一维、二维、三维高斯积分点及权重-Gauss integrations and weights
《一维、二维、三维高斯积分点及权重-Gauss integrations and weights》由会员分享,可在线阅读,更多相关《一维、二维、三维高斯积分点及权重-Gauss integrations and weights(20页珍藏版)》请在装配图网上搜索。
1、Gauss integrations and weights(Containing the program)目录1. 1D bar element(p181 computation mechanics)2. 2D triangle element(p230 computation mechanics)123. 2D quadrilateral element(p182 computation mechanics)154. 3D tetrahedron element(p231 computation mechanics)175. 3D hexahedron element (p187 comp
2、utation mechanics)191. 1D bar element(p181 computation mechanics)Order nAccuracy grade (2*n-1)Location gWeight w1110.02.0231-1/V31.021/V31.0351-V0.65/920.08/93V0.65/94710.8611363115940530.34785484513745420.3399810435848560.6521451548625463-0.3399810435848560.6521451548625464-0.8611363115940530.34785
3、48451374545910.9061798459386640.23692688505618920.5384693101056830.478628670499366300.5688888888888894-0.5384693101056830.4786286704993665-0.9061798459386640.23692688505618961110.9324695142031520.17132449237917020.6612093864662650.36076157304813930.2386191860831970.4679139345726914-0.238619186083197
4、0.4679139345726915-0.6612093864662650.3607615730481396-0.9324695142031520.17132449237917012231-0.9815606342467320.0471753363864754720.9041172563704520.10693932599536373-0.76990267419431770.16007832854335864-0.58731795428661430.20316742672306725-0.36783149899818040.23349253653835346-0.125233408511146
5、880.249147045813402770.125233408511146880.249147045813402780.36783149899818040.233492536538353490.58731795428661430.2031674267230672100.76990267419431770.1600783285433586110.9041172563704520.1069393259953637120.9815606342467320.04717533638647547root3 = 1./sqrt(3.) ; r15 = .2*sqrt(15.)nip = ubound( s
6、 , 1 )w = (/5./9.,8./9.,5./9./); v=(/5./9.*w,8./9.*w,5./9.*w/)select case (element) case(line)select case(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 = wcase(4) s(1,1)=.861136311594053 ; s(2,1)=.33998104358
7、4856 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
8、(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)case defaultprint*,wrong number of integrating points
9、 for a lineend select% Copyright (c) 2010, Thomas-Peter Fries, RWTH Aachen University function xxIntRef, wwIntRef = IntPoints1DGauss(nQ)% Set Gauss points in 1D reference element from -1, 1.if nQData.0.0000000000000000e+0002.0000000000000000e+000;elseif nQData.-5.7735026918962573e-0011.0000000000000
10、000e+0005.7735026918962573e-0011.0000000000000000e+000;elseif nQData.-7.7459666924148340e-0015.5555555555555558e-0010.0000000000000000e+0008.8888888888888884e-0017.7459666924148340e-0015.5555555555555558e-001;elseif nQData.-8.6113631159405257e-0013.4785484513745385e-001-3.3998104358485626e-0016.5214
11、515486254609e-0013.3998104358485626e-0016.5214515486254609e-0018.6113631159405257e-0013.4785484513745385e-001;elseif nQData.-9.0617984593866396e-0012.3692688505618908e-001-5.3846931010568311e-0014.7862867049936647e-0010.0000000000000000e+0005.6888888888888889e-0015.3846931010568311e-0014.78628670499
