A Point Collocation Method for Geometrically Nonlinear Membranes
This paper describes the development of a numerical model for geometrically nonlinear membranes and evaluates its performance for membranes at static equilibrium. The scheme has several features not commonly seen in structural finite element analysis: the point collocation method, group formulation, and a staggered mesh. In the point collocation finite element method, the partial differential equations are solved at each node instead of by integrating over elements. The group formulation simplifies the handling of nonlinearities by interpolating the nonlinear products of variables, as opposed to seeking the product of independently interpolated variables.
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International Journal of Solids and Structures
Kolsti, K. F., & Kunz, D. L. (2013). A point collocation method for geometrically nonlinear membranes. International Journal of Solids and Structures, 50(2), 288–296. https://doi.org/10.1016/j.ijsolstr.2012.08.025