The boundary element method with programming for engineers and scientists - phần 8 pps

... 0 x H , 0y H 388 The Boundary Element Method with Programming The Hankel functions can be expanded to 4 (14.12) where 0.57721 J (Euler constant) and here only the first terms of the expansion ... continuous elements and then with the program prog111_discont, the discontinuous version of the multi-region program. If we compare the tractions at inte...

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... 212 8. 3 PROGRAM 8. 2 : Replacing assembly by element- by -element procedure 213 8. 3.1 Sample input file 219 8. 3.2 Sample output file 219 16 The Boundary Element Method with Programming When the ... 203 8. 1 The Element by Element Concept 204 8. 1.1 Element- by -element storage requirements 206 8. 2 PROGRAM 8. 1 : Replacing direct by iterative solution 206...

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... -0 .02236 0.00079 0.00079 -0 .00 787 -0 .00123 - 0.00 787 -0 .005 08 -0 .005 08 -0 .005 08 -0 .00 787 - 0.00 787 -0 .00123 -1 0.00000 0.00000 0.00000 -1 0.00000 0.00000 0.00000 -1 0.00000 0.00000 0.00000 -1 0.00000 ... distinguish between values inside the domain and on the boundary. For the computation of results the integral e...

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... 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 ... 332 The Boundary Element Method with Programming We now investigate the other possibilities for the location of i P . i P is located at one...

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... 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 ... ()ut 4 38 The Boundary Element Method with Programming Figure 16.2 Interface between finite element and boundary regions showing interface forces...

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... linear elements (c) one quadratic element 40 The Boundary Element Method with Programming If the element shape functions for the quadratic element are derived from Lagrange polynomials, then there ... is substituted for i,j and (4. 58) is the Kronecker Delta. For the boundary element method we also need the solutions for the boundary str...

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... be written and used for numerical experiments. As the 1 38 The Boundary Element Method with Programming We see that since R cancels out, the integral is valid for any radius of the circle, ... 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 discretised form u...

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... 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 ... So the information that is needed for the assembly is the Connectivity or Destination vector and the boundary code for each element. Note that the bo...

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... Results, Element 6 u= -0 .075 -0 .5 08 0.075 -0 .5 08 0.000 -0 .5 08 t= 0.000 -1 0.000 0.000 -1 0.000 0.000 -1 0.000 272 The Boundary Element Method with Programming Required are the displacements and the ... EXAMPLES 287 Results, Element 3 u= 0. 480 E-04 0. 480 E-0 4-0 .467E-03 0.744E-04 0.000E+0 0-0 .468E-03 0.000E+00 0.000E+...

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Ngày tải lên: 13/08/2014, 08:21