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Three-dimensional stress analysis for beam-like structures using Serendipity Lagrange shape functions

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Show simple item record Minera, A. Patni, M. Carrera, E. Weaver, Paul M. Pirrera, A. 2018-07-05T14:13:34Z 2018-07-05T14:13:34Z 2018
dc.description peer-reviewed en_US
dc.description.abstract Simple analytical and finite element models are widely employed by practising engineers for the stress analysis of beam structures, because of their simplicity and acceptable levels of accuracy. However, the validity of these models is limited by assumptions of material heterogeneity, geometric dimensions and slenderness, and by Saint-Venant’s Principle, i.e. they are only applicable to regions remote from bound- ary constraints, discontinuities and points of load application. To predict accurate stress fields in these locations, computationally expensive three-dimensional (3D) finite element analyses are routinely per- formed. Alternatively, displacement based high-order beam models are often employed to capture lo- calised three-dimensional stress fields analytically. Herein, a novel approach for the analysis of beam-like structures is presented. The approach is based on the Unified Formulation by Carrera and co-workers, and is able to recover complex, 3D stress fields in a computationally efficient manner. As a novelty, pur- posely adapted, hierarchical polynomials are used to define cross-sectional displacements. Due to the nature of their properties with respect to computational nodes, these functions are known as Serendip- ity Lagrange polynomials. This new cross-sectional expansion model is benchmarked against traditional finite elements and other implementations of the Unified Formulation by means of static analyses of beams with different complex cross-sections. It is shown that Serendipity Lagrange elements solve some of the shortcomings of the most commonly used Unified Formulation beam models based on Taylor and Lagrange expansion functions. Furthermore, significant computational efficiency gains over 3D finite ele- ments are achieved for similar levels of accuracy. en_US
dc.language.iso eng en_US
dc.publisher Elsevier en_US
dc.relation 642121 en_US
dc.relation.ispartofseries International Journal of Solids and Structures;141-142, pp. 279-296
dc.subject finite elements en_US
dc.subject unified formulation en_US
dc.subject 3D stress fields en_US
dc.subject T section en_US
dc.title Three-dimensional stress analysis for beam-like structures using Serendipity Lagrange shape functions en_US
dc.type info:eu-repo/semantics/article en_US
dc.type.supercollection all_ul_research en_US
dc.type.supercollection ul_published_reviewed en_US
dc.identifier.doi 10.1016/j.ijsolstr.2018.02.030
dc.contributor.sponsor ERC en_US
dc.contributor.sponsor H2020 Marie Skłodowska- Curie European Training NetworK en_US
dc.relation.projectid 642121 en_US
dc.relation.projectid EP/M013170/1 en_US
dc.rights.accessrights info:eu-repo/semantics/openAccess en_US

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