12、36647e-0019.0617984593866396e-0012.3692688505618908e-001;elseif nQData.-9.3246951420315205e-0011.7132449237917036e-001-6.6120938646626448e-0013.6076157304813861e-001-2.3861918608319688e-0014.6791393457269104e-0012.3861918608319688e-0014.6791393457269104e-0016.6120938646626448e-0013.6076157304813861e
13、-0019.3246951420315205e-0011.7132449237917036e-001;.2948496616886970e-001.7970539148927664e-001.8183005050511892e-0011795918367346940e-0018183005050511892e-0017970539148927664e-0012948496616886970e-001.0122853629037626e-001.2238103445337448e-001.1370664587788727e-001.6268378337836199e-00162683783378
14、36199e-0011370664587788727e-0012238103445337448e-0010122853629037626e-001.1274388361574412e-002.8064816069485740e-001.6061069640293544e-001.1234707704000286e-0013023935500125978e-0011234707704000286e-0016061069640293544e-0018064816069485740e-0011274388361574412e-002.6671344308688138e-002.49451349150
15、58059e-001.1908636251598204e-001.6926671930999635e-001.9552422471475287e-0019552422471475287e-0016926671930999635e-0011908636251598204e-0014945134915058059e-0011231233812361222elseif nQ = 7Data = .-9.4910791234275849e-001 -7.4153118559939446e-001 -4.0584515137739718e-0010.0000000000000000e+000 44.05
16、84515137739718e-001 37.4153118559939446e-001 2 9.4910791234275849e-001 1 ;elseif nQ = 8Data = .-9.6028985649753618e-001-7.9666647741362673e-001-5.2553240991632899e-001 -1.8343464249564978e-0011.8343464249564978e-001 35.2553240991632899e-001 37.9666647741362673e-001 2 9.6028985649753618e-001 1 ;elsei
17、f nQ = 9Data = .-9.6816023950762609e-001-8.3603110732663577e-001-6.1337143270059036e-001 -3.2425342340380892e-0010.0000000000000000e+000 33.2425342340380892e-001 36.1337143270059036e-001 28.3603110732663577e-001 1 9.6816023950762609e-001 8 ;elseif nQ = 10 Data = .-9.7390652851717174e-001-8.650633666
18、8898454e-001-6.7940956829902444e-001-4.3339539412924721e-001-1.4887433898163116e-0011.4887433898163116e-001 24.3339539412924721e-001 26.7940956829902444e-001 28.6506336668898454e-001 1511224112224911229.7390652851717174e-001 6.6671344308688138e-002 ;elseif nQ = 11 Data = .-9.7822865814605697e-001-8.
19、8706259976809532e-001-7.3015200557404936e-001-5.1909612920681181e-001-2.6954315595234501e-0010.0000000000000000e+000 22.6954315595234501e-001 25.1909612920681181e-001 27.3015200557404936e-001 18.8706259976809532e-001 1 9.7822865814605697e-001 5 ;elseif nQ = 12 Data = .-9.8156063424671924e-001-9.0411
20、725637047491e-001-7.6990267419430469e-001-5.8731795428661737e-001-3.6783149899818024e-001-1.2523340851146891e-0011.2523340851146891e-001 23.6783149899818024e-001 25.8731795428661737e-001 27.6990267419430469e-001 19.0411725637047491e-001 1 9.8156063424671924e-001 4 ;elseif nQ = 13 Data = .-9.84183054
21、71858814e-001-9.1759839922297792e-001-8.0157809073330988e-001-6.4234933944034023e-001-4.4849275103644681e-001-2.3045831595513477e-0010.0000000000000000e+000 22.3045831595513477e-001 24.4849275103644681e-001 26.4234933944034023e-001 1.5668567116173663e-002.2558036946490461e-001.8629021092773426e-001.
