The boundary element method with programming for engineers and scientists - phần 3 doc

... & Mech, 12, 34 3- 3 46. 5. Mindlin R.D. (1 936 ) Force at a point in the interior of a semi-infinite solid. Physics 7: 19 5-2 02. 134 The Boundary Element Method with Programming 6 .3. 1 Singular ... 1.0 32 1.0 0.7 18 0. -5 . 0. -4 .5 0. -4 . 0. -3 .5 0. -3 . 0. -2 .5 0. -2 . 0. -1 .5 BOUNDARY INTEGRAL EQUATIONS 117 or in discretis...

Ngày tải lên: 13/08/2014, 08:21

... Element Method with Programming 3. 2 One-dimensional boundary elements 32 3. 3 Two-dimesional elements 36 3. 4 Three-dimensional cells 44 3. 5 Elements of infinite extent 44 3. 6 Subroutines for ... 7.7 References 202 8 Element- by -element techniques and Parallel Programming 2 03 8.1 Introduction 2 03 8.1 The Element by Element Concept 204 8.1.1 Ele...

Ngày tải lên: 13/08/2014, 08:21

... (3. 30) where (3. 31) For the “plane strain” infinite element the variation is given simply by (3. 32) For the two-dimensional “decay” infinite element we have (3. 33) 1 2 3 1 1 q 1 3 q 1 2 q ()q [ 1 ... presented for the one-dimensional finite boundary elements, () () kn N K f are the same infinite shape functions as for the one-dimensional elem...

Ngày tải lên: 13/08/2014, 08:21

... matrices and then solve for the boundary unknowns and another where the assembly and solution are intermixed. The analogy to this in the FEM is the direct solution and the Element by Element ... x y 1 1 -x 1 y 1 3 2 x 3 -y 3 2 1 -x 2 y 2 2 2 -x 2 -y 2 2 3 x 2 -y 2 For potential problems we have u 2 1 = u 2 2 = u 2 3 = u 2 , u 1 1 = u 1...

Ngày tải lên: 13/08/2014, 08:21

... -0 .02 236 0.00079 0.00079 -0 .00787 -0 .001 23 - 0.00787 -0 .00508 -0 .00508 -0 .00508 -0 .00787 - 0.00787 -0 .001 23 -1 0.00000 0.00000 0.00000 -1 0.00000 0.00000 0.00000 -1 0.00000 0.00000 0.00000 -1 0.00000 ... ee nn nn NN [[KK ww ww   wwww ¦¦ uu uu 212 The Boundary Element Method with Programming 598 133 135 599 599 135...

Ngày tải lên: 13/08/2014, 08:21

... Results, Element 3 u= 0.480E-04 0.480E-0 4-0 .467E- 03 0.744E-04 0.000E+0 0-0 .468E- 03 0.000E+00 0.000E+0 0-0 .723E- 03 0.000E+00 0.744E-0 4-0 .468E- 03 t= 0.000 0.000 -0 .707 0.000 0.000 -0 .707 ... 0.000E+0 0-0 .468E- 03 0.480E-04 0.480E-0 4-0 .467E- 03 0.113E- 03 0.113E- 03 0.000E+00 t= 0.000 0.000 0.000 0.000 0.000 -0 .707 0.000 0.000...

Ngày tải lên: 13/08/2014, 08:21

... side of the beam are the same and agree very well with the analytical solution, except for the coarse mesh with continuous elements. For the discontinuous mesh with 3 elements and for the continuous ... 33 2 The Boundary Element Method with Programming We now investigate the other possibilities for the location of i P . i P is located at o...

Ngày tải lên: 13/08/2014, 08:21

... Nodes 4 ! Elements 1.000 1.000 0.707 0.707 1.000 0.000 0.707 -0 .707 0.000 -1 .000 1 2 3 4 36 4 The Boundary Element Method with Programming where ( 13. 30) The discretised form can be ... version of the multi-region program. If we compare the tractions at interface elements in Figures 12.7, 12.8 with 12.9 at the interface between regions we 37...

Ngày tải lên: 13/08/2014, 08:21

... previously if the point a P is not one of the cell nodes. If P a coincides with the nodes of cells, then the integrand tends to infinity with o(r 2 ) for 2-D and o(r 3 ) for 3- D problems and special ... Numer. Methods Eng. 36 (21), 35 7 9 -3 594. 428 The Boundary Element Method with Programming the interface nodes. Since the beam is fixed on...

Ngày tải lên: 13/08/2014, 08:21

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Ngày tải lên: 13/08/2014, 08:21