一维二维三维高斯积分点及权重Gaussintegrationsandweights.docx
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一维二维三维高斯积分点及权重Gaussintegrationsandweights
Gaussintegrationsandweights
(Containingtheprogram)
高斯积分点以及权重
1.1Dbarelement(p181computationmechanics)
Ordern
Accuracygrade
(2*n-1)
Locationξ
Weightw
1
1
1
0.0
2.0
2
3
1
1.0
2
1/√3
1.0
3
5
1
-
5/9
2
0.0
8/9
3
√0.6
5/9
4
7
1
0.861136311594053
0.347854845137454
2
0.339981043584856
0.652145154862546
3
-0.339981043584856
0.652145154862546
4
-0.861136311594053
0.347854845137454
5
9
1
0.906179845938664
0.236926885056189
2
0.538469310105683
0.478628670499366
3
0
0.568888888888889
4
-0.538469*********
0.478628670499366
5
-0.906179845938664
0.236926885056189
6
11
1
0.932469514203152
0.171324492379170
2
0.661209386466265
0.360761573048139
3
0.238619186083197
0.467913934572691
4
-0.238619186083197
0.467913934572691
5
-0.661209386466265
0.360761573048139
6
-0.932469514203152
0.171324492379170
12
23
1
-0.981560634246732
.0471********
2
0.904117256370452
0.1069393259953637
3
-0.7699026741943177
0.1600783285433586
4
-0.5873179542866143
0.2031674267230672
5
-0.3678314989981804
0.2334925365383534
6
-0.12523340851114688
0.2491470458134027
7
0.12523340851114688
0.2491470458134027
8
0.3678314989981804
0.2334925365383534
9
0.5873179542866143
0.2031674267230672
10
0.7699026741943177
0.1600783285433586
11
0.904117256370452
0.1069393259953637
12
0.981560634246732
.0471********
root3=1./sqrt(3.);r15=.2*sqrt(15.)
nip=ubound(s,1)
w=(/5./9.,8./9.,5./9./);v=(/5./9.*w,8./9.*w,5./9.*w/)
selectcase(element)
case('line')
selectcase(nip)
case
(1)
s(1,1)=0.;wt
(1)=2.
case
(2)
s(1,1)=root3;s(2,1)=-s(1,1);wt
(1)=1.;wt
(2)=1.
case(3)
s(1,1)=r15;s(2,1)=.0;s(3,1)=-s(1,1)
wt=w
case(4)
s(1,1)=.861136311594053;s(2,1)=.339981043584856
s(3,1)=-s(2,1);s(4,1)=-s(1,1)
wt
(1)=.347854845137454;wt
(2)=.652145154862546
wt(3)=wt
(2);wt(4)=wt
(1)
case(5)
s(1,1)=.906179845938664;s(2,1)=.538469310105683
s(3,1)=.0;s(4,1)=-s(2,1);s(5,1)=-s(1,1)
wt
(1)=.236926885056189;wt
(2)=.478628670499366
wt(3)=.568888888888889;wt(4)=wt
(2);wt(5)=wt
(1)
case(6)
s(1,1)=.932469514203152;s(2,1)=.661209386466265;s(3,1)=.238619186083197
s(4,1)=-s(3,1);s(5,1)=-s(2,1);s(6,1)=-s(1,1)
wt
(1)=.171324492379170;wt
(2)=.360761573048139;wt(3)=.467913934572691
wt(4)=wt(3);wt(5)=wt
(2);wt(6)=wt
(1)
casedefault
print*,"wrongnumberofintegratingpointsforaline"
endselect
%Copyright(c)2010,Thomas-PeterFries,RWTHAachenUniversity
function[xxIntRef,wwIntRef]=IntPoints1DGauss(nQ)
%SetGausspointsin1Dreferenceelementfrom[-1,1].
ifnQ==1
Data=[...
0.0000000000000000e+0002.0000000000000000e+000
];
elseifnQ==2
Data=[...
-5.7735026918962573e-0011.0000000000000000e+000
5.7735026918962573e-0011.0000000000000000e+000
];
elseifnQ==3
Data=[...
