A new boundary spectral strip method for non-periodical geometrical entities based on analytical integrations

Steady state elastodynamics solutions using boundary spectral line strips

“…The T i terms of equation ( 11) yield singularities of ln S multiplied by geometrical terms only when n = 0 or n = 1. Using the geometrical characteristics of the straight line entity (Michael et al, 1996b) including the geometrical terms of equation ( 10), we find that the integrations to be calculated are:…”

“…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.…”

“…This approximation is more adequate for non-periodical geometries such as straight lines. When using this approximation for problem boundaries which include straight lines one obtains the following integrals (Michael et al, 1996b):…”

Boundary spectral strip for geometries with arbitrary curvature

“…These integrations can be performed analytically for circular strips 3,4 or for straight line strips 4,5 (the integrations are found analytically for the Laplace equation, elastostatics equations and elastodynamics equations). For more complicated geometries, however, the integrations cannot be obtained analytically and numerical integration is inevitable.…”