Thermoelastic2D

Thermoelastic2D#

../../_images/thermoelastic2d.png

Version

0

Design space

Box(0.0, 1.0, (64, 64), float32)

Objectives

structural_compliance: ↓

thermal_compliance: ↓

volume_fraction: ↓

Conditions

fixed_elements: [[0 0 0 … 0 0 0] [0 0 0 … 0 0 0] [0 0 0 … 0 0 0] … [0 0 0 … 0 0 0] [0 0 0 … 0 0 0] [0 0 0 … 0 0 0]]

force_elements_x: [[0 0 0 … 0 0 0] [0 0 0 … 0 0 0] [0 0 0 … 0 0 0] … [0 0 0 … 0 0 0] [0 0 0 … 0 0 0] [0 0 0 … 0 0 0]]

force_elements_y: [[0 0 0 … 0 0 0] [0 0 0 … 0 0 0] [0 0 0 … 0 0 0] … [0 0 0 … 0 0 0] [0 0 0 … 0 0 0] [0 0 0 … 0 0 0]]

heatsink_elements: [[0 0 0 … 0 0 0] [0 0 0 … 0 0 0] [0 0 0 … 0 0 0] … [0 0 0 … 0 0 0] [0 0 0 … 0 0 0] [0 0 0 … 0 0 0]]

volfrac: 0.3

rmin: 1.1

weight: 0.5

Dataset

IDEALLab/thermoelastic_2d_v0

Import

from engibench.problems.thermoelastic2d.v0 import ThermoElastic2D

Truss 2D integer optimization problem.

Problem Description#

This is 2D topology optimization problem for minimizing weakly coupled thermo-elastic compliance subject to boundary conditions and a volume fraction constraint.

Design space#

The design space is represented by a 2D tensor of continuous design variables in the range [0, 1] that represent the material density at each voxel in the design space.

Objectives#

The objectives are defined and indexed as follows: 0. structural_compliance: Structural compliance to minimize.

  1. thermal_compliance: Thermal compliance to minimize.

  2. volume_fraction: Volume fraction error to minimize.

Boundary Conditions#

Creating a problem formulation requires defining a python dict with the following info:

  • fixed_elements: Encodes a binary NxN matrix of the structurally fixed elements in the domain.

  • force_elements_x: Encodes a binary NxN matrix specifying elements that have a structural load in the x-direction.

  • force_elements_y: Encodes a binary NxN matrix specifying elements that have a structural load in the y-direction.

  • heatsink_elements: Encodes a binary NxN matrix specifying elements that have a heat sink.

  • volfrac: Encodes the target volume fraction for the volume fraction constraint.

  • rmin: Encodes the filter size used in the optimization routine.

  • weight: Allows one to control which objective is optimized for. 1.0 Is pure structural optimization, while 0.0 is pure thermal optimization.

Dataset#

The dataset linked to this problem is on huggingface Hugging Face Datasets Hub. Relevant datapoint fields include:

  • optimal_design: An optimized design for the set of boundary conditions

  • strain: The strain field for the initial uniform design

  • vm_stress: The von Mises stress field for the initial uniform design

  • fixed_elements: Encodes a binary NxN matrix of the structurally fixed elements in the domain.

  • force_elements_x: Encodes a binary NxN matrix specifying elements that have a structural load in the x-direction.

  • force_elements_y: Encodes a binary NxN matrix specifying elements that have a structural load in the y-direction.

  • heatsink_elements: Encodes a binary NxN matrix specifying elements that have a heat sink.

  • volume_fraction: The volume fraction value of the optimized design

  • structural_compliance: The structural compliance of the optimized design

  • thermal_compliance: The thermal compliance of the optimized design

  • nelx: The number of elements in the x-direction

  • nely: The number of elements in the y-direction

  • volfrac: The volume fraction target of the optimized design

  • rmin: The filter size used in the optimization routine

  • weight: The domain weighting used in the optimization routine

The dataset is generated by enumerating different boundary condition components, and taking the cartesian product of these components. The following components are enumerated:

  • fixed_elements: 2 fixed elements that can lie anywhere on the left or top boundary

  • force_elements_x: 1 force element that can lie anywhere on the right boundary

  • force_elements_y: 1 force element that can lie anywhere on the bottom boundary

  • heatsink_elements: N heat sink elements that can lie anywhere on the left or top boundary (N is also enumerated to have different sizes)

  • volfrac: The volume fraction target of the optimized design

Simulator#

The evaluation code models the problem as a weakly coupled thermo-elastic problem. The code is written in pure python, and the evaluation is done in a single process.

Lead#

Gabriel Apaza @gapaza

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