-7.7459666924148340e-0015.5555555555555558e-001
0.0000000000000000e+0008.8888888888888884e-001
7.7459666924148340e-0015.5555555555555558e-001
];
elseifnQ==4
Data=[...
-8.6113631159405257e-0013.4785484513745385e-001
-3.3998104358485626e-0016.5214515486254609e-001
3.3998104358485626e-0016.5214515486254609e-001
8.6113631159405257e-0013.4785484513745385e-001
];
elseifnQ==5
Data=[...
-9.0617984593866396e-0012.3692688505618908e-001
-5.3846931010568311e-0014.7862867049936647e-001
0.0000000000000000e+0005.6888888888888889e-001
5.3846931010568311e-0014.7862867049936647e-001
9.0617984593866396e-0012.3692688505618908e-001
];
elseifnQ==6
Data=[...
-9.3246951420315205e-0011.7132449237917036e-001
-6.6120938646626448e-0013.6076157304813861e-001
-2.3861918608319688e-0014.6791393457269104e-001
2.3861918608319688e-0014.6791393457269104e-001
6.6120938646626448e-0013.6076157304813861e-001
9.3246951420315205e-0011.7132449237917036e-001
];
elseifnQ==7
Data=[...
-9.4910791234275849e-0011.2948496616886970e-001
-7.4153118559939446e-0012.7970539148927664e-001
-4.0584515137739718e-0013.8183005050511892e-001
0.0000000000000000e+0004.1795918367346940e-001
4.0584515137739718e-0013.8183005050511892e-001
7.4153118559939446e-0012.7970539148927664e-001
9.4910791234275849e-0011.2948496616886970e-001
];
elseifnQ==8
Data=[...
-9.6028985649753618e-0011.0122853629037626e-001
-7.9666647741362673e-0012.2238103445337448e-001
-5.2553240991632899e-0013.1370664587788727e-001
-1.8343464249564978e-0013.6268378337836199e-001
1.8343464249564978e-0013.6268378337836199e-001
5.2553240991632899e-0013.1370664587788727e-001
7.9666647741362673e-0012.2238103445337448e-001
9.6028985649753618e-0011.0122853629037626e-001
];
elseifnQ==9
Data=[...
-9.6816023950762609e-0018.1274388361574412e-002
-8.3603110732663577e-0011.8064816069485740e-001
-6.1337143270059036e-0012.6061069640293544e-001
-3.2425342340380892e-0013.1234707704000286e-001
0.0000000000000000e+0003.3023935500125978e-001
3.2425342340380892e-0013.1234707704000286e-001
6.1337143270059036e-0012.6061069640293544e-001
8.3603110732663577e-0011.8064816069485740e-001
9.6816023950762609e-0018.1274388361574412e-002
];
elseifnQ==10
Data=[...
-9.7390652851717174e-0016.6671344308688138e-002
-8.6506336668898454e-0011.4945134915058059e-001
-6.7940956829902444e-0012.1908636251598204e-001
-4.3339539412924721e-0012.6926671930999635e-001
-1.4887433898163116e-0012.9552422471475287e-001
1.4887433898163116e-0012.9552422471475287e-001
4.3339539412924721e-0012.6926671930999635e-001
6.7940956829902444e-0012.1908636251598204e-001
8.6506336668898454e-0011.4945134915058059e-001
9.7390652851717174e-0016.6671344308688138e-002
];
elseifnQ==11
Data=[...
-9.7822865814605697e-0015.5668567116173663e-002
-8.8706259976809532e-0011.2558036946490461e-001
-7.3015200557404936e-0011.8629021092773426e-001
-5.1909612920681181e-0012.3319376459199048e-001
-2.6954315595234501e-0012.6280454451024665e-001
0.0000000000000000e+0002.7292508677790062e-001
2.6954315595234501e-0012.6280454451024665e-001
5.1909612920681181e-0012.3319376459199048e-001
7.3015200557404936e-0011.8629021092773426e-001
8.8706259976809532e-0011.2558036946490461e-001
9.7822865814605697e-0015.5668567116173663e-002
];
elseifnQ==12
Data=[...
