The analog equation method for large deflection analysis of heterogeneous orthotropic membranes: a boundary-only solution

• Published in: Engineering analysis with boundary elements 2001-09, Vol.25 (8), p.655-667
• Main Authors: Katsikadelis, J.T., Tsiatas, G.C.
• Format: Article
• Language: English
• Subjects: Analog equation; Boundary element method; Boundary-integral methods; Computational techniques; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heterogeneous; Large deflections; Mathematical methods in physics; Membrane; Membranes, rods and strings; Nonlinear; Orthotropic; Physics; Solid mechanics; Structural and continuum mechanics; Structural mechanics (beam, string...); Theory and numerical methods
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/S0955-7997(01)00033-9

In this paper, the analog equation method (AEM) is applied to nonlinear analysis of heterogeneous orthotropic membranes with arbitrary shape. In this case, the transverse deflections influence the in-plane stress resultants and the three partial differential equations governing the response of the membrane are coupled and nonlinear with variable coefficients. The present formulation, being in terms of the three displacement components, permits the application of geometrical in-plane boundary conditions. The membrane may be prestressed either by prescribed boundary displacements or by tractions. Using the concept of the analog equation, the three coupled nonlinear equations are replaced by three uncoupled Poisson's equations with fictitious sources under the same boundary conditions. Subsequently, the fictitious sources are established using a procedure based on the BEM and the displacement components as well as the stress resultants are evaluated from their integral representations at any point of the membrane. Several membranes are analyzed which illustrate the method, and demonstrate its efficiency and accuracy. Moreover, useful conclusions are drawn for the nonlinear response of heterogeneous anisotropic membranes. The method has all the advantages of the pure BEM, since the discretization and integration are limited only to the boundary.