The Boundary Strip Method in Elastostatics and Potential Equations

Abstract

SUMMARYThe present paper develops the idea of the boundary strip method, and presents its fundamentals, merits, applications and also some closed-form or non-element solutions based on it. The present approach combines the Boundary Integral Equation Method (BIEM) and the finite strip method, taking the advantages of both. The finite strip method is installed into the BIEM by expanding the unknown parameters of problems in terms of trigonometric series. This combination creates a new powerful numerical method with three advantages over other numerical methods, namely, a shorter computation time, a better accuracy and a reduction of one and a half dimensions in mesh generation. Applications in two-dimensional potential and field problems demonstrate the efficiency and the accuracy of the proposed method. Finally, closed-form presentations for Laplace equation and elastostatics are given, along circular segments.

Steady state elastodynamics solutions using boundary spectral line strips

“…Two kinds of spectral approximation are suggested. The first approximation (Michael et al, 1994;1996a) uses harmonic spectral series, thus the functions f k are trigonometric functions (sine and cosine). This approximation becomes attractive when the geometry of the boundary is periodical and smooth, since it has a periodical behavior.…”

“…The method uses spectral expansions for the primary and secondary variables and therefore allows a free mesh solution, with high accuracy and a low number of degrees of freedom (DOF). The method suggests the use of Fourier expansion for periodical geometries (Michael et al, 1994(Michael et al, , 1996a and a high order polynomial expansion for nonperiodical geometries (Michael et al, 1996b). The BSM has an important EC 15,2…”

“…advantage in potential equations and in elastostatics in cases of circular geometries (Michael et al, 1996a), straight line geometries (Michael et al, 1996b) or a combination of the two. For these cases all integrations which are involved with the solution can be solved analytically, if the collocation point lies along the integration path (singular case) or off the integration path.…”

“…These integrations can be derived analytically when the geometry of the boundary consists of circular entities for the Laplace equation, elastostatics (Michael et al, 1996a) and frequency domain elastodynamics (Michael, 1996).…”