Finite Element Formulation for Linear Stability Analysis of Axially Functionally Graded Nonprismatic Timoshenko Beam

An improved approach based on the power series expansions is proposed to exactly evaluate the static and buckling stiffness matrices for the linear stability analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section and fixed–free boundary condition. Based on the Tim...

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Published inInternational journal of structural stability and dynamics Vol. 19; no. 2; p. 1950002
Main Authors Soltani, Masoumeh, Asgarian, Behrouz
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 01.02.2019
World Scientific Publishing Co. Pte., Ltd
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ISSN0219-4554
1793-6764
DOI10.1142/S0219455419500020

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Abstract An improved approach based on the power series expansions is proposed to exactly evaluate the static and buckling stiffness matrices for the linear stability analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section and fixed–free boundary condition. Based on the Timoshenko beam theory, the equilibrium equations are derived in the context of small displacements, considering the coupling between the transverse deflection and angle of rotation. The system of stability equations is then converted into a single homogeneous differential equation in terms of bending rotation for the cantilever, which is solved numerically with the help of the power series approximation. All the mechanical properties and displacement components are thus expanded in terms of the power series of a known degree. Afterwards, the shape functions are gained by altering the deformation shape of the AFG nonprismatic Timoshenko beam in a power series form. At the end, the elastic and buckling stiffness matrices are exactly determined by the weak form of the governing equation. The precision and competency of the present procedure in stability analysis are assessed through several numerical examples of axially nonhomogeneous and homogeneous Timoshenko beams with clamped-free ends. Comparison is also made with results obtained using ANSYS and other solutions available, which indicates the correctness of the present method.
AbstractList An improved approach based on the power series expansions is proposed to exactly evaluate the static and buckling stiffness matrices for the linear stability analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section and fixed–free boundary condition. Based on the Timoshenko beam theory, the equilibrium equations are derived in the context of small displacements, considering the coupling between the transverse deflection and angle of rotation. The system of stability equations is then converted into a single homogeneous differential equation in terms of bending rotation for the cantilever, which is solved numerically with the help of the power series approximation. All the mechanical properties and displacement components are thus expanded in terms of the power series of a known degree. Afterwards, the shape functions are gained by altering the deformation shape of the AFG nonprismatic Timoshenko beam in a power series form. At the end, the elastic and buckling stiffness matrices are exactly determined by the weak form of the governing equation. The precision and competency of the present procedure in stability analysis are assessed through several numerical examples of axially nonhomogeneous and homogeneous Timoshenko beams with clamped-free ends. Comparison is also made with results obtained using ANSYS and other solutions available, which indicates the correctness of the present method.
Author Soltani, Masoumeh
Asgarian, Behrouz
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Cites_doi 10.1016/j.jcsr.2013.11.001
10.1016/0045-7949(94)00554-G
10.1016/S0960-0779(00)00009-6
