Optimal design of functionally graded material for stress concentration reduction

Zhou, Yicong; Lin, Qiyin; Hong, Jun; Yang, Nan

doi:10.1016/j.istruc.2020.11.053

Cited by 17 publications

(3 citation statements)

References 33 publications

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“…In this study, we investigate the mode shapes as well as the energy distribution of functionally graded (position-dependent stiffness) elastic rods with elastic and viscous boundary conditions. Continuous changes in the properties of the functionally graded materials have engineering relevance, since this material behavior yields a lot of engineering benefits, such as avoiding the occurrence of large shear stresses 21 . For example, Shi et al 22 investigated carbon-nanotube-reinforced composite beams where different nanotube distributions were assumed including functionally graded distributions through the thickness of the beams.…”

Section: Introductionmentioning

confidence: 99%

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Lelkes,

Bak,

Kalmár-Nagy

2024

Sci Rep

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Functionally graded materials have broad engineering applications including mechanical engineering, electronics, chemistry, and biomedical engineering. One notable advantage of such materials is that their stiffness distribution can be optimized to avoid stress concentration. A novel approach for solving the equations describing the longitudinal vibration of functionally graded rods with viscous and elastic boundary conditions is proposed. The characteristic equation of the system is derived for the solution of the undamped case for the constant stiffness rod. Then, a homotopy method is applied to compute the eigenvalues and mode shapes of graded rods for viscoelastic boundary conditions. The changes of the eigenvalues and mode shapes as function of the damping parameters are investigated. The optimal damping of the system is computed. It is shown that the qualitative behavior depends on the relation between the actual damping and the optimal damping of the system. The energy density distribution of graded rods is also discussed. An energy measure, the mean scaled energy density distribution is introduced to characterize the energy distribution along the rod in the asymptotic time limit. The significance of such a measure is that it reveals how the energy tends to distribute along the rod. It is shown that the energy distribution can be manipulated by changing the damping parameters. Qualitative changes depending on the relation between the actual damping and the optimal damping are highlighted.

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Section: Introductionmentioning

confidence: 99%

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Lelkes,

Bak,

Kalmár-Nagy

2024

Sci Rep

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“…In this study, we investigate the mode shapes as well as the energy distribution of functionally graded (position-dependent stiffness) elastic rods with elastic and viscous boundary conditions. Continuous changes in the properties of the functionally graded materials have engineering relevance, since this material behavior yields a lot of engineering benefits, such as avoiding the occurrence of large shear stresses [21]. The static and dynamic characteristics of functionally graded materials are favorable in many scientific and engineering fields, such as aerospace, automobile, electronics, optics, chemistry, biomedical engineering, nuclear engineering and mechanical engineering [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Lelkes

Bak

Kalmár‐Nagy

2023

Preprint

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A novel approach for solving the equations describing the longitudinalvibration of functionally graded rods with viscous and elastic boundaryconditions is proposed. The characteristic equation of the system is derivedand a homotopy method is applied to compute the eigenvalues and mode shapesfor any type of boundary condition, including fixed, free, elastic and/orviscous. Examples are provided for different graded rods with elastic andviscous boundary conditions. The optimal damping of the system is computedbased on the spectral abscissa criterion. It is shown that the qualitativebehavior depends on whether the damping of the system exceeds the optimaldamping. The energy density distribution of the different graded rods is alsodiscussed. An energy measure, the mean scaled energy density distribution isintroduced to characterize the energy distribution along the rod in theasymptotic time limit. It is shown that the energy distribution alsoqualitatively depends on the relation between the actual damping and theoptimal damping of the system.

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“…Zhou [18] implemented a finite element analysis to obtain the stress distribution to develop an optimization in the Young's modulus algorithm. Said algorithmic optimization results in obtaining an effective approximation for the optimal design of functionally graded material for stress concentration reduction.…”

Section: Introductionmentioning

confidence: 99%

Stress concentration reduction in an axially loaded rectangular bar with an elliptical hole

Ramírez Monares,

Gamboa Soto

2023

CULCyT

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Two-dimensional finite element analysis was used for stress concentration factors estimation in a wide range of bar-ellipse height and height-width elliptical hole ratios in a tensile bar. Least squares polynomial equations were fit to the design points. These equations agreed and tension stress concentration factor for elliptical holes was described. Such equation reproduces the curves and through its derivative the optimal values that minimize the concentration factor are estimated. The path of the minimal concentration factor was illustrated in a contour plot.

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Optimal design of functionally graded material for stress concentration reduction

Cited by 17 publications

References 33 publications

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions

Stress concentration reduction in an axially loaded rectangular bar with an elliptical hole

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