unbalanced force and the value for total deflection. The Newton–Raphson method gives the response of a structure allowing for various second-order effects at a specified design load level, normally taken as the design load.