Concurrent multiscale topology optimization of hollow structures considering geometrical nonlinearity

Lattice materials and hollow structures possess excellent mechanical properties, which are beneficial to satisfy the lightweight demands of the products, especially for the large deformation situation. Therefore, a concurrent topology optimization method is presented for multiscale hollow design with explicit lattice cells considering the geometrical nonlinearity. Geometrical parameters of macro-hollow moving morphable bars and micro-solid moving morphable bars are used to optimize the macro-structure and the micro-lattice cell, respectively. The macro-hollow moving morphable bars are projected onto the lattice cells to construct the macro-element density function, which further determines the macro-optimized result. Then, the constitutive tensor and shape of the lattice cell can be obtained by the extended energy-based homogenization method, which is derived by the micro-element density function with micro-solid moving morphable bars. This constitutive tensor is taken into account in finite-element analysis with geometrical nonlinearity. Subsequently, the concurrent hollow topology optimization model considering the geometrical nonlinearity is established for multiscale hollow design, and the adjoint method is used to derive the corresponding sensitivities. Finally, several examples demonstrate the effectiveness of the extended energy-based homogenization method for the design of explicit lattice cells, and validate the proposed method to concurrently achieve the explicit multiscale hollow design with lattice cells.