OptFEM3DP1 Toolbox  V1.0
Matlab/Octave Optimized P1-Lagrange Finite Element Method in 3D
 All Files Functions Variables Pages
ElemStiffElasMatBaVecP1D0OptV0.m
Go to the documentation of this file.
1 function [Kg]=ElemStiffElasMatBaVecP1D0OptV0(q,me,volumes,lambda,mu)
2 %----------------------------------------
3 % Automatic generation with sage
4 % (c) Cuvelier F. email:cuvelier@math.univ-paris13.fr
5 % Copyright:
6 % See \ref license
7 order=1;
8 ndf=(order+1)*(order+2)/2;
9 dim=2*ndf;
10 ndf2=dim*dim;
11 G=ComputeGradientVec(q,me);
12 coef=6*sqrt(volumes);
13 for il=1:4,for i=1:3, G{il}(i,:)=G{il}(i,:)./coef;end, end
14 Kg=zeros(ndf2,size(me,2));
15 
16 T1=G{1}(1,:).^2;
17 T2=G{1}(2,:).^2;
18 T3=G{1}(3,:).^2;
19 C=mu*(T1+ T2 + T3);
20 Kg(1,:) =(lambda + mu)*T1 + C;
21 Kg(14,:)=(lambda + mu)*T2 + C;
22 Kg(27,:)=(lambda + mu)*T3 + C;
23 
24 T1=G{2}(1,:).^2;
25 T2=G{2}(2,:).^2;
26 T3=G{2}(3,:).^2;
27 C=mu*(T1+ T2 + T3);
28 Kg(40,:)=(lambda + mu)*T1 + C;
29 Kg(53,:)=(lambda + mu)*T2 + C;
30 Kg(66,:)=(lambda + mu)*T3 + C;
31 
32 T1=G{3}(1,:).^2;
33 T2=G{3}(2,:).^2;
34 T3=G{3}(3,:).^2;
35 C=mu*(T1+ T2 + T3);
36 Kg(79,:)=(lambda + mu)*T1 + C;%Kg(79,:)=(lambda + 2.*mu).*G{3}(1,:).^2 + mu.*G{3}(2,:).^2 + mu.*G{3}(3,:).^2;
37 Kg(92,:)=(lambda + mu)*T2 + C;%Kg(92,:)=(lambda + 2.*mu).*G{3}(2,:).^2 + mu.*G{3}(1,:).^2 + mu.*G{3}(3,:).^2;
38 Kg(105,:)=(lambda + mu)*T3 + C;%Kg(105,:)=(lambda + 2.*mu).*G{3}(3,:).^2 + mu.*G{3}(1,:).^2 + mu.*G{3}(2,:).^2;
39 
40 T1=G{4}(1,:).^2;
41 T2=G{4}(2,:).^2;
42 T3=G{4}(3,:).^2;
43 C=mu*(T1+ T2 + T3);
44 Kg(118,:)=(lambda + mu)*T1 + C;%(lambda + 2.*mu).*G{4}(1,:).^2 + mu.*G{4}(2,:).^2 + mu.*G{4}(3,:).^2;
45 Kg(131,:)=(lambda + mu)*T2 + C;%(lambda + 2.*mu).*G{4}(2,:).^2 + mu.*G{4}(1,:).^2 + mu.*G{4}(3,:).^2;
46 Kg(144,:)=(lambda + mu)*T3 + C;%(lambda + 2.*mu).*G{4}(3,:).^2 + mu.*G{4}(1,:).^2 + mu.*G{4}(2,:).^2;
47 
48 
49 Kg(2,:)=(lambda+mu)*G{1}(1,:).*G{1}(2,:);%lambda.*G{1}(1,:).*G{1}(2,:) + mu.*G{1}(1,:).*G{1}(2,:);
50 Kg(3,:)=(lambda+mu)*G{1}(1,:).*G{1}(3,:); %lambda.*G{1}(1,:).*G{1}(3,:) + mu.*G{1}(1,:).*G{1}(3,:);
51 
52 T1=G{1}(1,:).*G{2}(1,:);
53 T2=G{1}(2,:).*G{2}(2,:);
54 T3=G{1}(3,:).*G{2}(3,:);
55 C=mu*(T1+ T2 + T3);
