Solid Orthotropic Material with Penalisation
The code is based on top99: less efficient, restricted to 2D. But More readable for beginners ;)
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
function [dcn]=check(nelx,nely,rmin,x,dc) : top99 MESH-INDEPENDENCY FILTER
[c, dt]=top_obj(x) : output compliance c and dc/drho, dc/dtheta
function [cneq, ceq, gradc, gradceq] = myConstrFcn(x) : output nonlinear constraints and derivative
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;
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;
Symbolic integration of Ke for a fixed material. Not used in Optimization
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
needed for output of the objective function
Convolution filter to smooth fiber orientation
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 to88_heaviside_MMA.m for stress constrained and MMA demo
use top99neo.m with MMA for 3D problem code
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