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 [147], for example, uses the commercial FEM software package ABAQUS for mechanical analysis, together with a BEM code FastCap [112] 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 [61].

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 [98] or Sladek and Sladek [151]). 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 [143] 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 [39] .