The p‐version of the finite element method for three‐dimensional curved thin walled structures

By Alexander Düster, H. Bröker, Ernst Rank. 2001

216 citations recorded by the source corpus.

In this paper we present an implementation of a three‐dimensional p‐version for structural problems of solids with almost arbitrarily curved surfaces. Applying the blending function method, complex structures can often be modelled by a few p‐elements, being the basis for a higher order approximation. Numerical examples will demonstrate, that the p‐version with anisotropic Ansatz spaces allows to predict the structural behaviour of three‐dimensional plates and shells with approximately the same amount of degrees of freedom as in the two‐dimensional case, yet significantly more accurate due to the three‐dimensional model. Furthermore, it is advantageous to compute complex structures exclusively with three‐dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three‐dimensional solid elements. Using the p‐version with anisotropic Ansatz spaces the whole structure can be efficiently discretized with solid elements, even if the aspect ratio of the elements becomes very large. Copyright © 2001 John Wiley Sons, Ltd.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/110bb5fe75e51e29f7979267159d7cba3cda5daa

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In Mechanics of Materials

Citations in the corpus

The p-Version of the Finite Element and Finite Cell Methods (2017, methodology): “In this way, one can introduce anisotropic element formulations for the analysis of shell-like solids, also called “thin solids” (Szabó and Sahrmann, 1978; Szabó and Babuška, 1991; Düster et al., 2001).”
Isogeometric contact: a review (2014, methodology): “These can be described exactly using the blending function method (Gordon and Hall 1973, Szabó and Babuška 1991, Düster et al. 2001), which introduces a non-isoparametric mapping.”
A unified 3D‐based technique for plate bending analysis using scaled boundary finite element method (2012, background): “[42,43] also emphasised that because of the introduction of the plate theories in the governing equations, the inconsistency of those theories to the 3D theory was embedded in the element development at an early stage.”
An efficient mixed variational reduced‐order model formulation for nonlinear analyses of elastic shells (2018, unknown): “∂U ∂q = ∫Ω0 B̃(q) Tσ(q) = f int(q), (38)”
Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review (2015, methodology): “The p-version of the FEM and the IGA have been used mainly for static or modal analyses [68, 102, 219, 221].”
Local enrichment of the finite cell method for problems with material interfaces (2013, methodology): “The reference solution for this example is provided by a conventional p-FEM approach where the geometry of the inclusion and hole are exactly resolved by taking high-order elements with blending functions into consideration [31,33,53].”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “For the three-dimensional basis, see [30,31,49,50].”
High‐order plate bending analysis based on the scaled boundary finite element method (2013, background): “Nevertheless, the ongoing new developments in plate elements [7,41–43], numerical methods [36,44–46] and theory [6, 47] demonstrate the need of continuous improvement for plate bending analysis, regarding the aspects of physical consistency [48, 49], simplicity [50] and computational efficiency.”