A directional shape-preserving topology optimization method with multi-point constraints

Shape preservation of aerodynamic surfaces and functional surfaces was an important aspect in aircraft stiffness design. An extended topology optimization method was presented with directional shape-preserving constraints, which suppressed the warping deformation of structural local domains in particular directions and generated required deformation patterns. On the one hand, artificial weak elements (AWEs) were established with respect to the finite control points in local shape-preserving domains. Multi-point constraints (MPCs) were further applied to transfer nodal displacements at the control points to nodes of the AWEs. Strain energy of the AWEs was then constrained to suppress the warping deformation. On the other hand, the MPCs were properly defined to transfer only the displacements of the specified degrees of freedom to be suppressed. Directional shape preservation was in turn achieved. The numerical examples and optimized designs prove the validity of the proposed method in maintaining directional shape preservation based on the stiffness maximization topology optimization. Compared with the existing shape-preserving topology optimization design method, the proposed directional shape-preserving one brings more flexibility in controlling the local structural deformation.