The boundary element method with programming for engineers and scientists - phần 5 pps

... -0 .02236 0.00079 0.00079 -0 .00787 -0 .00123 - 0.00787 -0 .0 050 8 -0 .0 050 8 -0 .0 050 8 -0 .00787 - 0.00787 -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 ... 59 6 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 59 7 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 59 8 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 59 9 -1 0.0 ... the domain and on the boundary. For the computation of results the integral equation for 232 The Boundary Element Method with Programming the displacement (5. 16) or temperature/potential (5. 20)...

The boundary element method with programming for engineers and scientists - phần 1 pps

... solutions 85 4.4. Conclusions 94 4 .5. References 94 5 Boundary Integral Equations 95 5. 1 Introduction 95 5. 2 Trefftz method 96 5. 3 PROGRAM 5. 1: Flow around cylinder, Trefftz method 99 5. 3.1 ... 7.7 References 202 8 Element- by -element techniques and Parallel Programming 203 8.1 Introduction 203 8.1 The Element by Element Concept 204 8.1.1 Element- by -element storage requirements ... 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 array is no longer used, then the space...

The boundary element method with programming for engineers and scientists - phần 7 ppsx

... 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 iP . iP is located at one of the discontinuous nodes inside the element and the ... quadratic elements along the length and the second has 5 elements along the length. For both one element for the height is used. As is shown in Figure 12 .5 the vertical displacements at the length...

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

... beam The expected error for the discontinuous displacement at common nodes of adjacent elements nodes is less then 0.1%. -0 .06 -0 . 05 -0 .04 -0 .03 -0 .02 -0 .01 0 0 1 2 3 4 5 Discont 5 Elem ... of the finite regions. -0 .03 -0 .0 25 -0 .02 -0 .0 15 -0 .01 -0 .0 05 0 0 3 6 9 12 15 displacements uy [m]chainage [m]LC1LC2LC3LC4LC5 - LC9LC10 LC1 LC2 LC3 LC4 LC5 LC6 LC7 LC8 LC9 ... 0xH,0yH 388 The Boundary Element Method with Programming The Hankel functions can be expanded to4 (14.12) where 0 .57 721J (Euler constant) and here only the first terms of the expansion...

The boundary element method with programming for engineers and scientists - phần 9 ppsx

... previously if the point aP is not one of the cell nodes. If Pa coincides with the nodes of cells, then the integrand tends to infinity with o(r2) for 2-D and o(r3) for 3-D problems and special ... The Boundary Element Method with Programming Figure 16.2 Interface between finite element and boundary regions showing interface forces In the first method of coupling we propose that the boundary ... Numer. Methods Eng. 36 (21), 357 9-3 59 4. 428 The Boundary Element Method with Programming the interface nodes. Since the beam is fixed on the left our problem has only 2 interface unknowns. For...

The boundary element method with programming for engineers and scientists - phần 2 pptx

... 3 (cubic) 3 5 (quintic) Table 3 .5 Gauss point coordinates and weights I [i Wi 1 0.0 2.0 2 0 .57 7 35 , -0 .57 7 35 1.0,1.0 3 0.77 459 , 0.0 , -0 .77 459 0 .55 555 , 0.88888, 0 .55 555 111IiiiIfdWf[[[ ... 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 ... equation as follows: (4 .57 ) where x,y 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 stresses (tractions)...

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

... 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 using line segments (5. 51) where (5. 52) The flows at Pa in x- and ... two-dimensional problems as (5. 54) For constant boundary elements, equation (5. 53) can be replaced by (5. 55) where the integrals (5. 56) can be evaluated analytically over element e. ¦¦ '' ... (5. 25) can be re-written as eight equations (5. 32) Where ue and te is the temperature and flow at the centre of element e. Note that as there is a smooth surface at the centres of the elements...

The boundary element method with programming for engineers and scientists - phần 4 pot

... 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 boundary code is defined locally for each element ... then the number of unknowns for the problem is reduced to the nodes on the right hand side of the symmetry plane and on the plane itself. The only additional computational effort will be the...

The boundary element method with programming for engineers and scientists - phần 6 pot

... Results, Element 6 u= -0 .0 75 -0 .50 8 0.0 75 -0 .50 8 0.000 -0 .50 8 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 ... 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 ... [ 250 .x 00. [ 50 . [01. [268 The Boundary Element Method with Programming Stress: -3 6.182 0.2 05 0.000 -1 7.311 Coordinates: 2.00 0 .50 u: 0.000 -0 .107 Stress: 0.000 0.000 0.000 -1 7.886...

the boundary element method with programming for engineers and scientists - phần 10 pot

... 1-2 Q ( 1- QQ 1-2 Q C4 2  3 C 5 1 ( 1- QQ 1-2 Q C6 4  5 C7 1-4 Q ( 1-3 QQ 1-4 Q C8 -1 /8Q - Q/8 -1 / 15 Q C9 3-4 Q ( 3- QQ 4 -5 Q C10 ... C10 1 ( 1-3 QQ 1 -5 Q C11 -1 /16GQ - Q/16G -1 /30GQ C12 1 1 7 -5 Q C13 1-4 Q ( 1-3 QQ 2-1 0 Q C14 1-2 Q ( 1-3 QQ 1-4 Q C 15 1 ( 1- QQ 1-2 Q C16 ... 0 .5 0 .5 1.00 .5 0 .5 1.02 5/ , =0EkNmν=2 50 0 / , =0ENm21/Nm460 The Boundary Element Method with Programming The overburden above crown is about 75 m. In the analysis therefore the ground surface...

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