The efficient geometrical nonlinear analysis method for civil engineering structures

In civil engineering, linear analysis is common for solving structural problems. However, it is important to note that nonlinear analysis becomes nowadays essential in determining the maximum force that can lead to the collapse of the structure. Due to the diversity of structural behaviors, geometries and applied loads, there is no universal method that could be applied to all structural engineering in practice. Therefore, this article focuses on this problem by point up different numerical methods of nonlinear solutions for various engineering applications. Thus, the analysis of symmetric sheds and bending beams is carried out using a MATLAB code developed in study to perform the numerical analysis. The results obtained are discussed, interpreted and compared to the analytical and reference solutions available in the literature. It is concluded that the Newton–Raphson method presents a failure during Snap Through problem. However, the arc length method overcomes this problem and provides good results comparable to the analytical solution, also, its competence for the geometrical nonlinear analysis for engineering structures is justified. Moreover, the efficiency of the developed algorithm is confirmed. These results constitute a very beneficial finding for researchers and civil engineering applications.