美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes16

Numerical integration Consider He 4-D integral =+(s 1 Seek n-point apploxiwisfions G~2M(外 =1 are the weights and 3ae+e6as(awp巾 Gauss Quadrature: select Hhe"M"sampling points Bind weights so that the rule is exact for tNe polynomial ot nignest or der passible . One-point formula() )=Wf(5s) we neve one wel

and one saMpling point(s, to deter wine. We saaa be able to integrate exadiy a polynowied wilh two Parameters, i.e., a linear'fonchton f. o+a, -(+95-2a Setting I(f=I(f, / We obtain yves tor tue Parameers 2。=W4(a0+a5 6s机:5=0,W=2 cidn gives the"midpoint ru④=2+(o) +() 1

③ 10-point formula(n=2) I(f=w,f(s) +uf(s2 2 Gus points, 2 weild dynamIa We ih 4 parameters =0o+1+ Q25+a5(cubic Exac integral r(2a++029+029)ds 20o+202 3 Approxiate integral 工()=+)+(451+吗51 4+4分2+分引3 +W2 LW.LW=1 以属努=3 +分=0

Examples:+(=Cos(9) Exat I:[ coss ds =-sin sl 2Sin1-163 工1=2cs(0)=2 工2=C0s (+(合=26(合 + cos 4.676 two-ciMnensione Integrals f(so ds dw 1-1 w M z2z吗+s,()=-B=