Molding direction constraints

The molding direction constraints ensure that the design does not contradict with the casting system, i.e. that it is possible to remove the molds after the cast part has solidified (see Chapter 4 in my Ph.D Thesis: "Manufacturing Constraints and Multi-Phase Shape and Topology Optimization via a Level-Set Method").

3d box: compliance minimization under a volume constraint.
Boundary conditions. Optimized shape using two molds and d=(1,0,0) as molding direction (2). Optimized shape using one mold, d=(1,0,0) as molding direction and a maximum thickness constraint. Optimized shape without molding direction constraint. Optimized shape using two molds and d=(0,0,1) as molding direction. Optimized shape using two molds, d=(0,0,1) as molding direction and a minimum thickness constraint. Optimized shape using two molds and d=(1,0,0) as molding direction (1). Optimized shape using one mold and d=(0,0,1) as molding direction. Optimized shape using one mold, d=(0,0,1) as molding direction and a minimum thickness constraint.

Uniform cross-section surface constraint

A particular type of molding direction constraint is that of imposing a uniform cross-section profile in some direction. This is a sufficient, but not necessary condition for castability in the corresponding direction.

3d cantilever: compliance minimization under a volume constraint.
Boundary conditions. Optimized shape without uniform cross-section. Optimized shape with uniform cross-section.