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1、Gauss integrations and weights(Containing the program)高斯积分点以及权重目录1.1D bar element(p181 computation mechanics)22.2D triangle element(p230 computation mechanics)43.2D quadrilateral element(p182 computation mechanics)74.3D tetrahedron element(p231 computation mechanics)95.3D hexahedron element (p187 co
2、mputation mechanics)111. 1D bar element(p181 computation mechanics)Order nAccuracy grade(2*n-1)Location Weight w1110.02.0231-1/31.021/31.0351-0.65/920.08/930.65/94710.8611363115940530.34785484513745420.339981043584856 0.6521451548625463-0.3399810435848560.6521451548625464-0.8611363115940530.34785484
3、51374545910.9061798459386640.23692688505618920.538469310105683 0.478628670499366300.5688888888888894-0.5384693101056830.4786286704993665-0.9061798459386640.23692688505618961110.9324695142031520.17132449237917020.6612093864662650.36076157304813930.2386191860831970.4679139345726914-0.2386191860831970.
4、4679139345726915-0.6612093864662650.3607615730481396-0.9324695142031520.17132449237917012231-0.9815606342467320.0471753363864754720.9041172563704520.1069393259953637 3-0.76990267419431770.16007832854335864-0.58731795428661430.20316742672306725-0.36783149899818040.23349253653835346-0.1252334085111468
5、80.249147045813402770.125233408511146880.249147045813402780.36783149899818040.233492536538353490.58731795428661430.2031674267230672100.76990267419431770.1600783285433586110.9041172563704520.1069393259953637120.9815606342467320.04717533638647547root3 = 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 = w case(4) s(1,1)=.861136311594053 ; s(2,1)=.
7、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(
8、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) case default print*,wrong number of
9、integrating points for a line end select% Copyright (c) 2010, Thomas-Peter Fries, RWTH Aachen Universityfunction xxIntRef, wwIntRef = IntPoints1DGauss(nQ) % Set Gauss points in 1D reference element from -1, 1. if nQ = 1 Data = . 0.0000000000000000e+000 2.0000000000000000e+000 ;elseif nQ = 2 Data = .
10、 -5.7735026918962573e-001 1.0000000000000000e+000 5.7735026918962573e-001 1.0000000000000000e+000 ;elseif nQ = 3 Data = . -7.7459666924148340e-001 5.5555555555555558e-001 0.0000000000000000e+000 8.8888888888888884e-001 7.7459666924148340e-001 5.5555555555555558e-001 ;elseif nQ = 4 Data = . -8.611363
11、1159405257e-001 3.4785484513745385e-001 -3.3998104358485626e-001 6.5214515486254609e-001 3.3998104358485626e-001 6.5214515486254609e-001 8.6113631159405257e-001 3.4785484513745385e-001 ;elseif nQ = 5 Data = . -9.0617984593866396e-001 2.3692688505618908e-001 -5.3846931010568311e-001 4.786286704993664
12、7e-001 0.0000000000000000e+000 5.6888888888888889e-001 5.3846931010568311e-001 4.7862867049936647e-001 9.0617984593866396e-001 2.3692688505618908e-001 ;elseif nQ = 6 Data = . -9.3246951420315205e-001 1.7132449237917036e-001 -6.6120938646626448e-001 3.6076157304813861e-001 -2.3861918608319688e-001 4.6791393457269104e-001 2.3861918608319688e-001 4.6791393457269104e-001 6.6120938646626448e-001 3.6076157304813861e-001 9.3246951420315205e-001 1.7132449237917036e-001
