第四章程序：一维配点型无网格法MATLAB程序.zip_-baijiahao_matlab一维网格_无网格法MATLAB编程_无

% % CBMM1D - ONE DIMENSIONAL Collocation-based MESHLESS PROGRAM FOR SOLVING A 1D BAR OF UNIT LENGTH % SUBJECTED TO A LINEAR BODY FORCE OF MAGNITUDE X WHOSE EXACT SOLUTION IS GIVEN BY % u = (x/2 - x^3/6)/E % clear all % SET UP NODAL COORDINATES ALONG BAR dx = 0.1; % Distance between adjacent nodes xi = [0.0 : dx : 1.0]; % Nodal coordinates nnodes = length(xi); % SET MATERIAL PROPERITES E = 1.0; % Elastic modulus area = 1.0; % Area of cross section % DETERMINE RADIUS OF SUPPORTS FOR EACH NODE scale = 2.5; dm = scale*dx*ones(1,nnodes); K = zeros(nnodes); % Coefficient matrix P = zeros(nnodes,1); % Right-hand side vector [PHI, DPHI, DDPHI] = MLS1DShape(2, nnodes, xi, nnodes, xi, dm, 'SPLIN', 0.0); K(1,:) = PHI(1,:); % The 1st equation is the prescribed displacement condition at P(1) = 0.0; % the left end of the bar for i = 2:nnodes-1 % The 2nd to (nnodes-1)th equations are the equilibrium K(i,:) = E * DDPHI(i,:); % equations at all inner nodes P(i) = -xi(i); end K(nnodes,:) = DPHI(nnodes,:); % The last equation is the prescribed traction condition P(nnodes) = 0.0; % at the right end of the bar d = K \ P; uh = PHI * d; % Nodal displacements sh = E * DPHI * d; % Nodal stress ue = (xi/2.0 - xi.*xi.*xi/6.0)/E; % Exact solution se = (1 - xi.*xi)/2.0; erru = norm(ue'-uh)/norm(ue)*100 errs = norm(se'-sh)/norm(se)*100 % PLOT RESULTS figure subplot(1,2,1); plot(xi, ue, xi, uh); subplot(1,2,2); plot(xi, se, xi, sh); % Output nodal displacements and stresses fid1 = fopen('C1DBarDis.dat','w'); fid2 = fopen('C1DBarStr.dat','w'); fprintf(fid1,'%10s%10s%10s\n', 'x', 'ue','uh'); fprintf(fid2,'%10s%10s%10s\n', 'x', 'se','sh'); for j = 1 : nnodes fprintf(fid1,'%10.4f%10.4f%10.4f\n', xi(j), ue(j), uh(j)); fprintf(fid2,'%10.4f%10.4f%10.4f\n', xi(j), se(j), sh(j)); end fclose(fid1); fclose(fid2);