An approximate geometric nonlinear formulation for flat shell elements

Date

2025-11-12

Author

Çetin, İrem Nur

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Slender structures widely used in modern engineering exhibit high sensitivity to geometric nonlinear effects, such as large displacements and rotations, which linear analysis cannot capture accurately. Approximate geometrically nonlinear methods provide a practical balance between accuracy and computational efficiency. However, assessing the performance and limitations of approximate methods using different flat shell element types remains a critical topic for research. In this study, four different flat shell elements were constructed using the membrane element with incompatible modes and the quadrilateral membrane element with drilling degrees of freedom for the membrane behavior and the DKQ and PQI plate element formulations for the plate behavior. The accuracy and computational efficiency of the approximate method for geometrically nonlinear analysis were assessed using these four flat shell element types formulated as geometrically linear within the updated Lagrangian framework. To this end, a completely new finite element code was developed in MATLAB employing the full Newton-Raphson iteration. The analysis results were compared with benchmark problems available in the literature and with example problems possessing analytical solutions. It was observed that the approximate method provides reliable results at analysis steps where the small-strain assumption holds and the rotations remain below 90 degrees in bifurcation and limit-point buckling analyses, as well as in the analysis of geometrically nonlinear benchmark problems, while remaining computationally efficient. This approximate method can serve as an effective alternative approach for geometrically nonlinear analyses under these kinematic limitations.

Subject Keywords

Geometrically nonlinear analysis, Updated Lagrangian, Flat shell element

URI

https://hdl.handle.net/11511/117412

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Graduate School of Natural and Applied Sciences, Thesis