Appendix A

Derivatives of r and Kernels, Particular Solutions and Tangential Derivatives

Abstract

This Appendix presents various derivatives of the two-dimensional Euclidean distance between any two points of the plane domain occupied by the plate. These derivatives facilitate the differentiation of the kernels of the integral equations. Additionally, the derivatives of the kernels producing the stress resultants and a table containing the particular solutions of certain Poisson’s equations, which are used in the Green’s reciprocal identity to convert domain integrals into boundary line integrals, are included. This appendix ends with derivation of the expressions for the third-order tangential derivatives along the curvilinear boundary and as ...

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