56 Kg(4,:) =(lambda + mu)*T1 + C;%(lambda + 2.*mu).*G{1}(1,:).*G{2}(1,:) + mu.*G{1}(2,:).*G{2}(2,:) + mu.*G{1}(3,:).*G{2}(3,:);
57 Kg(17,:)=(lambda + mu)*T2 + C;%(lambda + 2.*mu).*G{1}(2,:).*G{2}(2,:) + mu.*G{1}(1,:).*G{2}(1,:) + mu.*G{1}(3,:).*G{2}(3,:);
58 Kg(30,:)=(lambda + mu)*T3 + C;;%(lambda + 2.*mu).*G{1}(3,:).*G{2}(3,:) + mu.*G{1}(1,:).*G{2}(1,:) + mu.*G{1}(2,:).*G{2}(2,:);
59 
60 T1=G{1}(1,:).*G{2}(2,:);
61 T2=G{1}(2,:).*G{2}(1,:);
62 Kg(5,:) =lambda*T1+mu*T2; %lambda.*G{1}(1,:).*G{2}(2,:) + mu.*G{1}(2,:).*G{2}(1,:);
63 Kg(16,:)=lambda*T2+mu*T1; %lambda.*G{1}(2,:).*G{2}(1,:) + mu.*G{1}(1,:).*G{2}(2,:);
64 
65 T1=G{1}(1,:).*G{2}(3,:);
66 T2=G{1}(3,:).*G{2}(1,:);
67 Kg(6,:) =lambda*T1+mu*T2; %lambda.*G{1}(1,:).*G{2}(3,:) + mu.*G{1}(3,:).*G{2}(1,:);
68 Kg(28,:)=lambda*T2+mu*T1; %lambda.*G{1}(3,:).*G{2}(1,:) + mu.*G{1}(1,:).*G{2}(3,:);
69 
70 T1=G{1}(1,:).*G{3}(1,:);
71 T2=G{1}(2,:).*G{3}(2,:);
72 T3=G{1}(3,:).*G{3}(3,:);
73 C=mu*(T1+ T2 + T3);
74 Kg(7,:) =(lambda + mu)*T1 + C; %(lambda + 2.*mu).*G{1}(1,:).*G{3}(1,:) + mu.*G{1}(2,:).*G{3}(2,:) + mu.*G{1}(3,:).*G{3}(3,:);
75 Kg(20,:)=(lambda + mu)*T2 + C; %(lambda + 2.*mu).*G{1}(2,:).*G{3}(2,:) + mu.*G{1}(1,:).*G{3}(1,:) + mu.*G{1}(3,:).*G{3}(3,:);
76 Kg(33,:)=(lambda + mu)*T3 + C; %(lambda + 2.*mu).*G{1}(3,:).*G{3}(3,:) + mu.*G{1}(1,:).*G{3}(1,:) + mu.*G{1}(2,:).*G{3}(2,:);
77 
78 T1=G{1}(1,:).*G{3}(2,:);
79 T2=G{1}(2,:).*G{3}(1,:);
80 Kg(8,:) = lambda*T1+mu*T2; %lambda.*G{1}(1,:).*G{3}(2,:) + mu.*G{1}(2,:).*G{3}(1,:);
81 Kg(19,:)= lambda*T2+mu*T1; %lambda.*G{1}(2,:).*G{3}(1,:) + mu.*G{1}(1,:).*G{3}(2,:);
82 
83 T1=G{1}(1,:).*G{3}(3,:);
84 T2=G{1}(3,:).*G{3}(1,:);
85 Kg(9,:) = lambda*T1+mu*T2; %lambda.*G{1}(1,:).*G{3}(3,:) + mu.*G{1}(3,:).*G{3}(1,:);
86 Kg(31,:)= lambda*T2+mu*T1; %lambda.*G{1}(3,:).*G{3}(1,:) + mu.*G{1}(1,:).*G{3}(3,:);
87 
88 T1=G{1}(1,:).*G{4}(1,:);
89 T2=G{1}(2,:).*G{4}(2,:);
90 T3=G{1}(3,:).*G{4}(3,:);
91 C=mu*(T1+ T2 + T3);
92 Kg(10,:)=(lambda + mu)*T1 + C; %(lambda + 2.*mu).*G{1}(1,:).*G{4}(1,:) + mu.*G{1}(2,:).*G{4}(2,:) + mu.*G{1}(3,:).*G{4}(3,:);
93 Kg(23,:)=(lambda + mu)*T2 + C; %(lambda + 2.*mu).*G{1}(2,:).*G{4}(2,:) + mu.*G{1}(1,:).*G{4}(1,:) + mu.*G{1}(3,:).*G{4}(3,:);
