Topology optimization of geometrical nonlinear continuum structures based on a bionics approach.

*(Chinese. English summary)*Zbl 1174.74330Summary: The topology optimization of geometrical nonlinear and linear elastic continuum structures is investigated by the bionics method based on Wolff’s law in biomechanics. In the present approach, the design variable is called the fabric tensor, which is introduced to express both of geometry of the microstructure and the elasticity properties of a material point in the design domain. Simultaneously, the interval of reference strain for the structure is adopted and is applied to renew the fabric tensor of a point together with Wolff’s law. The mesh-dependence of the optimal topology of a structure and the influences of the interval of reference strain on the optimal topology are investigated. By numerical examples, several conclusions are drawn as follows: Firstly, the optimal topology of a structure is not dependent on the mesh-refine. Secondly, the optimal topology of a structure with geometric nonlinearity obviously depends on the specified interval of reference strain. Thirdly, if the length of the interval of reference strain equals zero and the loading conditions are specified displacements on the structure, then changing the supremum of the interval and the given displacements proportionally, the optimal topology and the amount of material of the final structure are approximately identical.

##### MSC:

74P15 | Topological methods for optimization problems in solid mechanics |