22、3319376459199048e-001.6280454451024665e-0017292508677790062e-0016280454451024665e-0013319376459199048e-0018629021092773426e-0012558036946490461e-0015668567116173663e-002.7175336386511828e-002.0693932599531843e-001.6007832854334622e-001.0316742672306592e-001.3349253653835481e-001.4914704581340277e-00
23、14914704581340277e-0013349253653835481e-0010316742672306592e-0016007832854334622e-0010693932599531843e-0017175336386511828e-002.0484004765315877e-002.2121499837728452e-002.3887351021978725e-001.7814598076194574e-001.0781604753688851e-001.2628318026289723e-0013255155323087390e-0012628318026289723e-00
24、10781604753688851e-0017814598076194574e-0013887351021978725e-0018.0157809073330988e-001 13811122371111126919.1759839922297792e-001 9.2121499837728452e-0029.8418305471858814e-001 4.0484004765315877e-002 ;elseif nQ = 14 Data = .-9.8628380869681231e-001-9.2843488366357352e-001-8.2720131506976502e-001-6
25、.8729290481168548e-001-5.1524863635815410e-001-3.1911236892788974e-001-1.0805494870734367e-0011.0805494870734367e-001 23.1911236892788974e-001 25.1524863635815410e-001 16.8729290481168548e-001 18.2720131506976502e-001 19.2843488366357352e-001 8 9.8628380869681231e-001 3 ;elseif nQ = 15 Data = .-9.87
26、99251802048538e-001-9.3727339240070595e-001-8.4820658341042721e-001-7.2441773136017007e-001-5.7097217260853883e-001-3.9415134707756339e-001 -2.0119409399743449e-0010.0000000000000000e+000 22.0119409399743449e-001 13.9415134707756339e-001 15.7097217260853883e-001 17.2441773136017007e-001 18.482065834
27、1042721e-001 19.3727339240070595e-001 7 9.8799251802048538e-001 3 ;elseif nQ = 16 Data = .-9.8940093499164994e-001-9.4457502307323260e-001-8.6563120238783176e-001.5119460331751860e-002.0158087159760208e-002 .2151857068790319e-001 .5720316715819355e-001 .8553839747793782e-001 .0519846372129560e-001 .
28、1526385346315779e-001 1526385346315779e-001 0519846372129560e-001 8553839747793782e-001 5720316715819355e-001 2151857068790319e-001 0158087159760208e-002 5119460331751860e-002.0753241996117269e-002.0366047488108124e-002 .0715922046717194e-001 .3957067792615432e-001 .6626920581699392e-001 .8616100001
29、556221e-001 .9843148532711158e-001 0257824192556129e-001 9843148532711158e-001 8616100001556221e-001 6626920581699392e-001 3957067792615432e-001 0715922046717194e-001 0366047488108124e-002 0753241996117269e-002.7152459411754096e-002.2253523938647894e-002.5158511682492786e-002.2462897125553388e-001-7
30、.5540440835500300e-001111125811111247111111-6.1787624440264377e-001-4.5801677765722737e-001-2.8160355077925892e-001-9.5012509837637427e-002 9.5012509837637427e-002 1 2.8160355077925892e-001 1 4.5801677765722737e-001 1 6.1787624440264377e-001 1 7.5540440835500300e-001 1 8.6563120238783176e-001 9 9.44
31、57502307323260e-001 6 9.8940093499164994e-001 2 ;elseif nQ = 17Data = .-9.9057547531441736e-001-9.5067552176876780e-001-8.8023915372698591e-001-7.8151400389680137e-001-6.5767115921669084e-001-5.1269053708647694e-001-3.5123176345387630e-001-1.7848418149584788e-001 0.0000000000000000e+000 1 1.78484181
