# RD-E: 5102 Topology Optimization for Solids

This example outlines how to set up a topology optimization for solid elements part. A concentrated load is applied to the entire top of the part by using a rigid body. The lower part of the hook is the design space for the toplogy optimization.

- Objective (minimize volume of the structure in this example)
- Constraints (maximum displacement less than 5mm in this example)
- Design variables (topology optimization of the design in hook example)

The setup of optimization requires an extra input optimization input file named <name>.radopt which defines the optimization objective, optimization constraints, design variables, and optimization responses.

For more Radioss optimization details, refer to Design Optimization in the User Guide.

## Options and Keywords Used

## Input Files

## Model Description

Units: mm, s, ton, N, and MPa

- Objective: Minimize volume of hook (to saving materials)
- Constraint: Maximum of total displacement in node group 120 less than 5.0 [mm]

### Detailed Optimization Setup

### Optimization Objective

/DESOBJ is used to define optimization objective. In this example, the objective is to minimize response #10.

Response #10 defines an optimization response that is the volume of defined optimization part.

`RTYPE`=3 is Volume.

`PTYPE`=3 and

`grpart`=4 defined group part ID of 4 which is the design space where the optimization occurs.

### Optimization Constraint

In this example, total displacement under concentrated load is limited to less than
5.0 mm to guarantee the quality of hook after topology optimization. In
<name>.radopt file set total displacement of selected
node group (ID) as response #11 and limit response #11 under maximum value 5.0.
Depending on your own optimization criteria, the value in `cmax`
may differ.

### Topology Optimization

`TMIN`- Minimum thickness
`STRESS`- Stress constraint
`MEMBSIZ`- Member Size Conrol
`MESH`- Mesh type
`DRAW`- Draw Direction Constraints
`EXTR`- Extrusion Constraints
`PATRN`- Pattern Grouping
`PATREP`- Pattern Repetition

The member size control function is enabled using
`MEMBSIZ`=1 to improve the quality of the
topology optimization. In this example the minimum diameter of members is set to
`MINDIM`=2.5. It is recommended that
`MINDIM` be at least 3 times, and no greater than 12 times, the
average element size for all elements referenced by that /DTPL.

Draw direction for topology optimization is activated using
`DRAW`=1. This results in a design that can be
manufactored easier. `DTYP` is used to define the draw direction
constraint type. In this example a “single die” type
(`DTYP`=1) is used.

## Results

- Review the optimization results file to make sure that optimized design is
satisfies the constraints and objective. This information is in the
*.out file (hook_opt.out).
- Design is good
`FEASIBLE DESIGN (ALL CONSTRAINTS SATISFIED)`- Design does not meet the constraints defined
`INFEASIBLE DESIGN (AT LEAST ONE CONSTRAINT VIOLATED)`

The Radioss simulation for each design is included in the outer directories created during the simulation. All the animation results can be loaded by opening the hook_opt.mvw session file in HyperView.

- In the *.out file (hook_opt.out),
check/verify the optimization definition.
`Objective Function: Minimize VOLUM`,`Run Type: Topology Optimization`and so on. The Optimization results can be plotted in HyperGraph using the hook_opt.hgdata file. - By running the Optimization in Radioss, an equivalent OptiStruct model will also be automatically created and named *.fem (hook_opt.fem).

- In the original model, the volume is 324.7 mm
^{3} - After topology optimization, the volume is 251.0 mm
^{3}

After the topology optimization, the element densities of the different design iterations can be plotted in HyperView using the hook_opt_des.h3d file.