Investigation of critical load of structures using modified energy method in nonlinear-geometry solid mechanics problems

Geometrically nonlinear analysis is required for resolving issues such as loading causes failure and structure buckling analysis. Although numerical methods are recommended for estimating the exact solution, they lack the necessary convergence in the presence of bifurcation points, making it challenging to find the equilibrium path using these methods. Thus, the modified energy method is employed instead of the numerical method, frequently used to solve quasi-static problems with nonlinear nature and bifurcation points. The ultimate goal of this study is to determine the critical load of structures through the modified energy method rather than other methods in which the relationship between force, displacement, and constraint is used to solve the problem. This study first describes the energy method for this type of problem and then details its computational steps progressively. This method yields numerical results when applied to numerical examples such as truss and frame structures and coded in MATLAB software. These findings are compared to the analytical results. The energy method is more precise than the alternative methods and superior to the Newton–Raphson method at crossing the load–displacement curve’s bifurcation points.