Optimization of geometrically nonlinear truss structures under dynamic loading

Abstract

The goal of this article is to present the formulation of the optimization problem of truss structures with geometric nonlinearity under dynamic loads and provide examples of this problem. The formulated optimization problem aims to determine the cross-sectional area of the bars that minimizes the weight of the structure, imposing constraints on nodal displacements and axial stresses. To solve this problem, computational routines were developed in MATLAB ® using Sequential Quadratic Programming (SQP), the algorithm of which is available on MATLAB's Optimization Toolbox™. The nonlinear finite space truss element is described by an updated Lagrangian formulation. The geometric nonlinear dynamic analysis performed combines the Newmark method with Newton-Raphson iterations. It was validated by a comparison with solutions available in literature and with solutions generated by the ANSYS ® software. Optimization examples of trusses under different dynamic loading were studied considering their geometric nonlinearity. The results indicate a significant reduction in structure weight for both undamped and damped cases.