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 ... computers. The method may also be used for coupling boundary with finite elements, as outlined in Chapter 12. We will therefore only discuss the second method here. For the explanation of the first...

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), 3 57 9-3 594. 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 1 pps

... direct method, one region 1 87 7. 4.1 User’s manual 195 7. 4.2 Sample input file 198 7. 5 Conclusions 199 7. 6 Exercises 200 7. 7 References 202 8 Element- by -element techniques and Parallel Programming ... engineering 470 17. 6.1 Borehole stability 470 17. 7 Conclusions 472 17. 8 References 473 18 Advanced topics 475 18.1 Introduction 475 18.2 Heterogeneous Domains 476 18.2.1 Theory 476 18.2.2 ... 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 2 pptx

... 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 ... are the same infinite shape functions as for the one-dimensional element, with K substituted for [ and the values for m(n) and k(n) are given in Table 3.3 Table 3.3 Values for m and k ... 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

... 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 1 17 or in discretised form using line segments (5.51) where (5.52) The flows ... Math. & Mech,12, 34 3-3 46. 5. Mindlin R.D. (1936) 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 ... ns= 1,nseg-1 Thet= Thet + Delth xB(1,ns)= rqo*COS(Thet) xB(2,ns)= rqo*SIN(Thet) xA(1,ns+1)= xB(1,ns) xA(2,ns+1)= xB(2,ns) END DO & 102 The Boundary Element Method with Programming...

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 ... required for 174 The Boundary Element Method with Programming The assembly procedure has to be modified, so that we put all known values on the right hand side and all unknown ones on the left ... no. 1 local (element) node no. 1 element no. 178 The Boundary Element Method with Programming For assembly of the system of equations this means that the coefficients of the mirrored...

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

... -0 .02236 0.00 079 0.00 079 -0 .0 078 7 -0 .00123 - 0.0 078 7 -0 .00508 -0 .00508 -0 .00508 -0 .0 078 7 - 0.0 078 7 -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 ... AND SOLUTION 199 3 4 4 5 5 6 6 7 7 8 8 1 0 ! no Dirichlet BC’s 8 ! Neuman BC’c 1 1.000 0 .70 7 2 0 .70 7 0.000 3 0.000 -0 .70 7 4 -0 .70 7 -1 .000 5 -1 .000 -0 .70 7 6 -0 .70 7 ... Time before eq solution is 1.85099999999 875 It took BiCGSTAB_L 4 iterations to converge -0 .00508 0.00508 0.00508 -0 .0 078 7 0.00123 0.0 078 7 0.00 079 -0 .00 079 0.02236 -0 .00123 0.0 078 7 0.0 078 7 ...

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

... 0.480E-0 4-0 .467E-03 0 .74 4E-04 0.000E+0 0-0 .468E-03 0.000E+00 0.000E+0 0-0 .72 3E-03 0.000E+00 0 .74 4E-0 4-0 .468E-03 t= 0.000 0.000 -0 .70 7 0.000 0.000 -0 .70 7 0.000 0.000 -1 .000 0.000 0.000 -0 .70 7 ... Results, Element 6 u= -0 . 075 -0 .508 0. 075 -0 .508 0.000 -0 .508 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 ... 0 .70 7 0.000 0 .70 7 0.500 0.500 0 .70 7 0 .70 7 0 .70 7 0.000 0.000 0 .70 7 0 .70 7 0.000 1.000 0.000 0.000 0.000 1.000 1 2 3 4 4 3 5 6 3 2 7 5 0 3 1 0. 0. 0. 0. 0. -0 .70 7 0. 0. -0 .70 7...

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

... Nodes 4 ! Elements 1.000 1.000 0 .70 7 0 .70 7 1.000 0.000 0 .70 7 -0 .70 7 0.000 -1 .000 1234364 The Boundary Element Method with Programming where (13.30) The discretised form can be ... 0000( ) 0 for ( ) 1 for Htt t tHtt t t  t() ( ) ( )du t P d h tWW W 0() ( ) ( )tut P ht dWWW ³BODY FORCES 379 -0 .70 7 -0 .70 7 -1 .000 0.000 -0 .70 7 0 .70 7 1 3 2 ... 0xH,0yH 388 The Boundary Element Method with Programming The Hankel functions can be expanded to4 (14.12) where 0. 577 21J (Euler constant) and here only the first terms of the expansion...

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

... 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 C15 1 ( 1- QQ 1-2 Q C16 ... 1-2 Q ( 1- QQ 1-2 Q C4 2  3 C5 1 ( 1- QQ 1-2 Q C6 4 5 C 7 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 ... shortening of the region. 466 The Boundary Element Method with Programming Figure 17. 17 shows a view of the hydroelectric facility and Figure 17. 18 a plan of the layout showing the existing...

Xem thêm