SOMP

Solid Orthotropic Material with Penalisation

The code is based on top99: less efficient, restricted to 2D. But More readable for beginners ;)

Tutorial

main.m

main.m : main programm setup the constrained optimization problem and solve it with interior-point method (fmincon)

x0 is the initial design vector x0 = [rho0(:);theta0(:)];

global nelx nely vol volfrac ang angle penal rmin % global variable

check.m

function [dcn]=check(nelx,nely,rmin,x,dc) : top99 MESH-INDEPENDENCY FILTER

top_obj.m

[c, dt]=top_obj(x) : output compliance c and dc/drho, dc/dtheta

myConstrFcn.m

function [cneq, ceq, gradc, gradceq] = myConstrFcn(x) : output nonlinear constraints and derivative

lk0d.m

function [KE,dKE]=lkOd(angle); CLT for 1-layer composite membrane fully integrated KE(8x8 matrix), and derivative with respect to angle dKE, called in FE.m Orthotropic equivalent function to TOP99 lk.m

For a fixed material: Ex=1; Ey=5; nuxy = 0.3; nuyx = 0.3;

lk0d_laminate.m

function [KE,dKE]=lkOd_laminate(angle); CLT for 1-layer composite membrane fully integrated Ke (8x8 matrix), and derivative with respect to angle, called in FE.m with fixed material:

Ex=44.8e+03; % longitudinal Elastic modulus [MPa] Ey=4.2e+03; % transversal Elastic modulus [MPa] %Glt=1.9e+03; % Shear Modulus [MPa] nuxy=0.49; % Poisson ratio nuyx=nuxy*Ey/Ex;

integK_laminate.m

Symbolic integration of Ke for a fixed material. Not used in Optimization

FE.m

function [U]=FE(nelx,nely,vol,ang,penal); output displacement as a function of the actual iteration (and x vector) similar to TOP99 FE.m

myOutputFcn.m

needed for output of the objective function

Postprocessing

Convolution filter to smooth fiber orientation

TO GO FURTHER

use top88.m for vectorization/speed/memory demo

use top88_fmincon.m to compare with this code

use top88_MMA.m with MMA (need svanberg's files mmasub, subsolv) to see the ability of MMA to tackle the XO sensitivity ?

use to88heavisideMMA.m for stress constrained and MMA demo

use top99neo.m with MMA for 3D problem code

Bibliography

Begineer's guide in FE with matlab and abaqus

Topology and printing orientation optimization of orthotropic material for additive manufacturing https://yorkspace.library.yorku.ca/xmlui/handle/10315/38783

An Anisotropic Topology Optimization Method For Carbon Fiber-Reinforced Fused Filament Fabrication https://baylor-ir.tdl.org/handle/2104/9821

Three dimensional topology optimization with orthotropic material orientation design for additive manufacturing structures. https://baylor-ir.tdl.org/handle/2104/10163

Jiang's journal paper https://www.mdpi.com/2079-6439/7/2/14/htm