Exact finite element formulation in generalized beam theory
| Autor: | A. Habtemariam, C. Könke, M. J. Bianco, V. Zabel |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Timoshenko beam theory
Completeness coefficient matrix 020101 civil engineering 02 engineering and technology Generalized beam theory lcsh:TH1-9745 0201 civil engineering Stiffness matrix Transformation matrix 0203 mechanical engineering medicine Thin-walled circular hollow section Coefficient matrix Civil and Structural Engineering Mathematics Exact solution business.industry Mathematical analysis Stiffness Torsion (mechanics) Structural engineering Hermitian matrix Finite element method 020303 mechanical engineering & transports lcsh:TA1-2040 medicine.symptom lcsh:Engineering (General). Civil engineering (General) business lcsh:Building construction |
| Zdroj: | International Journal of Advanced Structural Engineering International Journal of Advanced Structural Engineering, Vol 10, Iss 3, Pp 295-323 (2018) |
| ISSN: | 2008-6695 2008-3556 |
| DOI: | 10.1007/s40091-018-0199-8 |
| Popis: | This paper presents the formulation of exact stiffness matrices applied in linear generalized beam theory (GBT) under constant and/or linear loading distribution in the longitudinal direction. Also, the assortment of the correct exact stiffness matrix and the corresponding shape function are presented based on main transversal deformation mode, which can be divided into: (1) dominant distortion mode; (2) dominant torsion mode; (3) and critical distortion–torsion mode. Special attention is given to the hyperbolic–trigonometric shape functions, which are organized in a system of vector in function of longitudinal direction and a coefficient matrix obtained from the completeness requirement. This approach has the benefit of compacting the terms of the stiffness matrix and systematizing the boundary conditions of an element by applying the completeness coefficient matrix as a transformation matrix. As a result, in linear analysis, a single element can represent the stress and displacement fields. Moreover, due to the higher-order continuous derivatives properties of hyperbolic–trigonometric shape functions, the generalized internal shear is obtained without the typical discontinuity of Hermitian shape functions. A full and detailed example, applied in a thin-walled circular hollow cross section, provides not only an illustration of the presented approach, but also a quick introduction point in GBT. |
| Databáze: | OpenAIRE |
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