/////////////////////////////////////////////////////////////// // Copyright G. Allaire, A. Karrman, October 2009 // // A Scilab toolbox for 2-d structural optimization // by the level set method. // // Based on the work of G. Allaire, F. Jouve, A.-M. Toader, // J. Comp. Phys. Vol 194/1, pp.363-393 (2004). //////////////////////////////////////////////////////////////// // // This file contains the parameters of the following test case: // long cantilever //////////////////////////////////////////////////////////////// // clear ntop; // PARAMETERS nelx = 80 ; // element count in x direction nely = 40 ; // element count in y direction xlength = 2 ; // working domain length dx = xlength/nelx ; // x space step size dy = dx ; // y space step size yheight = dy*nely ; // working domain height hx = 5 ; // x direction holes hy = 3 ; // y direction holes r = .5 ; // hole size (between 0 and 1) eps = .001 ; // "hole" (or ersatz) material density lagV = 50. ; // the volume Lagrange multiplier lagP = 0 ; // the perimeter Lagrange multiplier e2 = 4*dx^2.; // coefficient for the regularization in front of the Laplacian nodex = linspace(0,xlength,nelx+1) ; // x space for nodes nodey = linspace(0, yheight,nely+1) ; // y space for nodes FEx = linspace(0,xlength,nelx) ; // x space for finite elements FEy = linspace(0, yheight,nely) ; // y space for finite elements RIiterinit = 50 ; // number of time steps in the reinitialization of the initial design RIiter = 5 ; // number of time steps in the reinitialization of further designs RIfreq = 5 ; // frequency of reinitialization, i.e. number of time steps in the // transport level set equation between two reinitializations HJiter0 = 20 ; // original number of transport time steps entire = 20 ; // total number of optimization iterations allow = .01 ; // fraction that the objective function can increase // FINITE ELEMENT MATRICES KE = lk(); // the stiffness matrix K = sparse([],[],[2*(nelx+1)*(nely+1), 2*(nelx+1)*(nely+1)]); // the global stiffness matrix F = sparse([],[],[2*(nely+1)*(nelx+1),2]); // the matrix of applied forces U = sparse([],[],[2*(nely+1)*(nelx+1),2]); // the vector displacement matrix // FINITE DIFFERENCES MATRIX K1 = sparse([],[],[(nelx+1)*(nely+1),(nelx+1)*(nely+1)]) ; //We define the matrix of the velocity regularization // SETTING OF THE ELASTICITY PROBLEM // THE FORCE // Each row corresponds to a different force. // The first two values are the fraction along the x and y axes of the working // domain (the origin is the top left corner). The third value is binary indicating // whether the force is horizontal (0) or vertical (1). The fourth value gives // the strength of the force and its direction (negative for leftward or downward // forces; positive for rightward or upward forces). forceMatrix = [1 .5 1 -1] ; forceCount = size(forceMatrix,1) ; // We count the number of applied forces for force = 1 : forceCount F(c(forceMatrix(force,1:3)),force) = forceMatrix(force,4) ; end // FIXED BOUNDARIES WITH DIRICHLET CONDITIONS fixeddofs = [1:2*(nely+1)] ; // We fix x and y degrees of freedoms for nodes alldofs = [1:2*(nely+1)*(nelx+1)]; freedofs = setdiff(alldofs,fixeddofs); // PASSIVE ELEMENTS // For this part we can make sure that certain areas in the working domain // are either always part of the structure or always not part of the structure. function FEthetaOut = passive(FEthetaIn) FEthetaOut = FEthetaIn ; endfunction // // INITIALIZATION phi0 = mesh0(hx, hy,r) ;