Eigenvector Aggregate

Description

Eigenvector aggregate is a method to approximate the eigenvector derivatives of the eigenvalue problem used in topology optimization. The method is described in the following paper "Topology Optimization using an Eigenvector Aggregate" by Bao Li, Yicong Fu and Graeme J. Kennedy. The paper is available on (To be added).

Contents

• simple_example.py contains the code for the simple example in paper section 3.1.
• demo.py contains the code for a demo to show exact eigenvector derivatives and approximate eigenvector derivatives described in paper sections 4 and 5, respectively.
• tube_opt.py is the main file that contains the code for the 2D tube optimization example. There are five problems in the tube example as follows:
  • plot_E is used to plot the E matrix shown in Figure 2 in the paper.
  • accuracy_analysis is used to plot the accuracy of the approximate eigenvector derivatives shown in section 8.1.1 in the paper.
  • optimization_eigenvalue runs the maximization of the fundamental frequency problem with a volume constraint.
  • optimization_displacement runs the maximization of the fundamental frequency problem with a volume constraint and displacement constraint.
  • optimization_stress runs the maximization of the fundamental frequency problem with a volume constraint and stress constraint.
• topo_opt.py is the main file for the topology optimization for the beam and square plate. The function parse_cmd_args takes the following arguments as input:
  • For the problem definition parameters:
    • domain is the domain of the problem, which can be beam or square.
    • objf is the objective function, which is set to be frequency by default.
    • confs is the constraint function, which is set to volume_ub by default.
    • vol-frac-ub is the upper bound of the volume fraction constraint.
    • stress-ub is the upper bound of the stress constraint.
    • dis-ub is the upper bound of the displacement constraint.
  • For the topology optimization parameters:
    • nx is the number of elements along the x direction.
    • filer is the density filter, which can be spectral or helmholtz, with corresponding filter radius r0 which is set to be 2.1 (2.1 times the element size) by default.
    • ptype-K is the material penalization method for the stiffness matrix K, which can be SIMP or RAMP, with corresponding penalization parameters p and q. It is set to SIMP with p=3 by default.
    • ptype-M is the material penalization method for the mass matrix M, which can be MSIMP, RAMP, or LINEAR.
    • optimizer is the optimizer used to solve the optimization problem, which can be pmma or tr, where pmma is the MMA method and tr is the trust region method.
    • maxit is the maximum number of iterations.
• output folder used to save the output figures and log files.
• other folder contains the code for generating the figures in the paper, helper functions, and bash scripts used to run the code on Georgia Tech's PACE cluster.
• run.sh is the bash script used to run the code.

Usage

The code is written in Python 3. To run the code, you need to install the following packages:

• ParOpt (version 2.0.2 is recommended) is a parallel gradient-based optimizer that integrates the MMA method and the trust region method. The dependencies of ParOpt are listed MPI, BLAS, LAPACK, mpi4py, Cython, numpy, scipy
• scienceplots, matplotlib, numpy, scipy, mpmath, icecream

To run the code, simply run the bash script run.sh:

./run.sh

The code will run the simple_example, demo, tube, beam, and square plate examples. The user can also run the code with different parameters by modifying the bash script run.sh. The output figures and log files will be saved in the output folder.

Citation

If you find this code useful in your research, please consider citing:

To be added

Contact

If you have any questions, please contact Bao Li, Yicong Fu, or Graeme J. Kennedy.