Two Ways of Solving System of Nonlinear Structural Equations

By applying the inner product of vectors, two objective functions are found. These vectors are taken from the structural equilibrium path. Via minimizing these functions, with respect to the load incremental parameter and the angle between particular vectors, two new constraint equalities are achieved. Since the scheme of authors is general, three more constraints are also reached. These formulations are similar to the previous presented nonlinear solvers, which confirm the legitimacy of new procedure. Afterward, several numerical tests are performed to prove the ability of the proposed techniques. Findings show that the new algorithms are capable in passing the load and displacement limit points of the various benchmark problems with severe nonlinear behaviors. Based on the number of increments and iterations and also the total analysis duration, the suggested methods have the maximum rapid convergence rate, in comparison to the normal plane, the updated normal plane and the cylindrical arc length strategies.