Skip to main content

2017 | OriginalPaper | Buchkapitel

Elastic and Inelastic Analysis of Frames with a Force-Based Higher-Order 3D Beam Element Accounting for Axial-Flexural-Shear-Torsional Interaction

verfasst von : João P. Almeida, António A. Correia, Rui Pinho

Erschienen in: Computational Methods in Earthquake Engineering

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

When one of the dimensions of a structural member is not clearly larger than the two orthogonal ones, engineers are usually compelled to simulate it with refined meshes of shell or solid finite elements that typically impose a large computational burden. The alternative use of classical beam theories, either based on Euler-Bernoulli or Timoshenko’s assumptions, will in general not accurately capture important deformation mechanisms such as shear, warping, distortion, flexural-shear-torsional interaction, etc. However, higher-order beam theories are a still largely disregarded avenue that requires an acceptable computational demand and simultaneously has the potential to account for the above mentioned deformation mechanisms, some of which can also be relevant in slender members. This chapter starts by recalling the main theoretical features of a recently developed higher-order beam element, which was combined for the first time with a force-based formulation. The latter strictly verifies the advanced form of beam equilibrium expressed in the governing differential equations. The main innovative theoretical aspects of the proposed element are accompanied by an illustrative application to members with linear elastic behaviour. In particular, the ability of the model to simulate the effect of different boundary conditions on the response of an axially loaded member is addressed, which is then followed by an application to a case where flexural-shear-torsional interaction takes place. The beam performance is assessed by comparison against refined solid finite element analyses, classical beam theory results, and approximate numerical solutions. Finally, with a view to a future extension to earthquake engineering, an example of the element behaviour with inelastic response is also carried out.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Alemdar BN, White DW (2005) Displacement, flexibility, and mixed beam-column finite element formulations for distributed plasticity analysis. J Struct Eng 131:1811–1819CrossRef Alemdar BN, White DW (2005) Displacement, flexibility, and mixed beam-column finite element formulations for distributed plasticity analysis. J Struct Eng 131:1811–1819CrossRef
2.
Zurück zum Zitat Almeida JP, Correia AA, Pinho R (2015) Force-based higher order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications. Eng Struct 89:218–235 Almeida JP, Correia AA, Pinho R (2015) Force-based higher order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications. Eng Struct 89:218–235
3.
Zurück zum Zitat Auricchio F, Taylor RL (1995) Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity. Int J Plast 11:65–98CrossRefMATH Auricchio F, Taylor RL (1995) Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity. Int J Plast 11:65–98CrossRefMATH
4.
Zurück zum Zitat Bathe K-J (1996) Finite element procedures. Prentice Hall Bathe K-J (1996) Finite element procedures. Prentice Hall
5.
Zurück zum Zitat Bickford WB (1982) A consistent higher order beam theory. Dev Theor Appl Mech 11:137–150 Bickford WB (1982) A consistent higher order beam theory. Dev Theor Appl Mech 11:137–150
6.
Zurück zum Zitat Ciampi V, Carlesimo L (1986) A nonlinear beam element for seismic analysis of structures. In: Eighth European Conference on Earthquake Engineering. Lisbon, Portugal, pp 73–80 Ciampi V, Carlesimo L (1986) A nonlinear beam element for seismic analysis of structures. In: Eighth European Conference on Earthquake Engineering. Lisbon, Portugal, pp 73–80
7.
Zurück zum Zitat Computers and Structures Inc. (2013) SAP2000—Version 16.0.1 Computers and Structures Inc. (2013) SAP2000—Version 16.0.1
8.
Zurück zum Zitat Correia AA, Almeida JP, Pinho R (2015) Force-based higher order beam element with flexural-shear-torsional interaction in 3D frames. Part I: Theory. Eng Struct 89:204–217 Correia AA, Almeida JP, Pinho R (2015) Force-based higher order beam element with flexural-shear-torsional interaction in 3D frames. Part I: Theory. Eng Struct 89:204–217
9.
Zurück zum Zitat Cowper GR (1966) The shear coefficient in Timoshenko’s beam theory. J Appl Mech 33:335–340CrossRefMATH Cowper GR (1966) The shear coefficient in Timoshenko’s beam theory. J Appl Mech 33:335–340CrossRefMATH
10.
