A novel topology framework for simultaneous topology, size and shape optimization of trusses under static, free vibration and transient behavior

This article proposes a novel topology framework for simultaneously optimizing topology, size and shape of truss structures with multiple constraints under static, free vibration and transient responses for the first time. To achieve such a purpose, the topology pseudo-area variable of members is newly proposed discretely assigning to either \(10^{-3}\) or 1 to respectively represent the absence or presence of a member. This suggestion aims at not only evading the numerical instability due to the singularity of global stiffness matrix when solving equilibrium equations in finite element analyses but also saving the computational effort owing to the intact preserve of FE model structure. The objective function of this study is to minimize the structural weight. The cross-sectional area of truss members is taken discrete/continuous design variables into account, whilst nodal coordinates are treated as continuous ones. In addition, kinematic stability, displacement, stress, Euler buckling loading, natural frequency and transient behavior are dealt with as constraints. The derivative-free adaptive hybrid evolutionary firefly algorithm is utilized as an optimizer to resolve such optimization problems including mixed continuous-discrete variables. A large number of benchmark examples are tested to verify the validity of the presented paradigm. Obtained outcomes indicate that the present methodology is effective and robust in searching better high-quality optimal solutions against many existing algorithms in the literature.