TopBuck250

The code can be dowloaded from here and the provided version solves the following problems:

1. Maximization of the fundamental BLF of a design, with compliance and volume constraints,
2. Minimum volume design, with compliance and buckling constraints,

other than the two simpler instances already covered in the top99neo:

3. Minimum compliance design with volume constraint,
4. Minimum volume design with compliance constraint.

The features that make possible a computationally efficient and self-contained implementation of the procedure are:
- Fast vectorized setup of the buckling eigenvalue problem and of the sensitivity computations for buckling loads,
- Use of an aggregation function, reducing several objectives/constraints to a single one;
- Use of the compact OC rule "ocUpdate" (DOWNLOAD LINK), based on MMA-like approximations.

The "ocUpdate" is an extremely simplified version of the MMA, which makes the provided code a standalone program.
However, the topBuck250 can be easily coupled with the MMA Matlab routine, or other mathematical programming tools, as needed by the user.

The code can be downloaded from "topBuck250.m" (DOWNLOAD LINK). Save the programs and start Matlab in the same directory and run the programs by writing, for example:
>> topBuck250(480,240,3,4,2,'N',0.5,2,[0.1,0.7,1.2],300,2,0,0,0,{['V','C'],2.5})
for running the minimum volume design problem for a compressed column with only a compliance constraint, and:
>> topBuck250(480,240,3,4,2,'N',0.5,2,[0.1,0.7,1.2],700,2,3,12,200,{['V','C','B'],[2.5,10]});
for running the same problem, now aso with a lower bound on the buckling load factor (BLF_min = 10).

Alternatively, the following call
>> topBuck250(480,240,3,4,2,'N',0.5,2,[0.1,0.7,1.2],750,2,3,12,200,{['B','C','V'],[2.5,0.25]},'x0.mat')
runs the buckling load factor maximization problem, starting from an initial guess for the density distribution, named "xInitial", and saved in the file "x0.mat".

NOTE: the codes contain the external function "fsparse" that is part of the "Fast" package by Stefan Engblom. The package can be downloaded here:
https://github.com/stefanengblom/stenglib
and installed in Matlab following the instructions in the README file.


Details of the implementation are discussed in the paper:
Ferrari, F., Sigmund, O. & Guest, J.K. Topology optimization with linearized buckling criteria in 250 lines of Matlab.
Struct Multidisc Optim (2021). https://doi.org/10.1007/s00158-021-02854-x

The ArXive version of the paper can be found here: https://arxiv.org/abs/2101.02973