Doubled-Curved Element for Mooney-Rivlin Membranes

by John W. Leonard, (M.ASCE), Prof. of Civ. Engrg.; Illinois Inst. of Tech., Chicago, Ill.,
Vijay K. Verma, Sr. Engrg. Analyst; Sargent & Lundy Engrg., Chicago, Ill.,

Serial Information: Journal of the Engineering Mechanics Division, 1976, Vol. 102, Issue 4, Pg. 625-641

Document Type: Journal Paper


In this study a finite element model for the nonlinear static behavior of extremely thin arbitrary shaped membrane shells has been developed using curved elements. The governing stiffness equations are derived from the fully nonlinear theory of hyperelasticity. No limitations are imposed on the magnitudes of displacements or strains. A curved quadrilateral element has been used for the membrane. The nonlinear equations obtained are solved using a combined incremental and Newton-Raphson iterative technique. Two example problems have been considered to demonstrate the potential of the curved elements derived. For those example problems considered close agreement with the results of others were obtained.

Subject Headings: Curvature | Membranes | Finite element method | Nonlinear analysis | Nonlinear response | Statics (mechanics) | Arbitration | Stiffening

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