By Subrata Mukherjee
------------------Description-------------------- Boundary tools: components, Contours, and Nodes offers the result of state of the art study in boundary-based mesh-free equipment. those tools mix the dimensionality benefit of the boundary elemen
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179, 190, 66]) to model deformation of the structure. The commercial software package MEMCAD , for example, uses the commercial FEM software package ABAQUS for mechanical analysis, together with a BEM code FastCap  for the electric ﬁeld analysis. Other examples of such work are [49, 148, 1]; as well as [147, 149] for dynamic analysis of MEMS. The focus of this section is the BEM analysis of the electric ﬁeld exterior to very thin conducting plates. A convenient way to model such a problem is to assume plates with vanishing thickness and solve for the sum of the charges on the upper and lower surfaces of each plate .
3 of this chapter. 2 Stress residual The stress residual is another important quantity in this work. 9) is solved ﬁrst. This yields the boundary tractions and displacements (1) (1) (1) τj and uj . The boundary stresses σij are next obtained from the boundary values of the tractions and the tangential derivatives of the displacements, together with Hooke’s law. This is a well-known procedure in the BIE literature (see, for example, Mukherjee  or Sladek and Sladek ). 34). 34) is collocated only at regular boundary points (where the boundary is locally smooth) inside boundary elements.
4. 11). A few comments are in order. 74) is the same as Rudolphi’s  equation (20) with (his) κ = 1 and (his) S0 set equal to S and renamed ∂B. 34)). e. for an outside approach to the boundary point x . Third, as noted before, x can be an edge or corner point on ∂B (provided, of course, that u(y) ∈ C 1,α at y = x - Rudolphi had only considered a regular boundary collocation point in his excellent paper that was published in 1991). 74) is analogous to the regularized stress BIE in linear elasticity - equation (28) in Cruse and Richardson  .