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

... Results, Element 3 u= 0.480E-04 0.480E-0 4-0 . 467 E-03 0.744E-04 0.000E+0 0-0 . 468 E-03 0.000E+00 0.000E+0 0-0 .723E-03 0.000E+00 0.744E-0 4-0 . 468 E-03 t= 0.000 0.000 -0 .707 0.000 0.000 -0 .707 ... 298.892 6. 277 0.000 0.000 0.000 0.000 … 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 ... [ 268 The Boundary Element Method with Programming Stress: -3 6. 182 0.205 0.000 -1 7.311 Coordinates: 2.00 0.50 u: 0.000 -0 .107 Stress: 0.000 0.000 0.000 -1 7.8 86 Coordinates: 2.00 0 .60 ...

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 10 pot

... ( 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 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 ... ( 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 C 16 G/4( 1- Q GQ/4 G/15( 1- Q C17 1-4 Q 12+10 Q C18 -1 /8( 1- Q - Q/8 -1 /30( 1- Q C19 ... Element Method with Programming (A.5) (A .6) where r is the distance between the source point P and the field point Q and in the outward normal. The derivative of r with respect to the Cartesian...

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

... 16. 1 Introduction 435 16. 2 Coupling theory 4 36 16. 2.1 Coupling to finite elements 4 36 16. 2.2 Coupling to boundary elements 443 16. 3 Example 444 16. 4 Dynamics 4 46 16. 4.1 Example 447 16. 5 ... 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 ... 6. 3.10 Implementation for three-dimensional problems 161 6. 4 Conclusions 166 6. 5 Exercises 167 6. 6 References 168 7 Assembly and Solution 169 7.1 Introduction 169 7.2 Assembly of system...

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

... presented for the one-dimensional finite boundary elements, ()()knNKf are the same infinite shape functions as for the one-dimensional element, with K substituted for [ and the values for ... 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 ... data is 76 The Boundary Element Method with Programming For anisotropic problems the fundamental solutions have been presented by Bonnet1. For example, the solution for temperature/potential...

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

... & Mech,12, 34 3-3 46. 5. Mindlin R.D. (19 36) 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 ... 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 ... integrals arise only for the T kernel and only if the collocation point Pi coincides with one of the element nodes. Let us rewrite equation (6. 10) (6. 15) where g(n) stands for the global node...

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

... inside 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 ... -0 .022 36 0.00079 0.00079 -0 .00787 -0 .00123 - 0.00787 -0 .00508 -0 .00508 -0 .00508 -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 ... 5 96 -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 0.0 597 -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 0.0 598 -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 0.0 599 -1 0.0...

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 8 pps

... Analysis with Boundary Elements 8: 10 9-1 12. 4. Aliabadi M. H. (2002) The Boundary Element Method (Volume 2). J. Wiley. 5. Stroud, A.H. and Secrest, D. (1 966 ) Gaussian Quadrature Formulas. ... 12.4 Cantilever 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 ... Nodes 4 ! Elements 1.000 1.000 0.707 0.707 1.000 0.000 0.707 -0 .707 0.000 -1 .000 1234 364 The Boundary Element Method with Programming where (13.30) The discretised form can be...

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

... 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 ... 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 ... Numer. Methods Eng. 36 (21), 357 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...

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