The simulation of two-dimensional plane problems using ordinary state-based peridynamics
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Jingjing Zhao
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Guangda Lu
Abstract
The ordinary state-based peridynamics (OSB PD) model is an integral nonlocal continuum mechanics model. And the three-dimensional OSB PD model can deal with linear elastic solid problems well. But for plane problems, the calculation results of existing models have large deviations. In this paper, a set of OSB PD models for plane problems is established by theoretical derivation. First, through the strain energy density function equivalence of peridynamics and classical continuum mechanics, the equivalent coefficients of the plane strain and plane stress problems of OSB PD are deduced. Then, consider the cantilever beam deformation simulation under concentrated load. The simulation results show that the maximum displacements are in good agreement with the corresponding analytical solutions in all directions. Finally, in the simulation of the slab with a hole, the two cases of uniform displacement and uniform load are considered, respectively. The simulation results are consistent with the ANSYS analysis results, and the deviation is small, which verifies the validity of the model.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11932006
Award Identifier / Grant number: 12002118
Award Identifier / Grant number: U1934206
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Author contribution: The publication has been approved by all co-authors. We have no conflict of interest to declare, all data generated or analyzed during this study are included in this published article.
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Research funding: This research is financially by the National Natural Science Foundation of China (Nos. 11932006, U1934206, 12002118). The snapshots were performed using the visualization tool Ensight.
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Conflict of interest statement: The authors claim that none of the material in the paper has been published or is under consideration for publication elsewhere. We have no conflict of interest to declare.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Testing of logarithmic-law for the slip with friction boundary condition
- A new clique polynomial approach for fractional partial differential equations
- The modified Rusanov scheme for solving the phonon-Bose model
- Delta-shock for a class of strictly hyperbolic systems of conservation laws
- The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
- Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
- The simulation of two-dimensional plane problems using ordinary state-based peridynamics
- Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
- Simulation of the crystallization processes by population balance model using a linear separation method
- PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
- Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
- Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
- The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
- Intelligent controller for maximum power extraction of wind generation systems using ANN
- A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
- Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
- A study on solvability of the fourth-order nonlinear boundary value problems
- Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
- Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
- Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
- Carleman framework filtering of nonlinear noisy phase-locked loop system
- Corrigendum
- Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Testing of logarithmic-law for the slip with friction boundary condition
- A new clique polynomial approach for fractional partial differential equations
- The modified Rusanov scheme for solving the phonon-Bose model
- Delta-shock for a class of strictly hyperbolic systems of conservation laws
- The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
- Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
- The simulation of two-dimensional plane problems using ordinary state-based peridynamics
- Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
- Simulation of the crystallization processes by population balance model using a linear separation method
- PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
- Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
- Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
- The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
- Intelligent controller for maximum power extraction of wind generation systems using ANN
- A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
- Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
- A study on solvability of the fourth-order nonlinear boundary value problems
- Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
- Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
- Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
- Carleman framework filtering of nonlinear noisy phase-locked loop system
- Corrigendum
- Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
