Popular benchmark problems for geometric nonlinear analysis of shells

By Kam-Yim Sze, X. Liu, S. Lo. 2004

438 citations recorded by the source corpus.

In most, if not all, of the previous work on finite element formulation and nonlinear solution procedures, results of geometric nonlinear benchmark problems of shells are presented in the form of load-deflection curves. In this paper, eight sets of popularly employed benchmark problems are identified and their detailed reference solutions are obtained and tabulated. It is hoped that these solutions will form a convenient basis for subsequent comparison and that the tedious yet inaccurate task of reconstructing data points by graphical measurement of previously reported load-deflection curves can be avoided. Moreover, the relative convergent difficulty of the problems are revealed by the number of load increments and the total number of iterations required by an automatic load incrementation scheme for attaining the converged solutions under the maximum loads.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/aba678fdbbf10d1a101646deb4a23254e0578814

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Isogeometric analysis: An overview and computer implementation aspects (2012, methodology): “s used to solve for the displacements. Fig. 39 shows the deformed conguration of the shell and in Fig.40 the load versus the z-displacement at point A is plotted together with the result reported in [140]. Figure 37: The open-end cylindrical shell subjected to radial pulling forces: problem setup [1”
A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Large deformation problems (2011, background): “[69] (8×8 shells) and Duarte Filho and Awruch [71] (10×10×4 one-point integration solids) are introduced as reference solutions.”
Geometrically nonlinear refined shell theories by Carrera Unified Formulation (2019, methodology): “[61], where the 40 40 S4R four-node shell elements in ABAQUS was used to calculate the large-deflection response for the same problem.”
Koiter analysis of folded structures using a corotational approach (2013, background): “The shell loaded by a transversal force normal to the surface is a classical test, which can also be found in Sze (2004).”
An isogeometric Reissner–Mindlin shell element based on Bézier dual basis functions: Overcoming locking and improved coarse mesh accuracy (2020, methodology): “The analytical solutions of the displacements at the free end are given by ux(M) = [sin( M M0 ) M0 M −1]L and uz(M) = [1 − cos( M M0 )] M0 M with M0 = EI L = 25 3 [56].”
Modeling of Composite Shells in 6–Parameter Nonlinear Theory with Drilling Degree of Freedom (2011, background): “The graphs show very good agreement with the reference solution [50].”