On the foundations of anisotropic interior beam theories

Research output: Contribution to journalArticleScientificpeer-review

Standard

On the foundations of anisotropic interior beam theories. / Karttunen, Anssi T.; Von Hertzen, Raimo.

In: Composites Part B: Engineering, Vol. 87, 15.02.2016, p. 299-310.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

APA

Vancouver

Author

Bibtex - Download

@article{c45412325dd34449bc3973c20efa15f8,
title = "On the foundations of anisotropic interior beam theories",
abstract = "This study has two main objectives. First, we use the Airy stress function to derive an exact general interior solution for an anisotropic two-dimensional (2D) plane beam. Second, we cast the solution into the conventional form of 1D beam theories to clarify some basic concepts related to anisotropic interior beams. The derived general solution provides the exact third-order interior kinematic description for the plane beam and includes the Levinson/Reddy-kinematics as a special case. By applying the Clapeyron's theorem, we show that the stresses acting as surface tractions on the lateral end surfaces of the interior beam need to be taken into account in all energy-based considerations related to the interior beam in order to avoid artificial end effects. Exact 1D interior beam equations are formed from the general 2D solution. Finally, we develop an exact interior beam finite element based on the general solution. With full anisotropic coupling, the stiffness matrix of the element becomes initially asymmetric due to the interior nature of the plane beam. By redefining the generalized nodal axial forces of the element, the stiffness matrix takes a symmetric form.",
keywords = "B. Anisotropy, B. Elasticity, C. Analytical modelling, C. Finite element analysis (FEA)",
author = "Karttunen, {Anssi T.} and {Von Hertzen}, Raimo",
year = "2016",
month = "2",
day = "15",
doi = "10.1016/j.compositesb.2015.10.026",
language = "English",
volume = "87",
pages = "299--310",
journal = "Composites Part B: Engineering",
issn = "1359-8368",
publisher = "Elsevier Limited",

}

RIS - Download

TY - JOUR

T1 - On the foundations of anisotropic interior beam theories

AU - Karttunen, Anssi T.

AU - Von Hertzen, Raimo

PY - 2016/2/15

Y1 - 2016/2/15

N2 - This study has two main objectives. First, we use the Airy stress function to derive an exact general interior solution for an anisotropic two-dimensional (2D) plane beam. Second, we cast the solution into the conventional form of 1D beam theories to clarify some basic concepts related to anisotropic interior beams. The derived general solution provides the exact third-order interior kinematic description for the plane beam and includes the Levinson/Reddy-kinematics as a special case. By applying the Clapeyron's theorem, we show that the stresses acting as surface tractions on the lateral end surfaces of the interior beam need to be taken into account in all energy-based considerations related to the interior beam in order to avoid artificial end effects. Exact 1D interior beam equations are formed from the general 2D solution. Finally, we develop an exact interior beam finite element based on the general solution. With full anisotropic coupling, the stiffness matrix of the element becomes initially asymmetric due to the interior nature of the plane beam. By redefining the generalized nodal axial forces of the element, the stiffness matrix takes a symmetric form.

AB - This study has two main objectives. First, we use the Airy stress function to derive an exact general interior solution for an anisotropic two-dimensional (2D) plane beam. Second, we cast the solution into the conventional form of 1D beam theories to clarify some basic concepts related to anisotropic interior beams. The derived general solution provides the exact third-order interior kinematic description for the plane beam and includes the Levinson/Reddy-kinematics as a special case. By applying the Clapeyron's theorem, we show that the stresses acting as surface tractions on the lateral end surfaces of the interior beam need to be taken into account in all energy-based considerations related to the interior beam in order to avoid artificial end effects. Exact 1D interior beam equations are formed from the general 2D solution. Finally, we develop an exact interior beam finite element based on the general solution. With full anisotropic coupling, the stiffness matrix of the element becomes initially asymmetric due to the interior nature of the plane beam. By redefining the generalized nodal axial forces of the element, the stiffness matrix takes a symmetric form.

KW - B. Anisotropy

KW - B. Elasticity

KW - C. Analytical modelling

KW - C. Finite element analysis (FEA)

UR - http://www.scopus.com/inward/record.url?scp=84948398928&partnerID=8YFLogxK

U2 - 10.1016/j.compositesb.2015.10.026

DO - 10.1016/j.compositesb.2015.10.026

M3 - Article

VL - 87

SP - 299

EP - 310

JO - Composites Part B: Engineering

JF - Composites Part B: Engineering

SN - 1359-8368

ER -

ID: 1684403