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Analytical particular solutions of augmented polyharmonic spline associated with Mindlin plate model
Author(s) -
Tsai ChiaCheng,
Wu Edward MingYang
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20702
Subject(s) - mathematics , polyharmonic spline , monomial , spline (mechanical) , partial differential equation , mathematical analysis , partial derivative , operator (biology) , thin plate spline , spline interpolation , pure mathematics , biochemistry , statistics , chemistry , structural engineering , repressor , transcription factor , engineering , bilinear interpolation , gene
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 Hörmander 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. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011