Large deformation analysis of functionally graded beam with variable cross-section by using peridynamic differential operator

Li, Zhiyuan; Huang, Dan; Yan, Kanghao; Xu, Yepeng

doi:10.1016/j.compstruct.2021.114788

Cited by 22 publications

(2 citation statements)

References 46 publications

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“…Vector d consists of the known value specified by Eq. ( 21) at the boundary points, and vector u represents the unknown vector [31][32][33].…”

Section: Numerical Implementationmentioning

confidence: 99%

Nonlocal numerical simulation of thermoelectric coupling field by using peridynamic differential operator

Zhu,

Yu,

Zhu

et al. 2024

Preprint

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This study developed a novel nonlocal numerical model based on the peridynamic differential operator to analyze the thermoelectric coupling field. The thermoelectric coupling equations and boundary conditions are transformed from the classical partial differential form to the nonlocal integral form. By introducing the peridynamic function, a one-dimensional nonlocal model is established. This model can accurately capture the spatial distributions of the temperature field and material parameters when considering temperature-dependent thermoelectric material parameters. The numerical solutions from this nonlocal peridynamic model were found to agree well with those from the homotopy analysis method. Using this model, the influence of temperature boundary conditions and structure length on output performance is studied. The intrinsic relationship between the material parameters and the output properties within the structure is revealed. This presented nonlocal model provides an accurate mathematical tool to solve the thermoelectric coupling field for thermoelectric structures performance analysis.

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“…Vector d consists of the known value specified by Eq. ( 21) at the boundary points, and vector u represents the unknown vector [31][32][33].…”

Section: Numerical Implementationmentioning

confidence: 99%

Nonlocal numerical simulation of thermoelectric coupling field by using peridynamic differential operator

Zhu,

Yu,

Zhu

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Chu et al [11] gave an elastic solution for two-dimensional elastic beams and functional gradient material beams under stress and bending conditions. Li et al [12][13][14] studied the bending, vibration, and large deformation of functionally gradient beams with variable cross-sections using the twodimensional elasticity theory. Lin and Muliana [15] and Su et al [16] studied the electromechanical and vibrational properties of gradient beams.…”

Section: Introductionmentioning

confidence: 99%

Accurate Solution for Orthotropic Beams with Continuously Variable Cross Sections

Fang

Chen

2022

Mathematical Problems in Engineering

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Orthotropic materials and components are widely used in various engineering fields, such as aerospace, energy, infrastructure, and water conservancy projects. The orthotropic components such as slabs and beams cannot be investigated accurately by using traditional beam theory because it is unable to take more elastic constants into account. The precise stress distribution of orthotropic simply supported beams of any thickness is determined in this article. Meanwhile, all undetermined coefficients of the stress function are derived by performing a Fourier sine series expansion upon the bottom and top surfaces of the beam. It shows that the resolution corresponds well with the numerical analysis findings from the finite element method. It indicates rapid convergence and can obtain high-precision and high stress analysis results, which has a good application prospect in engineering.

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Nonlocal numerical simulation of thermoelectric coupling field by using peridynamic differential operator

Zhu,

Yu,

Zhu

et al. 2024

Z. Angew. Math. Phys.

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Large deformation analysis of functionally graded beam with variable cross-section by using peridynamic differential operator

Cited by 22 publications

References 46 publications

Nonlocal numerical simulation of thermoelectric coupling field by using peridynamic differential operator

Nonlocal numerical simulation of thermoelectric coupling field by using peridynamic differential operator

Accurate Solution for Orthotropic Beams with Continuously Variable Cross Sections

Nonlocal numerical simulation of thermoelectric coupling field by using peridynamic differential operator

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