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

... -1 /8Q - Q/8 -1 /15Q C9 3-4 Q ( 3- QQ 4-5 Q C 10 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 ... ( 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 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 G/2SQ ... F()pt()ptt448 The Boundary Element Method with Programming displacements at the top of the column obtained from the analysis. The results compare well with a reference solution with the FEM that...

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 .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 ... 0.480E-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 0.000 0.000 -1 .000 0.000 0.000 -0 .707 ... 2.00 0.40 u: -0 .009 -0 .107 270 The Boundary Element Method with Programming Figure 10. 4 Finite element mesh Figure 10. 5 Comparison of results Table 10. 3 Results of finite element analysis...

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

... 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 ... common version of this method we subdivide the domain into elements and approximate 14 The Boundary Element Method with Programming be divided into many subtasks. Therefore, we will develop ... functions satisfy the DE exactly and the error in the satisfaction of the boundary conditions is minimised. Most readers of this book will be familiar with the finite element method. In the most common...

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 ... 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) acting on a surface with an outward...

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 ... 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 ... be written and used for numerical experiments. As the 138 The Boundary Element Method with Programming We see that since R cancels out, the integral is valid for any radius of the circle,...

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

... 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 0.0 0.0 -1 0.0 ... -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 -1 0.0 0.0 0.0 600 -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 1.E-9 50 4 .7 Young’s modulus is 100 0.0 and Poisson’s ratio zero. The iteration tolerance ... 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...

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

... cube with a distributed boundary load of 2 10 KN/mon the top of the cube. The geometry is shown in Figure 12.6 and the material parameters for all regions are E =100 0kN/m2, Q=0. For the purpose ... swelling. The effect of the swelling on the deformations at the boundary of the hole is required. The material properties for the domain are assumed to be E= 100 0.0 and Q  The swelling zone ... displacements for LC1 to LC5 for the calculation with continuous and discontinuous elements The reason for these errors is the erroneous calculation of tractions at corner nodes for continuous elements....

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 9-3 594. 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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