A simple method to determine the critical buckling loads for axially inhomogeneous beams with elastic restraint

Huang, Yong; Luo, Qi

doi:10.1016/j.camwa.2011.02.037

Cited by 55 publications

(42 citation statements)

References 22 publications

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“…The numerical computations were carried out for an FG beam with n segments of the same length. Non-dimensional critical buckling loads for an FG beam with functions ( ) ( ) Table 1 in comparison with those presented in [8] by Huang and Luo. It can be seen that the present results are in good agreement with these given in the paper [8].…”

Section: Numerical Computationsmentioning

confidence: 99%

“…Non-dimensional critical buckling loads for an FG beam with functions ( ) ( ) Table 1 in comparison with those presented in [8] by Huang and Luo. It can be seen that the present results are in good agreement with these given in the paper [8]. Table 1 Non-dimensional critical buckling loads of a beam with ( ) ( ) Next, we take into account functions ( ) ( )…”

Section: Numerical Computationsmentioning

confidence: 99%

“…The finite element approach to the free vibration and stability analysis of axially functionally graded tapered Timoshenko beams was applied by Shahba et al [7]. A new approach to exactly calculate the critical buckling loads of beams with arbitrarily axial inhomogeneity was presented by Huang and Luo in [8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new approach for buckling analysis of axially functionally graded beams

Rychlewska

2015

J. Appl. Math. Comput. Mech.

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Abstract. The object of considerations are axially functionally graded (FG) beams, which are loaded by an axial force varying along the length of the beam. The main idea presented here is to approximate FG beams by an equivalent beam with piecewise exponentially varying material properties, geometrical properties and axial load. Numerical solutions of the buckling analysis are obtained for four various types of boundary conditions associated with pinned and clamped ends. The usefulness of the proposed method is confirmed by comparing numerical results with those available for graded beams of special polynomial non-homogeneity.

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Section: Numerical Computationsmentioning

confidence: 99%

Section: Numerical Computationsmentioning

confidence: 99%

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A new approach for buckling analysis of axially functionally graded beams

Rychlewska

2015

J. Appl. Math. Comput. Mech.

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“…Li et al [14] analyzed the free vibration of axially inhomogeneous exponentially graded beams. A simple approach to calculate the critical buckling loads of beams with arbitrary axial inhomogeneity was developed by Huang and Luo [15]. Akgöz and Civalek [16] investigated vibration response of non-homogenous and non-uniform microbeams in conjunction with Bernoulli-Euler beam and modified couple stress theory.…”

Section: Introductionmentioning

confidence: 99%

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

Lohar¹,

Mitra

Sahoo³

2016

IFSL

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Abstract.A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton's principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

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“…Huang and Luo [11] presented the simple approach to exactly calculate the critical buckling loads of beams with arbitrarily axial inhomogeneity. The effects of gradient parameters on the critical buckling loads were elucidated.…”

Section: Introductionmentioning

confidence: 99%

Geometric nonlinear free vibration of axially functionally graded non-uniform beams supported on elastic foundation

Lohar¹,

Mitra

Sahoo³

2016

Curved and Layered Structures

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Abstract:In the present study non-linear free vibration analysis is performed on a tapered Axially Functionally Graded (AFG) beam resting on an elastic foundation with different boundary conditions. Firstly the static problem is carried out through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigen value problem. Minimum potential energy principle is used for the formulation of the static problem whereas for the dynamic problem Hamilton's principle is utilized. The free vibrational frequencies are tabulated for different taper profile, taper parameter and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane.

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A simple method to determine the critical buckling loads for axially inhomogeneous beams with elastic restraint

Cited by 55 publications

References 22 publications

A new approach for buckling analysis of axially functionally graded beams

A new approach for buckling analysis of axially functionally graded beams

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

Geometric nonlinear free vibration of axially functionally graded non-uniform beams supported on elastic foundation

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