-9.8156063424671924e-0014.7175336386511828e-002
-9.0411725637047491e-0011.0693932599531843e-001
-7.6990267419430469e-0011.6007832854334622e-001
-5.8731795428661737e-0012.0316742672306592e-001
-3.6783149899818024e-0012.3349253653835481e-001
-1.2523340851146891e-0012.4914704581340277e-001
1.2523340851146891e-0012.4914704581340277e-001
3.6783149899818024e-0012.3349253653835481e-001
5.8731795428661737e-0012.0316742672306592e-001
7.6990267419430469e-0011.6007832854334622e-001
9.0411725637047491e-0011.0693932599531843e-001
9.8156063424671924e-0014.7175336386511828e-002
];
elseifnQ==13
Data=[...
-9.8418305471858814e-0014.0484004765315877e-002
-9.1759839922297792e-0019.2121499837728452e-002
-8.0157809073330988e-0011.3887351021978725e-001
-6.4234933944034023e-0011.7814598076194574e-001
-4.4849275103644681e-0012.0781604753688851e-001
-2.3045831595513477e-0012.2628318026289723e-001
0.0000000000000000e+0002.3255155323087390e-001
2.3045831595513477e-0012.2628318026289723e-001
4.4849275103644681e-0012.0781604753688851e-001
6.4234933944034023e-0011.7814598076194574e-001
8.0157809073330988e-0011.3887351021978725e-001
9.1759839922297792e-0019.2121499837728452e-002
9.8418305471858814e-0014.0484004765315877e-002
];
elseifnQ==14
Data=[...
-9.8628380869681231e-0013.5119460331751860e-002
-9.2843488366357352e-0018.0158087159760208e-002
-8.2720131506976502e-0011.2151857068790319e-001
-6.8729290481168548e-0011.5720316715819355e-001
-5.1524863635815410e-0011.8553839747793782e-001
-3.1911236892788974e-0012.0519846372129560e-001
-1.0805494870734367e-0012.1526385346315779e-001
1.0805494870734367e-0012.1526385346315779e-001
3.1911236892788974e-0012.0519846372129560e-001
5.1524863635815410e-0011.8553839747793782e-001
6.8729290481168548e-0011.5720316715819355e-001
8.2720131506976502e-0011.2151857068790319e-001
9.2843488366357352e-0018.0158087159760208e-002
9.8628380869681231e-0013.5119460331751860e-002
];
elseifnQ==15
Data=[...
-9.8799251802048538e-0013.0753241996117269e-002
-9.3727339240070595e-0017.0366047488108124e-002
-8.4820658341042721e-0011.0715922046717194e-001
-7.2441773136017007e-0011.3957067792615432e-001
-5.7097217260853883e-0011.6626920581699392e-001
-3.9415134707756339e-0011.8616100001556221e-001
-2.0119409399743449e-0011.9843148532711158e-001
0.0000000000000000e+0002.0257824192556129e-001
2.0119409399743449e-0011.9843148532711158e-001
3.9415134707756339e-0011.8616100001556221e-001
5.7097217260853883e-0011.6626920581699392e-001
7.2441773136017007e-0011.3957067792615432e-001
8.4820658341042721e-0011.0715922046717194e-001
9.3727339240070595e-0017.0366047488108124e-002
9.8799251802048538e-0013.0753241996117269e-002
];
elseifnQ==16
Data=[...
-9.8940093499164994e-0012.7152459411754096e-002
-9.4457502307323260e-0016.2253523938647894e-002
-8.6563120238783176e-0019.5158511682492786e-002
-7.5540440835500300e-0011.2462897125553388e-001
-6.1787624440264377e-0011.4959598881657674e-001
-4.5801677765722737e-0011.6915651939500254e-001
-2.8160355077925892e-0011.8260341504492358e-001
-9.5012509837637427e-0021.8945061045506850e-001
9.5012509837637427e-0021.8945061045506850e-001
2.8160355077925892e-0011.8260341504492358e-001
4.5801677765722737e-0011.6915651