Zurück zum Zitat Dong SB, Alpdogan C, Taciroglu E (2010) Much ado about shear correction factors in Timoshenko beam theory. Int J Solids Struct 47:1651–1665CrossRefMATH Dong SB, Alpdogan C, Taciroglu E (2010) Much ado about shear correction factors in Timoshenko beam theory. Int J Solids Struct 47:1651–1665CrossRefMATH
11.
Zurück zum Zitat Frischkorn J, Reese S (2013) A solid-beam finite element and non-linear constitutive modelling. Comput Methods Appl Mech Eng 265:195–212MathSciNetCrossRefMATH Frischkorn J, Reese S (2013) A solid-beam finite element and non-linear constitutive modelling. Comput Methods Appl Mech Eng 265:195–212MathSciNetCrossRefMATH
12.
Zurück zum Zitat Hjelmstad KD (2002) Mixed methods and flexibility approaches for nonlinear frame analysis. J Constr Steel Res 58:967–993CrossRef Hjelmstad KD (2002) Mixed methods and flexibility approaches for nonlinear frame analysis. J Constr Steel Res 58:967–993CrossRef
13.
Zurück zum Zitat Hjelmstad KD, Taciroglu E (2005) Variational basis of nonlinear flexibility methods for structural analysis of frames. J Eng Mech 131:1157–1169CrossRef Hjelmstad KD, Taciroglu E (2005) Variational basis of nonlinear flexibility methods for structural analysis of frames. J Eng Mech 131:1157–1169CrossRef
14.
Zurück zum Zitat Kaneko T (1975) On Timoshenko’s correction for shear in vibrating beams. J Phys D Appl Phys 8:1927–1936CrossRef Kaneko T (1975) On Timoshenko’s correction for shear in vibrating beams. J Phys D Appl Phys 8:1927–1936CrossRef
15.
Zurück zum Zitat Menegotto M, Pinto PE (1973) Method of analysis for cyclically loaded RC plane frames including changes in geometry and non-elastic behaviour of elements under combined normal force and bending. In: IABSE Symposium on resistance and ultimate deformability of structures acted on by well defined repeated loads—Final report Menegotto M, Pinto PE (1973) Method of analysis for cyclically loaded RC plane frames including changes in geometry and non-elastic behaviour of elements under combined normal force and bending. In: IABSE Symposium on resistance and ultimate deformability of structures acted on by well defined repeated loads—Final report
16.
Zurück zum Zitat Mindlin RD, Deresiewicz H (1953) Timoshenko’s shear coefficient for flexural vibrations of beams, technical report No. 10, ONR Project NR064–388. New York Mindlin RD, Deresiewicz H (1953) Timoshenko’s shear coefficient for flexural vibrations of beams, technical report No. 10, ONR Project NR064–388. New York
17.
Zurück zum Zitat Neuenhofer A, Filippou FC (1997) Evaluation of nonlinear frame finite-element models. J Struct Eng 123:958–966CrossRef Neuenhofer A, Filippou FC (1997) Evaluation of nonlinear frame finite-element models. J Struct Eng 123:958–966CrossRef
18.
Zurück zum Zitat Pian THH, Tong P (1968) Rationalization in deriving element stiffness matrix by assumed stress approach. In: Conference on matrix methods in structural analysis (2nd), pp 441–469 Pian THH, Tong P (1968) Rationalization in deriving element stiffness matrix by assumed stress approach. In: Conference on matrix methods in structural analysis (2nd), pp 441–469
19.
Zurück zum Zitat Prathap G, Vinayak RU, Naganarayana BP (1996) Beam elements based on a higher order theory—II. Boundary layer sensitivity and stress oscillations. Comput Struct 58:791–796CrossRefMATH Prathap G, Vinayak RU, Naganarayana BP (1996) Beam elements based on a higher order theory—II. Boundary layer sensitivity and stress oscillations. Comput Struct 58:791–796CrossRefMATH
20.
Zurück zum Zitat Spacone E, Ciampi V, Filippou FC (1996) Mixed formulation of nonlinear beam finite element. Comput Struct 58:71–83CrossRefMATH Spacone E, Ciampi V, Filippou FC (1996) Mixed formulation of nonlinear beam finite element. Comput Struct 58:71–83CrossRefMATH
21.
Zurück zum Zitat Teixeira de Freitas JA, Moitinho de Almeida JP, Ribeiro Pereira EMB (1999) Non-conventional formulations for the finite element method. Comput Mech 23:488–501CrossRefMATH Teixeira de Freitas JA, Moitinho de Almeida JP, Ribeiro Pereira EMB (1999) Non-conventional formulations for the finite element method. Comput Mech 23:488–501CrossRefMATH
22.
Zurück zum Zitat The MathWorks Inc., 2009. MATLAB—Version 7.9 The MathWorks Inc., 2009. MATLAB—Version 7.9
23.
Zurück zum Zitat Vlassov BZ (1962) Pièces Longues en Voiles Minces. Éditions Eyrolles, Paris, France Vlassov BZ (1962) Pièces Longues en Voiles Minces. Éditions Eyrolles, Paris, France
Metadaten
Titel
Elastic and Inelastic Analysis of Frames with a Force-Based Higher-Order 3D Beam Element Accounting for Axial-Flexural-Shear-Torsional Interaction
verfasst von
João P. Almeida
António A. Correia
Rui Pinho
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-47798-5_5