C2-Continuous Elements for Boundary Element Analysis

Abstract

SUMMARYOverhauser's original idea of linearly blending two sets of quadratic C 0 -continuous basis functions to produce a set of C 1 -continuous basis functions is employed by linearly blending two sets of quadratic C 1 -continuous basis functions. The result is a set of eight basis functions which are C 2 -continuous from element to element and can be used for boundary element analysis where post-processing of the solution is required. Solutions to Laplace's equation in simple geometries are used to demonstrate the accuracy of the solutions obtained with the new elements. These new elements also provide more accurate values for the ÿrst and second derivatives of the solution in the tangential direction at all points on a smooth boundary and good approximations at corner points. ? 1997 by John Wiley & Sons, Ltd.

New identities for fundamental solutions and their applications to non-singular boundary element formulations

“…The integral identities in (1)± (3) and (5)±(7) for the fundamental solutions have been employed successful in the development of the weakly-singular forms of both conventional and hypersingular BIEs for potential, elastostatic, acoustic, elastodynamic and electromagnetic problems (Rudolphi 1991 (Poon, Mukherjee et al 1998) and thermoelasticity (Mukherjee, Shah et al 1999), and referenced by others (see, e.g., (Tanaka, Sladek et al 1994;Johnston 1997)). Using these identities offers a general and systematic approach to the development of the weaklysingular forms of the BIEs, as compared to the earlier approach where the explicit expressions of the fundamental solutions need to be exploited in great length in order to cancel the singularities in the BIEs (see, e.g., (Rudolphi, Krishnasamy et al 1988)).…”

“…The use of the identities in deriving the weakly-singular forms of the BIEs, especially those of the hypersingular BIEs (Krishnasamy, Rizzo et al 1991), have been applied successfully to stress analysis (Muci-Kuchler and Rudolphi 1993), acoustics (Liu and Rizzo 1992;Liu and Chen 1999), elastodynamics (Liu and Rizzo 1993) and electromagnetics (Chao, Liu et al 1995). This approach has also been adopted in others' work as well (see, e.g., (Tanaka, Sladek et al 1994;Johnston 1997)). This simple solution approach is successfully applied in Ref.…”

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

“…1016/j.ijsolstr.2006.04.008 necessity of replacing the continuous domains (or boundaries) with discrete ones, which in practice requires, particularly in complex boundary problems, an introduction of a large number of input data (nodes) and also resolving a considerable number of algebraic equation systems. Each day brings some original research work presenting new developments in the field and it would be impossible to mention all of them here (Camp and Gipson, 1991;Jonston, 1996Jonston, , 1997Sen, 1995;Liggett and Salmon, 1981;Durodola and Fenner, 1990;Gray and Soucie, 1993;Singh and Kalra, 1995). It should be noted, however, that the main idea behind all these papers is an attempt to improve existing BEM and FEM based on the traditional discretization of the domain or its boundary.…”

Modification of the boundary integral equation for the Navier–Lamé equations in 2D elastoplastic problems and its numerical solving

“…The separation of the boundary from the domain is evident in Equation (9). The boundary is defined by the formalism of boundary integrals (10) and (11). In our further considerations, integral (11) is used to describe transform Q P u Q n m .…”

“…After inserting (14) into (13) and then the resulting expression into (11), we obtain the convolution integral equation in the Fourier transform domain…”