Abstract
To do an in-depth analysis of geometrically nonlinear systems, it is absolutely necessary to construct statistical formulas that accurately represent load and provision circumstances and, more highly, that perfect the structure's rigidity and responsiveness. Critical points in nonlinear geometric structures commonly snap through when the structure is subjected to large loads. The structure might collapse as a result. We might find ourselves in a situation where we need to look into the post-buckling behavior of a structure at some time in its unstable load history. Major structures built of ductile materials will sag enough before failing for loads to be re-distributed, leading to unanticipated collapses that are occasionally disastrous and are impossible to forecast. Building collapses and potential fast snap-backs have repeatedly presented numerical hurdles to analysis approaches due to the responses and redistribution of internal loads. The nature of the phenomenon has led to these difficulties. These issues could show up due to the way the collapses are built. Numerical solutions must be able to overcome significant challenges to represent the nonlinear response in its entirety faithfully. Some of these impediments include arbitrary starting routes and critical stability spots. There are still certain obstacles to be overcome to ascertain the nonlinear responses of buildings to significant geometric changes. The ability to predict whether or not specific structures will snap through or snap back has proven challenging and time-consuming. Identifying the maximum load a structure can continue to support without being compromised is more challenging. The arc-length method follows the path to nonlinear equilibrium even when the system has limit points.
Keywords: Arc-Length, Bifurcation, Tangent Stiffness, Nonlinear, Nastran, Truss