Geometrically nonlinear topology optimization of porous structures

Porous structures are extensively used in engineering, and current designs of porous structures are constructed based on linear assumptions. In engineering, deformation cannot be ignored, so it is necessary to consider the effect of geometric nonlinearity in structural design. For the first time, this paper performs the geometrically nonlinear topology optimization of porous structures. This paper presents the theory of geometric nonlinear analysis, the bi-directional evolutionary method is used to search for the topological configurations of porous structures, the number of structural holes is determined by the number of periodicities. Furthermore, the optimization equation, sensitivity analysis, and optimization process are provided in detail. Lastly, four numerical examples are investigated to discuss the influence of geometric nonlinearity on the design of porous structures, such as comparisons between geometric nonlinear and linear design, the ability of geometric nonlinear design to resist cracks, changes in load amplitude and position and 3D porous designs. The conclusions drawn can provide strong reference for the design of high-performance porous structures.