Thermal Stresses in Functionally Graded Beams

Sankar, Bhavani V.; Tzeng, Jerome T.

doi:10.2514/2.1775

Cited by 174 publications

(28 citation statements)

References 5 publications

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“…The whole equations are solved iteratively. In each iterative step J, the nonlinear items in the nonlinear governing equations of motion ( 16), ( 17), (18) and boundary conditions (19) are linearized: ðx Á yÞ J ¼ ðxÞ J Á ðyÞ J P ; ð35Þ…”

Section: Solution Methodsmentioning

confidence: 99%

“…Apalak and Gunes 18 investigated the thermal elastic residual stresses occurring in FG plates using three-dimensional layered finite element. Sankar and Tzeng 19 obtained a closed-form solution for the thermal stress analysis of FG beams. As the shear deformation effects are pronounced for the moderately thick structures subjected to transverse load, the classical shell theory is not adequate to model the behavior of the shells.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear low-velocity impact analysis of functionally graded shallow spherical shells in thermal environments

Mao

2014

Journal of Thermoplastic Composite Materials

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This article presents the nonlinear dynamic response of functionally graded (FG) shallow spherical shells in thermal environments subjected to low-velocity impact by an elastic ball. The material properties of a FG shallow spherical shell vary continuously through the thickness according to a power law distribution of the volume fraction of the constituents. The temperature field is considered to vary along the thickness direction due to the steady state heat transfer. Based on the higher order shear deformation theory, the governing equations of motion for the shell, which account for geometric nonlinearity is obtained using Hamilton's principle. The contact force between the shell and the impactor is relative to local deformation and calculated using a numerical method. Then, the governing equations of motion are solved numerically by the Chebyshev collocation method and Newmark scheme. This is a complete model that can not only fully model the dynamic behavior of the shell but also fully model the impactor's dynamic behavior. In the numerical example, the effects of material properties, temperature, initial impact velocity and mass of the impactor on the dynamic behavior of the shells, and contact force are discussed in detail.

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Section: Solution Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear low-velocity impact analysis of functionally graded shallow spherical shells in thermal environments

Mao

2014

Journal of Thermoplastic Composite Materials

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“…Eslami et al (2013) reviewed the thermoelasticity theory and presented its application in some practical problems. Sankar and Tzeng (2002) presented a closed-form solution for the bending of FG beams under thermal loads. Xu and Zhou (2012) presented the thermoelastic analysis for beams with variable thickness subjected to thermomechanical loads.…”

Section: Introductionmentioning

confidence: 99%

Analysis of thick beams with temperature-dependent material properties under thermomechanical loads

Zhong

Zhou

et al. 2020

Advances in Structural Engineering

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This study focuses on the thermoelastic behavior of simply supported thick beams with temperature-dependent material properties under thermomechanical loads. The heat conduction analysis is based on the one-dimensional Fourier’s law, and the displacement and stress analysis is based on the two-dimensional thermoelasticity theory. The solution of temperature field across the thickness is obtained. By dividing the beam into a series of thin slices, the temperature and the material properties in each slice are considered to be uniform. The state space method is used to give the displacements and stresses for every slice. The transfer-matrix method is used to give the displacements and stresses for the beam. Finally, an example is conducted to analyze the temperature, displacement, and stress fields in a carbon steel beam. The example reveals that the temperature not only produces displacements and stresses itself but also affects the displacements and stresses induced by the mechanical load.

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“…Using the principle of stationary potential energy, the finite element form of static equilibrium equation for FGB was presented. Sankar et al [11] have introduced a solution for thermoelastic equilibrium equations for a functionally graded beam in a closed-form to obtain the axial stress distribution. The thermo-elastic constants of the beam and the temperature were assumed to vary exponentially through the thickness.…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Analysis of Functionally Graded Beam under Thermal Loading

El-Megharbel¹

2016

WJET

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Thermal Stresses in Functionally Graded Beams

Cited by 174 publications

References 5 publications

Nonlinear low-velocity impact analysis of functionally graded shallow spherical shells in thermal environments

Nonlinear low-velocity impact analysis of functionally graded shallow spherical shells in thermal environments

Analysis of thick beams with temperature-dependent material properties under thermomechanical loads

A Theoretical Analysis of Functionally Graded Beam under Thermal Loading

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