Optimization of a Solid Hook

Optimization of a solid 3D Hook subjected to multiple constraints.

Author: Armin Geiser

Kratos version: 9.0

Optimization Problem

Objective

• Minimize mass

  Constraints

  1. Strain energy of main load (LC1) ≤ initial value
  2. Strain energy of tip load (LC2) ≤ initial value
  3. No penetration of packaging (bounding) mesh

Optimization settings

• Algorithm type : gradient_projection
• Number of steps : 20
• Step size : 3.0
• Filter radius : 25.0
• Mesh motion : True

Results

Shape Evolution

The below image shows the shape of the hook during the optimization iterations. It can be seen how the cross section evolves towards an I-beam shape. This allows to minimize the mass is while satisfying the mechanical constraints. The shape evolution is bounded by the packaging geometry on the right side. The color plot in the cross section shows how the internal nodes are moved by the mesh motion solver according to the shape update of the surface.

Convergence

The below plots show the evolution of objective function (i.e. mass) and the constraints over the optimization iterations.

Objective	Improvement
mass	17.6%

Constraint	Violation	Remark
strain energy: main load	0.1%	-
strain energy: tip load	0.05%	-
packaging: bounding mesh	max nodal violation: 2.0	75% of step size

Note: The packaging constraint has an increasing value because more and more nodes are bounded by the constraint.