Nonlinear Analysis of Frames Using By Advanced Newmark Method

The equilibrium state of structures consisting of one dimensional elements can be described by an ordinary differential equation. response of these kind of structures under the loading, namely the relationship between the displacement field and the loading field, can be predicted by the solution of these differential equations and onsatisfying the given boundary conditions. When the effect of change of geometry under loading is taken into account in modeling of equilibrium state, then these differential equations are partially integrable in quaratures. They also exhibit instability characteristics when the structures are loaded compressively .The main purpose of this article is to introduce a new approximate procedure on the basis of the Newmark method .This method of buckling analysis frame considering the effect of the axial load. The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. In this method, stiffness matrix of the structure is considered to be constant. The most important advantage of such a method is that it obtains both upper and lower critical loads. The advanced of the present method is fast convergence, ability to use computer simulations, and ability to model structures with semi-rigid support conditions using linear and rotational spring. The results obtained in this Article are always compared and verified against other solutions derived from the results of closed form or numerical solutions and experimental studies obtained by other researchers

Keywords:

Nonlinear , Stability , Nonlinear , Advanced Newmark Method