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87 lines
2.9 KiB
87 lines
2.9 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-11-27 16:17:24
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% @LastEditTime: 2021-12-06 20:10:37
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%--------------------------
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function [B_1b, seg_num] = bezier_one_edge(microx, addNum)
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bdofs_num = 2*(microx+1);
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border = round(linspace(1, microx+1, addNum+2));
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seg_num = length(border)-1; % segment num divided by added macro dofs
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% macro dofs num of ONE boundary, e.g. u_c1,p1,p2,u_b,p3,p4,uc2
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% the dofs of u_b belong to seg of [u_c1,p1,p2,u_b] and [u_b,p3,p4,uc2]
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% seg_num*6 + 2 could remove duplicated dofs
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% if addNum = 0, seg_num = 1, var_num_1b = 8
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var_num_1b = seg_num*6 + 2;
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var_num_4b = 4 * (var_num_1b - 2);
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B_1b = zeros(bdofs_num, var_num_1b);
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% for every segment of one boundary, B maybe different
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ir = 1; ic = 1;
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for i = 1 : seg_num-1
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nodes_num = border(i+1) - border(i) + 1;
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B = parametric_B_one_boundary(nodes_num); % [2,8,x], x is nodes num of every seg
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% reshape B from [2, 8, x+1] to [2(x+1), 8]
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B1 = permute(B, [2,1,3]); % [8, 2, x+1]
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B2 = reshape(B1, 8, [])'; % [2(x+1), 8]
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% remove duplicated nodes caused by u_b
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% here 8 is caused by P_num = 2
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B_1b(ir:ir + nodes_num*2-2-1, ic:ic+8-1) = B2(1:end-2, :);
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ir = ir + nodes_num*2-2;
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ic = ic + 8-2;
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end
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% assemble B_1b with the last seg
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i = seg_num;
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nodes_num = border(i+1) - border(i) + 1;
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B = parametric_B_one_boundary(nodes_num); % [2,8,x], x is nodes num of every seg
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B1 = permute(B, [2,1,3]); % [8, 2, x+1]
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B2 = reshape(B1, 8, [])'; % [2(x+1), 8]
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% The last seg doesn't have duplicated nodes
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B_1b(ir:ir + nodes_num*2-1, ic:ic+8-1) = B2;
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end
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% nodes_num is the num of nodes on this boundary
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function B = parametric_B_one_boundary(nodes_num)
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B = zeros(2, 8, nodes_num);
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for i = 0 : nodes_num-1
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t = i / (nodes_num-1); % project to [0,1]
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B(:, :, i+1) = Bezier_matrix(t);
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end
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end
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function B = Bezier_matrix(t)
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b = [1, t, t^2, t^3] * [1, 0,0,0;
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-3,3,0,0;
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3,-6,3,0;
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-1,3,-3,1]; % 1,4
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I = eye(2, 2);
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B = kron(b, I); % 2,8
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end
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% test B
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% addNum = 2;
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% [~, ~, edofMat_ma1, ~] = macro_edofMat_bezier(nelx, nely, addNum);
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% [ref_nodes, ~, ~] = multi_generate_mesh(lx, nelx, nely, addNum);
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% U = reshape(ref_nodes', [], 1);
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% addNum = microx - 1;
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% [~, ~, edofMat_ma2, ~] = macro_edofMat_bezier(nelx, nely, microx-1);
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% alldofs = 2*(nelx+1)*(nely+1) + 2 * addNum*nely*(nelx+1) + 2 * addNum*nelx*(nely+1);
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% U2 = zeros(alldofs, 1);
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% for ele = 1:eleNum_ma
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% edof = edofMat_ma1(ele, :);
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% ub = bezier_B * U(edof);
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% edof = edofMat_ma2(ele, :);
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% U2(edof) = ub;
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% end
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% deform_nodes = reshape(U2, 2, [])';
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% figure; clf; scatter(deform_nodes(:,1), deform_nodes(:,2), 'b'); axis equal;
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% hold on; scatter(ref_nodes(:,1), ref_nodes(:,2), 'k', 'filled'); axis equal;
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