94 Kg(36,:)=(lambda + mu)*T3 + C; %(lambda + 2.*mu).*G{1}(3,:).*G{4}(3,:) + mu.*G{1}(1,:).*G{4}(1,:) + mu.*G{1}(2,:).*G{4}(2,:);
95 
96 T1=G{1}(1,:).*G{4}(2,:);
97 T2=G{1}(2,:).*G{4}(1,:);
98 Kg(11,:)= lambda*T1+mu*T2; %lambda.*G{1}(1,:).*G{4}(2,:) + mu.*G{1}(2,:).*G{4}(1,:);
99 Kg(22,:)= lambda*T2+mu*T1; %lambda.*G{1}(2,:).*G{4}(1,:) + mu.*G{1}(1,:).*G{4}(2,:);
100 
101 T1=G{1}(1,:).*G{4}(3,:);
102 T2=G{1}(3,:).*G{4}(1,:);
103 Kg(12,:)= lambda*T1+mu*T2; %lambda.*G{1}(1,:).*G{4}(3,:) + mu.*G{1}(3,:).*G{4}(1,:);
104 Kg(34,:)= lambda*T2+mu*T1; %lambda.*G{1}(3,:).*G{4}(1,:) + mu.*G{1}(1,:).*G{4}(3,:);
105 
106 Kg(15,:)=(lambda+mu)*G{1}(2,:).*G{1}(3,:);%lambda.*G{1}(2,:).*G{1}(3,:) + mu.*G{1}(2,:).*G{1}(3,:);
107 
108 T1=G{1}(2,:).*G{2}(3,:);
109 T2=G{1}(3,:).*G{2}(2,:);
110 Kg(18,:)= lambda*T1+mu*T2; %lambda.*G{1}(2,:).*G{2}(3,:) + mu.*G{1}(3,:).*G{2}(2,:);
111 Kg(29,:)= lambda*T2+mu*T1; %lambda.*G{1}(3,:).*G{2}(2,:) + mu.*G{1}(2,:).*G{2}(3,:);
112 
113 T1=G{1}(2,:).*G{3}(3,:);
114 T2=G{1}(3,:).*G{3}(2,:);
115 Kg(21,:)= lambda*T1+mu*T2; %lambda.*G{1}(2,:).*G{3}(3,:) + mu.*G{1}(3,:).*G{3}(2,:);
116 Kg(32,:)= lambda*T2+mu*T1; %lambda.*G{1}(3,:).*G{3}(2,:) + mu.*G{1}(2,:).*G{3}(3,:);
117 
118 T1=G{1}(2,:).*G{4}(3,:);
119 T2=G{1}(3,:).*G{4}(2,:);
120 Kg(24,:)= lambda*T1+mu*T2; %lambda.*G{1}(2,:).*G{4}(3,:) + mu.*G{1}(3,:).*G{4}(2,:);
121 Kg(35,:)= lambda*T2+mu*T1; %lambda.*G{1}(3,:).*G{4}(2,:) + mu.*G{1}(2,:).*G{4}(3,:);
122 
123 
124 Kg(41,:)= (lambda+mu)*G{2}(1,:).*G{2}(2,:); %lambda.*G{2}(1,:).*G{2}(2,:) + mu.*G{2}(1,:).*G{2}(2,:);
125 Kg(42,:)= (lambda+mu)*G{2}(1,:).*G{2}(3,:); %lambda.*G{2}(1,:).*G{2}(3,:) + mu.*G{2}(1,:).*G{2}(3,:);
126 
127 T1=G{2}(1,:).*G{3}(1,:);
128 T2=G{2}(2,:).*G{3}(2,:);
129 T3=G{2}(3,:).*G{3}(3,:);
130 C=mu*(T1+ T2 + T3);
131 Kg(43,:)=(lambda + mu)*T1 + C; % (lambda + 2.*mu).*G{2}(1,:).*G{3}(1,:) + mu.*G{2}(2,:).*G{3}(2,:) + mu.*G{2}(3,:).*G{3}(3,:);
132 Kg(56,:)=(lambda + mu)*T2 + C; % (lambda + 2.*mu).*G{2}(2,:).*G{3}(2,:) + mu.*G{2}(1,:).*G{3}(1,:) + mu.*G{2}(3,:).*G{3}(3,:);
133 Kg(69,:)=(lambda + mu)*T3 + C; % (lambda + 2.*mu).*G{2}(3,:).*G{3}(3,:) + mu.*G{2}(1,:).*G{3}(1,:) + mu.*G{2}(2,:).*G{3}(2,:);
134 
135 T1=G{2}(1,:).*G{3}(2,:);
136 T2=G{2}(2,:).*G{3}(1,:);