32、49584788e-001 1 3.5123176345387630e-001 1 5.1269053708647694e-001 1 6.5767115921669084e-001 1 7.8151400389680137e-001 1 8.8023915372698591e-001 8 9.5067552176876780e-001 5 9.9057547531441736e-001 2 ;elseif nQ = 18Data = .-9.9156516842093090e-001-9.5582394957139771e-001-8.9260246649755570e-001-8.0370
33、495897252314e-001-6.9168704306035322e-001-5.5977083107394754e-001-4.1175116146284263e-001-2.5188622569150554e-001.4959598881657674e-001.6915651939500254e-001 .8260341504492358e-001 .8945061045506850e-001 8945061045506850e-001 8260341504492358e-001 6915651939500254e-001 4959598881657674e-001 24628971
34、25553388e-001 5158511682492786e-002 2253523938647894e-002 7152459411754096e-002.4148302868547931e-002 .5459529373987203e-002 .5036148317179178e-002 .1188384719340397e-001 .3513636846852548e-001 .5404576107681028e-001 .6800410215645004e-001 .7656270536699264e-001 7944647035620653e-001 765627053669926
35、4e-001 6800410215645004e-001 5404576107681028e-001 3513636846852548e-001 1188384719340397e-001 5036148317179178e-002 5459529373987203e-002 4148302868547931e-002.1616013526483312e-002.9714548894969797e-002.6425730254889052e-002.0094204410628717e-001.2255520671147846e-001.4064291467065065e-001.5468467
36、512626524e-001.6427648374583273e-001.6914238296314360e-001-8.4775013041735292e-00214691111114681111118.4775013041735292e-002 12.5188622569150554e-001 14.1175116146284263e-001 15.5977083107394754e-001 16.9168704306035322e-001 18.0370495897252314e-001 18.9260246649755570e-001 79.5582394957139771e-001
37、4 9.9156516842093090e-001 2 ;elseif nQ = 19Data = .-9.9240684384358435e-001-9.6020815213483002e-001-9.0315590361481790e-001-8.2271465653714282e-001-7.2096617733522939e-001-6.0054530466168110e-001-4.6457074137596099e-001-3.1656409996362989e-001 -1.6035864564022539e-0010.0000000000000000e+000 11.60358
38、64564022539e-001 13.1656409996362989e-001 14.6457074137596099e-001 16.0054530466168110e-001 17.2096617733522939e-001 18.2271465653714282e-001 99.0315590361481790e-001 69.6020815213483002e-001 4 9.9240684384358435e-001 1 ;elseif nQ = 20 Data = .-9.9312859918509488e-001-9.6397192727791381e-001-9.12234
39、42825132595e-001-8.3911697182221878e-001-7.4633190646015080e-001-6.3605368072651502e-001-5.1086700195082702e-001-3.7370608871541955e-001-2.2778585114164507e-0016914238296314360e-0016427648374583273e-0015468467512626524e-0014064291467065065e-0012255520671147846e-0010094204410628717e-00164257302548890
40、52e-0029714548894969797e-0021616013526483312e-002.9461788229726478e-002 .4814226765699600e-002 .9044542737641226e-002 .1490021622449999e-002 .1156664554733399e-001 .2875396253933621e-001 .4260670217360660e-001 .5276604206585967e-001 .5896884339395434e-001 6105444984878370e-001 5896884339395434e-001
41、5276604206585967e-001 4260670217360660e-001 2875396253933621e-001 1156664554733399e-001 1490021622449999e-002 9044542737641226e-002 4814226765699600e-002 9461788229726478e-002.7614007139152118e-002.0601429800386939e-002.2672048334109068e-002.3276741576704755e-002.0193011981724044e-001.18194531961518
