Singular and non-singular concentrations of transversal forces in linear-elastic plates

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It is a goal of the currently intended research project to generate and formulate an extension of Kirchhoff's plate theory that goes a step into the direction of Reissner-Mindlin's plate theory in such a way that the resultant differential equations are of a homogeneous derivation order and thus allow the formulation and implementation of a corresponding method of complex potentials. Another goal is the actual solution of a set of well-selected boundary value problems. For that purpose the kinematic quantities w, psi_x and psi_y are to be represented by three holomorphic potentials in such a way that the three (coupled) differential equations for the kinematic quantities are fulfilled in an identical manner for an arbitrary choice of the complex potentials. In the case that the new extended plate theory and the corresponding complex potential method prove to be well suitable for the solution of problems with concentrations in the transverse cross-sectional forces a further goal will be a respective extension of the numerical tool of the scaled boundary finite element method. This extension eventually should be implemented in a new analysis code.