137 Kg(44,:)= lambda*T1+mu*T2; %lambda.*G{2}(1,:).*G{3}(2,:) + mu.*G{2}(2,:).*G{3}(1,:);
138 Kg(55,:)= lambda*T2+mu*T1; %lambda.*G{2}(2,:).*G{3}(1,:) + mu.*G{2}(1,:).*G{3}(2,:);
139 
140 T1=G{2}(1,:).*G{3}(3,:);
141 T2=G{2}(3,:).*G{3}(1,:);
142 Kg(45,:)= lambda*T1+mu*T2; %lambda.*G{2}(1,:).*G{3}(3,:) + mu.*G{2}(3,:).*G{3}(1,:);
143 Kg(67,:)= lambda*T2+mu*T1; %lambda.*G{2}(3,:).*G{3}(1,:) + mu.*G{2}(1,:).*G{3}(3,:);
144 
145 T1=G{2}(1,:).*G{4}(1,:);
146 T2=G{2}(2,:).*G{4}(2,:);
147 T3=G{2}(3,:).*G{4}(3,:);
148 C=mu*(T1+ T2 + T3);
149 Kg(46,:)=(lambda + mu)*T1 + C; % (lambda + 2.*mu).*G{2}(1,:).*G{4}(1,:) + mu.*G{2}(2,:).*G{4}(2,:) + mu.*G{2}(3,:).*G{4}(3,:);
150 Kg(59,:)=(lambda + mu)*T2 + C; % (lambda + 2.*mu).*G{2}(2,:).*G{4}(2,:) + mu.*G{2}(1,:).*G{4}(1,:) + mu.*G{2}(3,:).*G{4}(3,:);
151 Kg(72,:)=(lambda + mu)*T3 + C; % (lambda + 2.*mu).*G{2}(3,:).*G{4}(3,:) + mu.*G{2}(1,:).*G{4}(1,:) + mu.*G{2}(2,:).*G{4}(2,:);
152 
153 T1=G{2}(1,:).*G{4}(2,:);
154 T2=G{2}(2,:).*G{4}(1,:);
155 Kg(47,:)= lambda*T1+mu*T2; %lambda.*G{2}(1,:).*G{4}(2,:) + mu.*G{2}(2,:).*G{4}(1,:);
156 Kg(58,:)= lambda*T2+mu*T1; %lambda.*G{2}(2,:).*G{4}(1,:) + mu.*G{2}(1,:).*G{4}(2,:);
157 
158 T1=G{2}(1,:).*G{4}(3,:);
159 T2=G{2}(3,:).*G{4}(1,:);
160 Kg(48,:)= lambda*T1+mu*T2; %lambda.*G{2}(1,:).*G{4}(3,:) + mu.*G{2}(3,:).*G{4}(1,:);
161 Kg(70,:)= lambda*T2+mu*T1; %lambda.*G{2}(3,:).*G{4}(1,:) + mu.*G{2}(1,:).*G{4}(3,:);
162 
163 Kg(54,:)= (lambda+mu)*G{2}(2,:).*G{2}(3,:) ;%lambda*G{2}(2,:).*G{2}(3,:) + mu*G{2}(2,:).*G{2}(3,:);
164 
165 T1=G{2}(2,:).*G{3}(3,:);
166 T2=G{2}(3,:).*G{3}(2,:);
167 Kg(57,:)= lambda*T1+mu*T2; %lambda.*G{2}(2,:).*G{3}(3,:) + mu.*G{2}(3,:).*G{3}(2,:);
168 Kg(68,:)= lambda*T2+mu*T1; %lambda.*G{2}(3,:).*G{3}(2,:) + mu.*G{2}(2,:).*G{3}(3,:);
169 
170 T1=G{2}(2,:).*G{4}(3,:);
171 T2=G{2}(3,:).*G{4}(2,:);
172 Kg(60,:)= lambda*T1+mu*T2; %lambda.*G{2}(2,:).*G{4}(3,:) + mu.*G{2}(3,:).*G{4}(2,:);
173 Kg(71,:)= lambda*T2+mu*T1; %lambda.*G{2}(3,:).*G{4}(2,:) + mu.*G{2}(2,:).*G{4}(3,:);
174 
175 
176 Kg(80,:)=(lambda+mu)*G{3}(1,:).*G{3}(2,:);%lambda.*G{3}(1,:).*G{3}(2,:) + mu.*G{3}(1,:).*G{3}(2,:);
177 
178 Kg(81,:)=(lambda+mu)*G{3}(1,:).*G{3}(3,:);%lambda.*G{3}(1,:).*G{3}(3,:) + mu.*G{3}(1,:).*G{3}(3,:);
179 
