Geometrically nonlinear truss analysis using Python's optimization libraries

Resumo

This paper presents an efficient computational framework for analyzing trusses subject to geometric nonlinearities using Python common libraries for numerical optimization. Beginning with a brief discussion on truss kinematics and linear material behavior, we proceed to describe the deformed configuration of the truss and its internal energy based on nodal displacements. We then evaluate some numerical optimization libraries available to select the most suitable method for our problem, thus avoiding the explicit derivation of equilibrium equations and tangent matrices. The equilibrium of the truss is defined as the configuration with minimal potential energy and this is taken as the objective function of the optimization algorithm. Finally, we conclude with numerical examples comparing our approach with classical solutions based on a system of nonlinear equations. The proposed framework offers an interesting alternative for solving the nonlinear equilibrium problem, with particular potential for educational purposes and code prototyping. While our approach may not optimize computational runtime, it significantly streamlines coding time, thereby enhancing accessibility and usability in engineering applications.