Examples of density, orientation, and shape-optimal 2D-design for stiffness and/or strength with orthotropic materials
The balance between stiffness and strength design is considered in the present paper. For materials with different levels of orthotropy (including isotropy), we optimize the density distribution as well as the orientational distribution for a short cantilever problem, and discuss the tendencies in design and response (energy distributions and stress directions). For a hole in a biaxial stress field, the shape design of the boundary hole is also incorporated. The resulting tapered density distributions may be difficult to manufacture, for example, in micro-mechanics production. For such problems a penalization approach to obtain "black and white" designs, i.e. uniform material or holes, is often applied in optimal design. A specific example is studied to show the effect of the penalization, but is restricted here to an isotropic material. When the total amount of material is not specified, a conflict between optimal design for stiffness and optimal design for strength appears. The computational results of such a case study are shown.
orthotropic materials shape design orientational design