10.1016/0022-460X(80)90320-X
10.1016/j.apacoust.2012.08.003
10.1177/1077546310370691
10.1007/s12205-014-0278-8
10.12989/sem.2013.48.2.195
10.1260/1369-4332.14.2.319
10.1142/S0219455415500078
10.1080/15376490490452669
10.1016/j.jsv.2007.03.038
10.1590/1679-78252159
10.1006/jsvi.2000.2999
10.1016/j.compstruct.2016.10.017
10.1061/(ASCE)0733-9399(1987)113:9(1337)
10.12989/sem.2009.33.4.447
10.1007/s40430-014-0255-7
10.1016/j.compstruct.2016.02.040
10.1007/s10665-017-9937-3
10.1006/jsvi.1995.0490
10.1061/(ASCE)0733-9399(1987)113:10(1454)
10.1016/j.jsv.2009.12.029
10.1006/jsvi.2000.3009
10.1016/j.jsv.2006.02.011
10.1016/j.compositesb.2011.01.017
10.1155/2011/591716
10.1142/S0219455415500170
10.1016/j.tws.2007.08.018
10.1007/s12205-016-0149-6
10.1016/0045-7949(91)90312-A
10.1016/j.compositesb.2016.08.008
10.1016/j.apm.2010.07.006
10.1016/j.compstruct.2015.09.013
10.1016/j.advengsoft.2005.02.003
10.1016/j.jcsr.2004.03.004
10.1142/S0219455412500253
10.1142/S0219455417500778
10.1016/j.tws.2014.04.012
10.1142/S0219455412500575
10.1142/S0219455418500074
10.1007/s00419-014-0820-7
10.1016/j.amc.2016.05.034
10.1016/j.compositesb.2012.09.015
10.1016/j.compositesb.2009.03.001
10.1016/j.compositesb.2013.02.027
10.1080/15376494.2011.640971
10.1007/s40430-016-0701-9
10.1016/j.nonrwa.2007.11.019
10.1007/s00419-012-0689-2
10.1016/j.apm.2012.09.024
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Keywords Nonprismatic Timoshenko beam
critical buckling load
power series method (PSM)
axially functionally graded material (AFGM)
finite element solution
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References S0219455419500020BIB040
Zienkiewicz O. C. (S0219455419500020BIB051) 2005
S0219455419500020BIB009
S0219455419500020BIB007
S0219455419500020BIB008
S0219455419500020BIB005
S0219455419500020BIB049
S0219455419500020BIB006
S0219455419500020BIB003
S0219455419500020BIB047
S0219455419500020BIB004
S0219455419500020BIB048
S0219455419500020BIB001
S0219455419500020BIB045
S0219455419500020BIB002
S0219455419500020BIB046
S0219455419500020BIB043
S0219455419500020BIB044
S0219455419500020BIB041
S0219455419500020BIB042
Soltani M. (S0219455419500020BIB050) 2016; 2
Wang C. M. (S0219455419500020BIB053) 2005
S0219455419500020BIB018
S0219455419500020BIB019
S0219455419500020BIB016
S0219455419500020BIB017
S0219455419500020BIB014
S0219455419500020BIB015
S0219455419500020BIB012
S0219455419500020BIB013
S0219455419500020BIB010
S0219455419500020BIB054
S0219455419500020BIB011
S0219455419500020BIB055
S0219455419500020BIB029
S0219455419500020BIB027
S0219455419500020BIB028
S0219455419500020BIB025
S0219455419500020BIB026
S0219455419500020BIB023
S0219455419500020BIB024
S0219455419500020BIB021
Logan D. L. (S0219455419500020BIB052) 2007
S0219455419500020BIB022
S0219455419500020BIB020
S0219455419500020BIB038
S0219455419500020BIB039
S0219455419500020BIB036
S0219455419500020BIB037
S0219455419500020BIB034
S0219455419500020BIB035
S0219455419500020BIB032
S0219455419500020BIB033
S0219455419500020BIB030
S0219455419500020BIB031
References_xml – ident: S0219455419500020BIB048
  doi: 10.1016/j.jcsr.2013.11.001
– ident: S0219455419500020BIB004
  doi: 10.1016/0045-7949(94)00554-G
– ident: S0219455419500020BIB007
  doi: 10.1016/S0960-0779(00)00009-6
– ident: S0219455419500020BIB001
  doi: 10.1016/0022-460X(80)90320-X
– volume-title: A First Course in the Finite Element Method
  year: 2007
  ident: S0219455419500020BIB052
– ident: S0219455419500020BIB027
  doi: 10.1016/j.apacoust.2012.08.003
– ident: S0219455419500020BIB054
  doi: 10.1177/1077546310370691
– ident: S0219455419500020BIB032
  doi: 10.1007/s12205-014-0278-8
– ident: S0219455419500020BIB024
  doi: 10.12989/sem.2013.48.2.195
– ident: S0219455419500020BIB018
  doi: 10.1260/1369-4332.14.2.319
– ident: S0219455419500020BIB038
  doi: 10.1142/S0219455415500078
– ident: S0219455419500020BIB008
  doi: 10.1080/15376490490452669
– ident: S0219455419500020BIB012
