The direct boundary element method in plate bending

Abstract

SUMMARYThe direct boundary element method based on the Rayleigh-Green identity is employed for the static analysis of Kirchhoff plates. The starting point is a slightly modified version of Stern's equations. The focus is on the implementation of the method for linear elements and a Hermitian interpolation for the deflection w. The concept of element matrices is developed and the Cauchy principal values of the singular integrals are given in detail. The treatment of domain integrals, the handling of internal supports, the properties of the solution and the effect of singularities are discused. Numerical examples ilIustrate the various techniques. In the appendix the influence functions for the second and third derivatives of the deflection w are given.

Boundary integral equations for general laminated plates with coupled stretching–bending deformation

“…With α being the direction angle of the source point ξ whose applied momentm n is in the opposite tangent direction (figure 2), it can be proved that the results of equation (5.8b) are identical to those presented in Hartmann & Zotemantel (1986). Note that in Hartmann & Zotemantel (1986), a typing error occurs in the last term of their equation forċ 2 (x) in which sin 2 ϕn 2 should be corrected as (sin 2ϕ)n 2 .…”

“…Note that in Hartmann & Zotemantel (1986), a typing error occurs in the last term of their equation forċ 2 (x) in which sin 2 ϕn 2 should be corrected as (sin 2ϕ)n 2 .…”

“…Based on the boundary integral equations for different problems, several different boundary elements used in solid mechanics or fluid mechanics have been developed (Brebbia et al 1984). Among these boundary elements, the development of plate bending problems (Stern 1979;Hartmann & Zotemantel 1986;Shi & Bezine 1988) started relatively later than that of twodimensional or three-dimensional elastostatics (Rizzo 1967;Brebbia et al 1984). *chwu@mail.ncku.edu.tw For example, even though vast advances have been made in boundary element methods for two-and three-dimensional fracture problems (Li et al 1998;Frangi et al 2002;Rungamornrat & Mear 2008a,b), relatively few studies have been done on boundary element formulation for cracks in plates subjected to transverse loading or bending moments.…”

Simplified approach of free vibration analysis of plates supported in vicinity of the corners by BEM

“…The most popular approach was proposed by Bèzine [18] in which the forces at the internal supports are treated as unknown variables. This techniques is also used by de Paiva and Venturini [19,20], Hartmann and Zotemantel [21] and Abdel-Akher and Hartley [22]. Katsikadelis et al [23], Providakis and Toungelidis [24] applied technique of Bèzine to solve dynamic problems of thin plate.…”

Formulação do método dos elementos de contorno para placas enrijecidas considerando-se não-linearidades física e geométrica

“…Os primeiros trabalhos que trataram placas no contexto de estruturas de pisos de edifícios foram os de Bézine (1981), Hartmann & Zotemantel (1986) no contorno e outra para um ponto fora do domínio) em substituição à utilização da equação integral para a rotação normal nos pontos do contorno.…”