fem二维网格划分
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主要考虑非结构网格
详细文档https://wenku.baidu.com/view/5185c6d680eb6294dd886c99.html?from=search
按照上面的思路分为如下几步:
测试主程序:
clc; %clear all ; addpath(genpath(pwd)); pos=[0,5;0,0;2,0;2,2; ... 3,2;3,0;8,0;8,5]; boundary=[1 2 3 4 5 6 7 8 1]; length_max=0.5; [pos,nie]=makeGrid(pos,boundary,length_max);
划分网格函数主程序
function [pos,nie]=makeGrid(pos,boundary,length_max) %this function is to generate Grids for a single object %boundary is a matrix describe the point-index of the boundary, %described in a counter-clock direction. %find the special points [pos,boundary]=generate_Boundary_Points(pos,boundary,length_max); % drawGrid(pos,nie); [pos,nie]=initial_triangle(pos,boundary); [pos,nie]=lop_all(pos,nie); drawGrid(pos,nie); [pos,nie]=fill_points(pos,nie,boundary,[0.2,2]); end
(1)形成边界
本次程序采用均匀分割,设定一个最大的边界段值,如果代分割的边界比它大,则取中点
function [pos,boundary]=generate_Boundary_Points(pos,boundary,length_max) iP=length(pos(:,1)); i=1; while i<length(boundary) if get_distance(pos,boundary(i),boundary(i+1))>length_max pos=[pos;(pos(boundary(i),1)+pos(boundary(i+1),1))/2,(pos(boundary(i),2)+pos(boundary(i+1),2))/2]; iP=iP+1;%new Point boundary=[boundary(1:i), iP,boundary(i+1:end)]; else i=i+1; end end end
(2)形成初始三角形
思路:1.扫描边界所有点,如果以该点及相邻两点形成的三角形具有最大的三角形最小内角,且没有其他边界点在这个三角形中,则进行连接
2.删除该边界点,更新边界;
3.重复,直到所有点处理完成。
function [pos,nie]=initial_triangle(pos,boundary) nie=[]; boundary=[boundary(end-1),boundary]; while length(boundary)>4 i=2; max_min_angle=get_min_angle(pos(boundary(i-1:i+1),:)); %get the i of the max of the min angle for ii=3:length(boundary)-1 max_min_angle_temp=get_min_angle(pos(boundary(ii-1:ii+1),:)); if max_min_angle_temp>max_min_angle && ~is_any_inside_triangle(pos,boundary(ii-1:ii+1)) max_min_angle=max_min_angle_temp; i=ii; end end angle=get_point_angle(pos(boundary(i-1:i+1),:)); nie=[nie;boundary(i-1:i+1)]; drawGrid(pos,nie); boundary(i)=[]; boundary(end)=boundary(2); boundary(1)=boundary(end-1); end
(3) 填充内部点函数
范围锁定下面的三角形
1.三角形最小内边,在所有三角形最大
2.试探新点位于该三角形的外心,且至少有一个相邻三角形外接圆包含该新点
3.填充一个新点后进行 局部优化(lop)和平滑操作(smooth)。
function [pos,nie]=fill_points(pos,nie,boundary,range) flag=1; while flag flag=0; max_edge=0; %get the i of the max of the min angle edge=[]; tri_delete=[]; for ii=1:length(nie) [x_temp,y_temp,r]=get_outer_circle(pos(nie(ii,:),:)); [edge_temp,tri_delete_temp]=get_ploygon(pos,nie,ii,[x_temp,y_temp],0); edges=get_edges(pos(nie(ii,:),:)); if max_edge<min(edges)&& min(edges)>range(1) && length(edge_temp)>4 max_edge=min(edges); edge=edge_temp; tri_delete=tri_delete_temp; x=x_temp;y=y_temp; %center point ie=ii; flag=1; end end if mod(length(pos(:,1)),50)==0 flag=1; end %min_angle=get_min_angle(pos(nie(ie,:),:)); %[x,y]=get_new_point(pos(nie(ie,:),:)); [x,y,r]=get_outer_circle(pos(nie(ie,:),:)); % drawGrid(pos,nie);hold on % plot(x,y,\'--rs\');hold off if length(edge)>4 && is_inside_polygon(pos,[x,y],edge) tri_delete=[tri_delete,ie]; nie(tri_delete,:)=[]; %delete current element pos=[pos;x,y];% add new point ip_new=length(pos(:,1)); for i_edge=1:length(edge)-1;%add new elements nie=[nie;ip_new,edge(i_edge),edge(i_edge+1)]; % drawGrid(pos,nie); end end [pos,nie]=lop_all(pos,nie);drawGrid(pos,nie); pos=smooth_all(pos,nie,boundary);drawGrid(pos,nie); end
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