use mocktave;
use nalgebra;
fn mocktave_top(
nelx: usize,
nely: usize,
volfrac: f64,
penalMax: f64,
rmin: f64,
) -> nalgebra::DMatrix<f64> {
let script = format!(
"
function x = top(nelx,nely,volfrac,penal,rmin);
% INITIALIZE
x(1:nely,1:nelx) = volfrac;
loop = 0;
change = 1.;
% START ITERATION
while change > 0.01
loop = loop + 1;
xold = x;
% FE-ANALYSIS
[U]=FE(nelx,nely,x,penal);
% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
[KE] = lk;
c = 0.;
for ely = 1:nely
for elx = 1:nelx
n1 = (nely+1)*(elx-1)+ely;
n2 = (nely+1)* elx +ely;
Ue = U([2*n1-1;2*n1; 2*n2-1;2*n2; 2*n2+1;2*n2+2; 2*n1+1;2*n1+2],1);
c = c + x(ely,elx)^penal*Ue'*KE*Ue;
dc(ely,elx) = -penal*x(ely,elx)^(penal-1)*Ue'*KE*Ue;
end
end
% FILTERING OF SENSITIVITIES
[dc] = check(nelx,nely,rmin,x,dc);
% DESIGN UPDATE BY THE OPTIMALITY CRITERIA METHOD
[x] = OC(nelx,nely,x,volfrac,dc);
% PRINT RESULTS
change = max(max(abs(x-xold)));
disp([' It.: ' sprintf('%4i',loop) ' Obj.: ' sprintf('%10.4f',c) ...
' Vol.: ' sprintf('%6.3f',sum(sum(x))/(nelx*nely)) ...
' ch.: ' sprintf('%6.3f',change )])
end
%%%%%%%%%% OPTIMALITY CRITERIA UPDATE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [xnew]=OC(nelx,nely,x,volfrac,dc)
l1 = 0; l2 = 100000; move = 0.2;
while (l2-l1 > 1e-4)
lmid = 0.5*(l2+l1);
xnew = max(0.001,max(x-move,min(1.,min(x+move,x.*sqrt(-dc./lmid)))));
if sum(sum(xnew)) - volfrac*nelx*nely > 0;
l1 = lmid;
else
l2 = lmid;
end
end
end
%%%%%%%%%% MESH-INDEPENDENCY FILTER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [dcn]=check(nelx,nely,rmin,x,dc)
dcn=zeros(nely,nelx);
for i = 1:nelx
for j = 1:nely
ssum=0.0;
for k = max(i-floor(rmin),1):min(i+floor(rmin),nelx)
for l = max(j-floor(rmin),1):min(j+floor(rmin),nely)
fac = rmin-sqrt((i-k)^2+(j-l)^2);
ssum = ssum+max(0,fac);
dcn(j,i) = dcn(j,i) + max(0,fac)*x(l,k)*dc(l,k);
end
end
dcn(j,i) = dcn(j,i)/(x(j,i)*ssum);
end
end
end
%%%%%%%%%% FE-ANALYSIS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [U]=FE(nelx,nely,x,penal)
[KE] = lk;
K = sparse(2*(nelx+1)*(nely+1), 2*(nelx+1)*(nely+1));
F = sparse(2*(nely+1)*(nelx+1),1); U = zeros(2*(nely+1)*(nelx+1),1);
for elx = 1:nelx
for ely = 1:nely
n1 = (nely+1)*(elx-1)+ely;
n2 = (nely+1)* elx +ely;
edof = [2*n1-1; 2*n1; 2*n2-1; 2*n2; 2*n2+1; 2*n2+2; 2*n1+1; 2*n1+2];
K(edof,edof) = K(edof,edof) + x(ely,elx)^penal*KE;
end
end
% DEFINE LOADS AND SUPPORTS (HALF MBB-BEAM)
F(2,1) = -1;
fixeddofs = union([1:2:2*(nely+1)],[2*(nelx+1)*(nely+1)]);
alldofs = [1:2*(nely+1)*(nelx+1)];
freedofs = setdiff(alldofs,fixeddofs);
% SOLVING
U(freedofs,:) = K(freedofs,freedofs) \\ F(freedofs,:);
U(fixeddofs,:)= 0;
end
%%%%%%%%%% ELEMENT STIFFNESS MATRIX %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [KE]=lk()
E = 1.;
nu = 0.3;
k=[ 1/2-nu/6 1/8+nu/8 -1/4-nu/12 -1/8+3*nu/8 ...
-1/4+nu/12 -1/8-nu/8 nu/6 1/8-3*nu/8 ];
KE = E/(1-nu^2)*[ k(1) k(2) k(3) k(4) k(5) k(6) k(7) k(8)
k(2) k(1) k(8) k(7) k(6) k(5) k(4) k(3)
k(3) k(8) k(1) k(6) k(7) k(4) k(5) k(2)
k(4) k(7) k(6) k(1) k(8) k(3) k(2) k(5)
k(5) k(6) k(7) k(8) k(1) k(2) k(3) k(4)
k(6) k(5) k(4) k(3) k(2) k(1) k(8) k(7)
k(7) k(4) k(5) k(2) k(3) k(8) k(1) k(6)
k(8) k(3) k(2) k(5) k(4) k(7) k(6) k(1) ];
end
end
z = top({nelx},{nely},{volfrac},{penalMax},{rmin});
"
);
let y = mocktave::eval(&script).get_matrix("z").unwrap();
nalgebra::DMatrix::from_fn(nely, nelx, |i, j| y[i][j])
}
#[cfg(test)]
mod tests {
#[test]
fn silly_simple() {
let settings = topopt::Settings::new(2, 2, 0.5)
.with_left_bc(true, false)
.with_bottom_right_bc(false, true)
.with_top_left_load(0.0, -1.0)
.with_penalty_weight(3.0)
.with_filter_radius(1.5);
let x = topopt::solve(settings);
let y = super::mocktave_top(2, 2, 0.5, 3.0, 1.5);
assert!((x - y).norm() < 1e-10)
}
#[test]
fn baby_beam() {
let settings = topopt::Settings::new(10, 10, 0.5)
.with_left_bc(true, false)
.with_bottom_right_bc(false, true)
.with_top_left_load(0.0, -1.0)
.with_penalty_weight(3.0)
.with_filter_radius(1.5);
let x = topopt::solve(settings);
let y = super::mocktave_top(10, 10, 0.5, 3.0, 1.5);
assert!((x - y).norm() < 1e-10)
}
#[test]
fn mbb_half_resolution() {
let settings = topopt::Settings::new(30, 10, 0.5)
.with_left_bc(true, false)
.with_bottom_right_bc(false, true)
.with_top_left_load(0.0, -1.0)
.with_penalty_weight(3.0)
.with_filter_radius(1.5);
let x = topopt::solve(settings);
let y = super::mocktave_top(30, 10, 0.5, 3.0, 1.5);
assert!((x - y).norm() < 1e-10)
}
#[test]
fn mbb_full() {
let settings = topopt::Settings::new(60, 20, 0.5)
.with_left_bc(true, false)
.with_bottom_right_bc(false, true)
.with_top_left_load(0.0, -1.0)
.with_penalty_weight(3.0)
.with_filter_radius(1.5);
let x = topopt::solve(settings);
let y = super::mocktave_top(60, 20, 0.5, 3.0, 1.5);
assert!((x - y).norm() < 1e-8)
}
}