A Study of Solutions for the Anisotropic Plate Subjected to a Concentrated Force

• Published in: Journal of applied mechanics 1998-03, Vol.65 (1), p.273-276
• Main Authors: LaMattina, B., Klang, E. C., Eischen, J. W.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics
• ISSN: 0021-8936; 1528-9036
• DOI: 10.1115/1.2789039

Bending analysis of plates by BEM requires the use of two fundamental solutions: (1) the displacement field due to a transverse point load, and (2) the displacement field due to a point moment, both for plates of infinite extent. Fundamental solutions for anisotropic plates utilize complex variable theory following groundwork laid by Lekhnitskij (1968). Mossakowski (1955) presented a solution for a point force on an infinite plate using complex parameters of the first kind, and Suchar (1964) presented the solutions for a point force and point moment in terms of complex parameters of the second kind. LaMattina (1997) derived a solution for the point force using the same mapping functions as Mossakowski that is more general than the other two solutions. This note presents all three solutions and shows how they are applied to the BEM formulation. Differences between these solutions are illustrated and discussed. The implications of these discrepancies are examined for the infinite plate, as well as a typical boundary value problem. Another result of this work is related to an arbitrary constant, the reference radius. The purpose of the reference radius is discussed and suggestions are made on how to assign its value in numerical implementations of BEM. (Author)