180 T1=G{3}(1,:).*G{4}(1,:);
181 T2=G{3}(2,:).*G{4}(2,:);
182 T3=G{3}(3,:).*G{4}(3,:);
183 C=mu*(T1+ T2 + T3);
184 Kg(82,:) =(lambda + mu)*T1 + C; % (lambda + 2.*mu).*G{3}(1,:).*G{4}(1,:) + mu.*G{3}(2,:).*G{4}(2,:) + mu.*G{3}(3,:).*G{4}(3,:);
185 Kg(95,:) =(lambda + mu)*T2 + C; % (lambda + 2.*mu).*G{3}(2,:).*G{4}(2,:) + mu.*G{3}(1,:).*G{4}(1,:) + mu.*G{3}(3,:).*G{4}(3,:);
186 Kg(108,:)=(lambda + mu)*T3 + C; % (lambda + 2.*mu).*G{3}(3,:).*G{4}(3,:) + mu.*G{3}(1,:).*G{4}(1,:) + mu.*G{3}(2,:).*G{4}(2,:);
187 
188 T1=G{3}(1,:).*G{4}(2,:);
189 T2=G{3}(2,:).*G{4}(1,:);
190 Kg(83,:)= lambda*T1+mu*T2; %lambda.*G{3}(1,:).*G{4}(2,:) + mu.*G{3}(2,:).*G{4}(1,:);
191 Kg(94,:)= lambda*T2+mu*T1; %lambda.*G{3}(2,:).*G{4}(1,:) + mu.*G{3}(1,:).*G{4}(2,:);
192 
193 T1=G{3}(1,:).*G{4}(3,:);
194 T2=G{3}(3,:).*G{4}(1,:);
195 Kg(84,:) = lambda*T1+mu*T2; %lambda.*G{3}(1,:).*G{4}(3,:) + mu.*G{3}(3,:).*G{4}(1,:);
196 Kg(106,:)= lambda*T2+mu*T1; %lambda.*G{3}(3,:).*G{4}(1,:) + mu.*G{3}(1,:).*G{4}(3,:);
197 
198 
199 Kg(93,:)=(lambda+mu)*G{3}(2,:).*G{3}(3,:);%lambda.*G{3}(2,:).*G{3}(3,:) + mu.*G{3}(2,:).*G{3}(3,:);
200 
201 T1=G{3}(2,:).*G{4}(3,:);
202 T2=G{3}(3,:).*G{4}(2,:);
203 Kg(96,:) = lambda*T1+mu*T2; %lambda.*G{3}(2,:).*G{4}(3,:) + mu.*G{3}(3,:).*G{4}(2,:);
204 Kg(107,:)= lambda*T2+mu*T1; %lambda.*G{3}(3,:).*G{4}(2,:) + mu.*G{3}(2,:).*G{4}(3,:);
205 
206 
207 Kg(119,:)=(lambda + mu)*G{4}(1,:).*G{4}(2,:);% lambda.*G{4}(1,:).*G{4}(2,:) + mu.*G{4}(1,:).*G{4}(2,:);
208 Kg(120,:)=(lambda + mu)*G{4}(1,:).*G{4}(3,:);% lambda.*G{4}(1,:).*G{4}(3,:) + mu.*G{4}(1,:).*G{4}(3,:);
209 Kg(132,:)=(lambda + mu)*G{4}(2,:).*G{4}(3,:);% lambda.*G{4}(2,:).*G{4}(3,:) + mu.*G{4}(2,:).*G{4}(3,:);
210 
211 Kg([13, 25, 26, 37, 38, 39, 49, 50, 51, 52, 61, 62, 63, 64, 65, 73, 74, 75, 76, 77, 78, 85, 86, 87, 88, 89, 90, 91, 97, 98, 99, 100, 101, 102, 103, 104, 109, 110, 111, 112, 113, 114, 115, 116, 117, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143],:)=Kg([2, 3, 15, 4, 16, 28, 5, 17, 29, 41, 6, 18, 30, 42, 54, 7, 19, 31, 43, 55, 67, 8, 20, 32, 44, 56, 68, 80, 9, 21, 33, 45, 57, 69, 81, 93, 10, 22, 34, 46, 58, 70, 82, 94, 106, 11, 23, 35, 47, 59, 71, 83, 95, 107, 119, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132],:);