42、41e-001.3168863844917664e-001.4209610931838204e-001.4917298647260374e-001.5275338713072584e-001-7.6526521133497338e-0027.6526521133497338e-0022.2778585114164507e-0013.7370608871541955e-0015.1086700195082702e-0016.3605368072651502e-0017.4633190646015080e-0018.3911697182221878e-0019.1223442825132595e-
43、0019.6397192727791381e-0019.9312859918509488e-0011.5275338713072584e-0011.4917298647260374e-0011.4209610931838204e-0011.3168863844917664e-0011.1819453196151841e-0011.0193011981724044e-0018.3276741576704755e-0026.2672048334109068e-0024.0601429800386939e-0021.7614007139152118e-002;elseif nQ = 21Data =
44、 .-9.9375217062038945e-001-9.6722683856630631e-001-9.2009933415040079e-001-8.5336336458331730e-001-7.6843996347567789e-001-6.6713880419741234e-001-5.5161883588721983e-001-4.2434212020743878e-001-2.8802131680240106e-001-1.4556185416089507e-0011.6017228257774335e-0023.6953789770852494e-0025.7134425426
45、857205e-0027.6100113628379304e-0029.3444423456033862e-0021.0879729916714838e-0011.2183141605372853e-0011.3226893863333747e-0011.3988739479107315e-0011.4452440398997005e-0010.0000000000000000e+0001.4556185416089507e-0012.8802131680240106e-0014.2434212020743878e-0015.5161883588721983e-0016.67138804197
46、41234e-0017.6843996347567789e-0018.5336336458331730e-0019.2009933415040079e-0019.6722683856630631e-0019.9375217062038945e-0011.4608113364969041e-0011.4452440398997005e-0011.3988739479107315e-0011.3226893863333747e-0011.2183141605372853e-0011.0879729916714838e-0019.3444423456033862e-0027.610011362837
47、9304e-0025.7134425426857205e-0023.6953789770852494e-0021.6017228257774335e-002;elseerror( The number num2str(nQ) is not implemented.) end xxIntRef = Data(:, 1);wwIntRef = Data(:, 2);% % Plot situation.% reset(cla), reset(clf), hold onk*);% a = plot(xxIntRef, zeros(size(xxIntRef), % set(a, LineWidth,
48、 2, MarkerSize, 15) % a = line(-1 1, 0 0);% set(a, LineWidth, 2, Color, k)% box on, axis equal, axis(-1 1 -0.1 0.1)2. 2D triangle element(p230 computation mechanics)Order nLocation gLocationWeight w1(a)11/31/31.03(c)10.50.51/320.50.01/330.00.51/34(d)11/31/3-27/4823/51/525/4831/51/525/4841/53/525/486
49、10.8168475729804590.0915762135097710.109951743655322*0.520.0915762135097710.8168475729804590.109951743655322*0.530.0915762135097710.0915762135097710.109951743655322*0.540.1081030181680700.4459484909159650.223381589678011*0.550.4459484909159650.1081030181680700.223381589678011*0.560.4459484909159650.
50、4459484909159650.223381589678011*0.5121.8738219710169960.0630890144915020.050844906370207*0.52.0630890144915020.8738219710169960.050844906370207*0.53.0630890144915020.0630890144915020.050844906370207*0.54.5014265096581790.2492867451709100.116786275726379*0.55.2492867451709100.5014265096581790.116786
51、275726379*0.56.5014265096581790.5014265096581790.116786275726379*0.57.6365024991213990.3103524510337850.082851075618374*0.58.6365024991213990.0531450498448160.082851075618374*0.59.3103524510337850.6365024991213990.082851075618374*0.5100.3103524510337850.0531450498448160.082851075618374*0.511.0531450
52、498448160.6365024991213990.082851075618374*0.512.0531450498448160.3103524510337850.082851075618374*0.5case(triangle)select case(nip)case(1) ! for triangles weights multiplied by .5 s(1,1)=1./3. ; s(1,2)=1./3. ; wt(1)= .5case(3)s(1,1)=.5 ; s(1,2)=.5 ; s(2,1)=.5 s(2,2)=0.; s(3,1)=0. ; s(3,2)=.5 wt(1)=
