A Shape-Finding Finite Element Analysis for an Equally-Stressed Surface in Membrane Structures

by T. J. Kwun, Sung Kyun Kwan Univ, Suwon, Republic of korea,
S. Y. Sur, Sung Kyun Kwan Univ, Suwon, Republic of korea,
H. W. Cho, Sung Kyun Kwan Univ, Suwon, Republic of korea,

Document Type: Proceeding Paper

Part of: Spatial, Lattice and Tension Structures


A finite element method is proposed to obtain an equally-stressed surface in a membrane structure, where the displacements and rotations of a membrane are in general finite and nonlinear. Assuming that the forces of a triangular membrane element can be expressed in terms of generalized plane stresses, nonlinear effect of deformations is considered in the formulation of geometrical stiffness matrix within the framework of displacement-controlled finite element method. In the process of applying incremental steps, unbalanced forces caused by piecewise linearization of displacements are added to the forces of the next step to correct an error. The algorithm is applied to the case of catenoid membrane, for which the results show a close agreement with the exact solution.

Subject Headings: Finite element method | Membranes | Structural analysis | Linear analysis | Stress analysis | Nonlinear analysis | Matrix (mathematics) | Stress strain relations

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