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i và j là số cột và hàng của các nút. Số này là quy định trong hình 3,10. Các nút được cho bởi n (1,1) = 1 n (1,2) = 4 n (1,3) = 8 n (2,1) = 2 n (2,2) = 3 n (2,3) = 6 n (3,1) = 5 n (3,2) = 7 n (3,3) = 9 Serendipity và chức năng hình dạng Lagrange được so sánh trong Hình 3,11 Lagrange yếu tố bong bóng "chế độ bổ sung | MATERIAL MODELLING AND FUNDAMENTAL SOLUTIONS 91 Uxy P Q Px x v 0.0 v 0.5 y Figure 4.14 3-D Kelvin solution variation of displacements in y-direction due to Px 1.0 for Poissons ratio of 0.0 left figure and 0.5 right figure Figure 4.15 3-D Kelvin solution variation of Txx for n 1 0 0 . This is equivalent to ơx 92 The Boundary Element Method with Programming FUNCTION UK dxr r E ny Cdim FUNDAMENTAL SOLUTION FOR DISPLACEMENTS isotropic material Kelvin solution IMPLICIT NONE REAL INTENT IN dxr r x r y r z REAL INTENt in r r real intent in E Young s modulus real intent in ny eff. Poisson s ratio integer intEnt in Cdim Cartesian dimension REAL UK Cdim Cdim Function returns array REAL G c c1 onr clog conr Temps G E 2.0 1 ny c1 3.0 - 4.0 ny SELECT CASE Cdim CASE 2 Plane strain solut ion c 1.0 8.0 Pi G clog -c1 LOG r 1.0 - ny UK 1 1 c clog dxr 1 dxr 1 UK 2 2 c clog dxr 2 dxr 2 UK 1 2 c dxr 1 UK 2 1 UK 1 2 dxr 2 CASE 3 Three-dimensional solution c 1.0 16.0 Pi G conr c r 1.0 - ny UK 1 1 conr c1 dxr 1 dxr 1 UK 2 2 conr c1 dxr 2 dxr 2 UK 3 3 conr c1 dxr 3 dxr 3 UK 1 2 conr dxr 1 dxr 2 UK 1 3 conr dxr UK 2 1 UK 1 2 1 dxr 3 UK 2 3 conr dxr UK 3 1 UK 1 3 UK 3 2 UK 2 3 2 dxr 3 CASE DEFAULT END SELECT RETURN END FUNCTION UK Function TK requires one more parameter to be specified the vector normal to the boundary normal vector . MATERIAL MODELLING AND FUNDAMENTAL SOLUTIONS 93 FUNCTION TK dxr r Vnor ny Cdim J---------------------------------------------- FUNDAMENTAL SOLUTION FOR TRACTIONS J isotropic material Kelvin solution J---------1------------------------------------ IMPLICIT NONE REAL INTENT IN dxr J r x ry r z REAL INTENT in r J r REAL INTENT in Vnor J normal vector real intent in ny J eff. Poisson s ratio INTEGER INtEnT in Cdim J Cartesian dimension REAL TK Cdim Cdim J Function returns array REAL c2 c3 costh Conr J Temps c3 1.0 - 2.0 ny Costh DOTPRODUCT Vnor dxr SELECT CASE Cdim CASE 2 J plane strain c2 1.0 4.0 Pi 1.0 - ny Conr c2 r TK 1 1 - Conr C3 2.0 dxr 1 dxr 1 Costh TK 2 2
