Analytical particular solutions of augmented polyharmonic spline associated with Mindlin plate model

摘要

Analytical particular solutions of the augmented polyharmonic spline (APS) associated with the polyharmonic and poly-Helmholtz operators and their products were derived by Tsai et al. (Eng Anal Bound Elem 33 (2009), 514). In addition, it has been mentioned that the particular solution associated with a coupled system of partial differential equations (PDEs) can be derived from the prescribed solutions by using the H?rmander operator decomposition technique. In this article, this derivation procedure is demonstrated via Mindlin thick-plate problems, which are governed by a coupled system of three second-order PDEs. Analytical particular solutions of displacements, shear forces, and bending or twisting moments corresponding to the polyharmonic spline and monomials are all explicitly derived. These particular solutions are validated using numerical examples.