Geometrical nonlinearity infill topology optimization for porous structures using the parametric level set method

Recently, porous structures have received a wide of attention in engineering applications, due to outstanding mechanical properties, like the lightweight, enhanced strength-to-weight ratio, and robustness in material defects. However, the study on topology optimization for infill designs in porous structures considering the geometrical nonlinearity are in limited. In the current work, the main intention is to propose a Geometrical Nonlinearity Infill Topology Optimization (GN-ITO) method for the design of porous structures to achieve superior performance that can satisfy higher engineering demands. Firstly, the Parametric Level Set Method (PLSM) with numerical stability and high effectiveness is employed, where a boundary implicit description model is used for the representation of structural topology. Secondly, the constraint strategy is constructed for controlling the generation of local structural features using a modified Heaviside function, where local volume constraints for all finite elements are aggregated by implementing an upper limitation to generate porous infill pattern in design domain. Thirdly, the finite element formulation for geometrical nonlinearity in design domain is established using the Newton-Raphson method to solve unknown structural responses, subject to the large deformation assumption. In addition, the mathematical optimization formulation for the GN-ITO is developed for implementing infill designs of porous structures, where sensitivity analysis of the objective function with respect to design variables, namely expansion coefficients, is derived using the Lagrange adjoint method. Finally, several numerical examples are tested to demonstrate the effectiveness and advantages of the proposed GN-ITO method through static analysis and comparisons of diverse design parameters.