Abstract: Aiming at the problems of element distortion and stiffness criteria selection in topology optimization design of three-dimensional nonlinear structures, the hyperelastic structure involving geometric and material nonlinearities was taking as the research object, and topology optimization of three-dimensional nonlinear structures was investigated. Firstly, the physical variables were linearly multiplied with the Mooney-Rivlin model to characterize the hyperelasticity of the design domain, and a modified additive hyperelasticity technique for linear interpolation scheme was proposed, it added the Yeoh hyperelastic material into low-stiffness regions to alleviate the element distortion. Then, the mathematical formula for topology optimization of three-dimensional hyperelastic structures was constructed based on the three-field density model. Under this framework, two stiffness criteria, i.e., minimizing the end compliance and maximizing the total equilibrium potential energy, were compared, and the corresponding sensitivity expressions were derived. The floating projection method was adopted to impose the 0/1 constraint of design variables. Finally, the effectiveness of the proposed method was validated by two numerical examples. The research results demonstrate that their optimized results have significant differences in terms of topological configuration and structural response under large deformations, but all of them have better mechanical behaviors than the linear design.
Key words: three-dimensional structures; deformation of hyperelastic structure; nonlinear effect; stiffness criteria; floating projection method; Mooney-Rivlin model