Potential Energy Minimization of Nonlinear Structural Systems: a comparison of numerical algorithms for nonlinear programming

The main aim of the present work is to develop a formulation and some strategies for implementation and comparison of methods in nonlinear programming without restriction applied to the calculation of displacements in structural elements, presenting as example the analysis and calculation of the displacements in a truss element through the formulation of the minimum potential energy. The displacements had been calculated through the following methods: Univariant, Gradient Descent Method, Powell Conjugated Directions Method, Fletcher–Reeves Method, Standard Newton Raphson Method, Modified Newton Raphson Method, Rank One Correction Method, Rank Two Correction Method and BFGS Method. The algorithms had been implemented in Fortran language. After the solution of the problem if carries through comparisons between the methods.