53、1./3. ; wt(2)=wt(1) ; wt(3)=wt(1) ; wt = .5*wt case(6)s(1,1)=.816847572980459 ; s(1,2)=.091576213509771 s(2,1)=s(1,2); s(2,2)=s(1,1) ; s(3,1)=s(1,2); s(3,2)=s(1,2) s(4,1)=.108103018168070 ; s(4,2)=.445948490915965 s(5,1)=s(4,2) ; s(5,2)=s(4,1) ; s(6,1)=s(4,2) ; s(6,2)=s(4,2) wt(1)=.109951743655322 ;
54、 wt(2)=wt(1) ; wt(3)=wt(1) wt(4)=.223381589678011 ; wt(5)=wt(4) ; wt(6)=wt(4) ; wt = .5*wt case(7)s(1,1)=1./3. ; s(1,2)=1./3.;s(2,1)=.797426985353087 ;s(2,2)=.101286507323456 s(3,1)=s(2,2) ; s(3,2)=s(2,1) ; s(4,1)=s(2,2) ; s(4,2)=s(2,2) s(5,1)=.470142064105115 ; s(5,2)=.059715871789770 s(6,1)=s(5,2)
55、 ; s(6,2)=s(5,1); s(7,1)=s(5,1); s(7,2)=s(5,1) wt(1)=.225 ; wt(2)=.125939180544827 ; wt(3)=wt(2); wt(4)=wt(2) wt(5)=.132394152788506; wt(6)=wt(5) ; wt(7)=wt(5) ;wt = .5*wt case(12)s(1,1)=.873821971016996 ; s(1,2)=.063089014491502 s(2,1)=s(1,2) ; s(2,2)=s(1,1); s(3,1)=s(1,2) ; s(3,2)=s(1,2) s(4,1)=.5
56、01426509658179 ; s(4,2)=.249286745170910 s(5,1)=s(4,2); s(5,2)=s(4,1) ; s(6,1)=s(4,2) ; s(6,2)=s(4,2) s(7,1)=.636502499121399 ; s(7,2)=.310352451033785 s(8,1)=s(7,1) ; s(8,2)=.053145049844816 ; s(9,1)=s(7,2) ; s(9,2)=s(7,1) s(10,1)=s(7,2) ; s(10,2)=s(8,2) ; s(11,1)=s(8,2); s(11,2)=s(7,1) s(12,1)=s(8
57、,2) ; s(12,2)=s(7,2) wt(1)=.050844906370207 ; wt(2)=wt(1); wt(3)=wt(1) wt(4)=.116786275726379 ; wt(5)=wt(4); wt(6)=wt(4) wt(7)=.082851075618374 ; wt(8:12)=wt(7) ; wt = .5*wtcase(16)s(1,1)=1./3. ; s(1,2)=1./3. ; s(2,1)=.658861384496478 s(2,2)=.170569307751761 ; s(3,1)=s(2,2) ; s(3,2)=s(2,1) s(4,1)=s(
58、2,2) ; s(4,2)=s(2,2)s(5,1)=.898905543365938 ; s(5,2)=.050547228317031 s(6,1)=s(5,2); s(6,2)=s(5,1) ; s(7,1)=s(5,2) ; s(7,2)=s(5,2) s(8,1)=.081414823414554; s(8,2)=.459292588292723 s(9,1)=s(8,2) ; s(9,2)=s(8,1); s(10,1)=s(8,2) ; s(10,2)=s(8,2) s(11,1)=.008394777409958; s(11,2)=.263112829634638 s(12,1
59、)=s(11,1) ; s(12,2)=.728492392955404s(13,1)=s(11,2) ; s(13,2)=s(11,1) ; s(14,1)=s(11,2); s(14,2)=s(12,2) s(15,1)=s(12,2) ; s(15,2)=s(11,1) ; s(16,1)=s(12,2) ; s(16,2)=s(11,2) wt(1)=.144315607677787 ; wt(2)=.103217370534718 ; wt(3)=wt(2); wt(4)=wt(2) wt(5)=.032458497623198 ; wt(6)=wt(5); wt(7)=wt(5)wt(8)=.095091634267284 ; wt(9)=wt(8); wt(10)=wt(8)wt(11)=.027230314174435 ; wt(12:16) = wt(11) ; wt = .5*wtcase defaultprint*,wrong number of integrating points for a triangle end selectg点)高斯积分云賦荷存枳分时取样点IOrder nLocation ELocationWeight w110.00.04.0411/丿31/丿31.021/丿31/丿31.031/丿31
- 温馨提示:
1: 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
2: 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
3.本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
5. 装配图网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 一元回归及相关分析课件
- 第六章北方地区第四节-祖国的首都——北京(课堂ppt)课件
- 第十三课《规划每一天》ppt课件
- 第十三课从蒸汽机到互联网ppt课件
- 第八章-真核基因表达调控ppt课件
- 第10章-中枢神经系统感染性疾病ppt课件
- 第十一课-公正处理民事关系ppt课件
- 第十三课《人的本质与利己利他》-一、正确处理利己和利他的关系ppt课件
- 第十四章-消息标题ppt课件
- 第23章第1节生物的生存依赖一定的环境ppt课件
- 第十八章电功率第1节电能电功ppt课件
- 第十二章-公共关系评估ppt课件
- 第十二章-词的初创及晚唐五代词ppt课件
- 一元二次方程解法——配方法课件
- 第十四章-流变学基础ppt课件