A BEM based domain decomposition method for nonlinear analysis of elastic space membranes

Abstract

In this paper the Domain Decomposition Method (DDM) is developed for nonlinear analysis of both flat and space elastic membranes of complicated geometry which may have holes. The domain of the projection of the membrane on the xy plane is decomposed into non-overlapping subdomains and the membrane problem is solved sequentially in each subdomain starting from zero displacements on the virtual boundaries. The procedure is repeated until the traction continuity conditions are also satisfied on the virtual boundaries. The membrane problem in each subdomain is solved using the Analog Equation Method (AEM). According to this method the three coupled strongly nonlinear partial differential equations, governing the response of the membrane, are replaced by three uncoupled linear membrane equations (Poisson's equations) subjected to fictitious sources under the same boundary conditions. The fictitious sources are established using a meshless BEM procedure. Example problems are presented, for both flat and space membranes, which illustrate the method and demonstrate its efficiency and accuracy.

Nonlinear analysis of elastic space cable-supported membranes

“…For space membranes the analytical solutions are limited to axisymmetric membranes where the problem is highly simplified as it becomes one-dimensional. However, membranes of arbitrary shape encountered in realistic engineering problems can be analyzed only by numerical methods [1,[8][9][10][11]. Additional related references can be found in Ref.…”

“…Finally, the developed method can be combined with the domain decomposition method for nonlinear membranes [9] and offer an efficient computational tool for analyzing cablesupported membranes of complicated geometry encountered in realistic engineering tensile structures.…”

BEM for Large Deflection Analysis of Membranes

“…The minimal surface is taken as the initial shape for space membranes. The BEM solution for the space membrane problem was developed recently [20][21][22] Regarding the space membranes, the derivation of the field equations and their solution are extremely difficult mathematical problems.…”