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.

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The Somigliana identity is an integral representation of the displacement field of a body, i.e. the solution of the Cauchy-Navier equation in the classical theory of elasticity is represented by influence functions. This well established identity for bodies with smooth surfaces is extended in the present paper to cover two-and three-dimensional bodies with piecewise smooth surfaces. ZUSAMMENFASSUNGDie Somigliana Identitgtt ist die Integraldarstellung des Verschiebungsfeldes eines K6rpers, d.h. die L6sung der Cauchy-Navier'schen DGL in der klassischen Elastizitiitstheorie wird durch Einfluf~funk-tionen dargestellt. Diese Identitiit, die fiir K6rper mit glatter Oberflfiche wohl bekannt ist, wird in diesem Aufsatz auf K6rper und Scheiben mit stiickweise glatten Rfindern ausgedehnt.

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