  doi: 10.1016/j.jsv.2007.03.038
– ident: S0219455419500020BIB033
  doi: 10.1590/1679-78252159
– ident: S0219455419500020BIB009
  doi: 10.1006/jsvi.2000.2999
– ident: S0219455419500020BIB040
  doi: 10.1016/j.compstruct.2016.10.017
– ident: S0219455419500020BIB002
  doi: 10.1061/(ASCE)0733-9399(1987)113:9(1337)
– ident: S0219455419500020BIB015
  doi: 10.12989/sem.2009.33.4.447
– ident: S0219455419500020BIB031
  doi: 10.1007/s40430-014-0255-7
– volume-title: Exact Solutions for Buckling of Structural Members
  year: 2005
  ident: S0219455419500020BIB053
– ident: S0219455419500020BIB034
  doi: 10.1016/j.compstruct.2016.02.040
– ident: S0219455419500020BIB044
  doi: 10.1007/s10665-017-9937-3
– ident: S0219455419500020BIB005
  doi: 10.1006/jsvi.1995.0490
– ident: S0219455419500020BIB045
  doi: 10.1061/(ASCE)0733-9399(1987)113:10(1454)
– ident: S0219455419500020BIB016
  doi: 10.1016/j.jsv.2009.12.029
– ident: S0219455419500020BIB006
  doi: 10.1006/jsvi.2000.3009
– ident: S0219455419500020BIB010
  doi: 10.1016/j.jsv.2006.02.011
– ident: S0219455419500020BIB019
  doi: 10.1016/j.compositesb.2011.01.017
– ident: S0219455419500020BIB021
  doi: 10.1155/2011/591716
– ident: S0219455419500020BIB035
  doi: 10.1142/S0219455415500170
– ident: S0219455419500020BIB011
  doi: 10.1016/j.tws.2007.08.018
– ident: S0219455419500020BIB042
  doi: 10.1007/s12205-016-0149-6
– ident: S0219455419500020BIB003
  doi: 10.1016/0045-7949(91)90312-A
– ident: S0219455419500020BIB037
  doi: 10.1016/j.compositesb.2016.08.008
– ident: S0219455419500020BIB020
  doi: 10.1016/j.apm.2010.07.006
– ident: S0219455419500020BIB055
  doi: 10.1016/j.compstruct.2015.09.013
– ident: S0219455419500020BIB047
  doi: 10.1016/j.advengsoft.2005.02.003
– volume: 2
  start-page: 57
  year: 2016
  ident: S0219455419500020BIB050
  publication-title: Numer. Methods Civil Eng.
– ident: S0219455419500020BIB046
  doi: 10.1016/j.jcsr.2004.03.004
– ident: S0219455419500020BIB023
  doi: 10.1142/S0219455412500253
– ident: S0219455419500020BIB041
  doi: 10.1142/S0219455417500778
– ident: S0219455419500020BIB049
  doi: 10.1016/j.tws.2014.04.012
– ident: S0219455419500020BIB025
  doi: 10.1142/S0219455412500575
– ident: S0219455419500020BIB043
  doi: 10.1142/S0219455418500074
– ident: S0219455419500020BIB030
  doi: 10.1007/s00419-014-0820-7
– ident: S0219455419500020BIB036
  doi: 10.1016/j.amc.2016.05.034
– ident: S0219455419500020BIB017
  doi: 10.1016/j.compositesb.2012.09.015
– volume-title: The Finite Element Method for Solid and Structural Mechanics
  year: 2005
  ident: S0219455419500020BIB051
– ident: S0219455419500020BIB014
  doi: 10.1016/j.compositesb.2009.03.001
– ident: S0219455419500020BIB029
  doi: 10.1016/j.compositesb.2013.02.027
– ident: S0219455419500020BIB022
  doi: 10.1080/15376494.2011.640971
– ident: S0219455419500020BIB039
  doi: 10.1007/s40430-016-0701-9
– ident: S0219455419500020BIB013
  doi: 10.1016/j.nonrwa.2007.11.019
– ident: S0219455419500020BIB028
  doi: 10.1007/s00419-012-0689-2
– ident: S0219455419500020BIB026
  doi: 10.1016/j.apm.2012.09.024
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Snippet An improved approach based on the power series expansions is proposed to exactly evaluate the static and buckling stiffness matrices for the linear stability...
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SubjectTerms Beam theory (structures)
Boundary conditions
Deformation
Differential equations
Elastic buckling
Equilibrium equations
Finite element method
Free boundaries
Functionally gradient materials
Matrix methods
Mechanical properties
Nonlinear programming
Power series
Rotation
Shape functions
Stability analysis
Stiffness matrix
Timoshenko beams
Title Finite Element Formulation for Linear Stability Analysis of Axially Functionally Graded Nonprismatic Timoshenko Beam
URI http://www.worldscientific.com/doi/abs/10.1142/S0219455419500020
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