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T‐complete functions for thin and thick plates on elastic foundation
Author(s) -
Wróblewski Adam
Publication year - 2005
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.20022
Subject(s) - mathematics , foundation (evidence) , separation of variables , partial differential equation , mathematical analysis , set (abstract data type) , ordinary differential equation , partial derivative , homogeneous , order (exchange) , differential equation , combinatorics , computer science , finance , economics , programming language , archaeology , history
Abstract This article deals with Trefftz functional systems for thin and thick plates on one‐ and two‐parameter Winkler foundation. The T‐complete set is derived by solving the homogeneous equations of the problem. This can be done with the method of separation of variables. For each separation parameter we deal with ordinary, linear differential equations (4th order for the Kirchhoff plate and set of fourth‐ and second‐order equations for the Reissner‐Mindlin plate) so the demanded number of fundamental solutions (linearly independent) is equal to the order of equation. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005