A finite element interior-point implementation of tension field theory. (15th April 2015)

• Record Type: Journal Article
• Authors: de Rooij, R.; Abdalla, M.M.
• Is Part Of: Computers & structures. Volume 151(2015)
• Page Start: 30
• Page End: 41
• Publication Date: 2015-04-15
• Subjects: Membranes -- Relaxed strain energy function -- Interior-point method -- Wrinkling -- Variational formulation -- Finite element method; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2015.01.007
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: An interior-point implementation method of tension field theory is proposed. The relaxed strain energy function for membranes is reformulated. Convexity properties of the relaxed strain energy function are maintained. A set of governing equations is presented in a standard finite element format. First order convergence of the energy norm is demonstrated. Abstract: This paper presents an interior-point implementation method of the relaxed strain energy function to model the stress distribution in membranes in the presence of wrinkles. The relaxed strain energy function is reformulated using the interior-point method. This formulation is proven to be quasi-convex with respect to the deformation gradient. A set of governing equations for the membrane is developed in the standard finite element format. The solution to this set of equations is obtained using the interior-point method, and several numerical examples are presented for validation. The proposed method is shown to converge and to be robust and efficient.