OPTIMIZATION OF GEOMETRICALLY NONLINEAR LATTICE STRUCTURES UNDER DYNAMIC LOADING

Resumo

This study addresses the optimization of lattice structures with geometrically nonlinear

behavior under dynamic loading. The formulated optimization problem aims to determine the cross-
sectional area of the bars which minimizes the total mass of the structure, imposing constraints on

nodal displacements and stresses. In order to solve this optimization problem, it was developed a
computational program on MATLAB®, using the Interior Point method and the Sequential Quadratic
Programming method, the algorithms of which are available on Optimization ToolboxTM. 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, being validated by comparison with solutions available in the literature
and with solutions generated by the ANSYS® software. Examples of trusses under different dynamic
loading are solved using the developed computational program. The results show that the Sequential
Quadratic Programming method is the most efficient to solve the studied optimization problem and
that the consideration of structural damping can lead to a significant reduction in the total mass.