ABSTRACT

In linear analysis of structures, the equations of equilibrium are based on the undeformed geometry existing before load application. This is sufficiently accurate for many practical cases. However, some structures, such as cable nets and fabrics, trusses, and frames with slender members may have large deformations, so that it is necessary to consider equilibrium in the real deformed configurations. This requires nonlinear analysis involving iteration, which can be done using Newton-Raphson’s technique. The equilibrium equations are based on trial displacement values, whose accuracy is improved by iterations, so as to satisfy the equilibrium of the nodes or the members in their displaced positions or their deformed shapes. Nonlinearity caused by large deformations is referred to as geometric nonlinearity. We are dealing here with large deformation, but small strain with linear stress–strain relationship.