Reanalysis of 2D and 3D truss structures considering simultaneous variations in topology, geometry and size

Approximate reanalysis methods provide effective processes to achieve structural approximate responses without solving the complete set of modified implicit analysis equations. This paper presents methods for carrying out approximate reanalysis of 2D and 3D trusses. Apparently, for the first time, the simultaneous modifications in topology, geometry and size of the structures are taken into account. Three numerical methods, namely, combined approximation, rational approximation and Sherman–Morrison–Woodbury approximation (SMWA), are analyzed and compared for this purpose. The flowchart corresponding to each scheme is presented. Design variables considered are nodal coordinates and cross sectional properties. Moreover, an arrival with bounds between zero and arbitrary amounts includes the variations of the variables. Unlike most works, large trusses with many members are analyzed as numerical examples. Based on obtained outcomes in the several instances, a comparison is conducted between the three schemes and benefits and drawbacks of each method are thoroughly discussed.