Two-dimensional double horizon peridynamics for membranes

Zhenghao Yang; Erkan Oterkus; Selda Oterkus; Zhenghao Yang; Erkan Oterkus; Selda Oterkus

doi:10.3934/nhm.2024027

Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 611-633. doi: 10.3934/nhm.2024027

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Two-dimensional double horizon peridynamics for membranes

1.
Otto von Guericke University, Universitätspl. 2, Magdeburg 39106, Germany
2.
PeriDynamics Research Centre, Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, 100 Montrose Street, Glasgow G4 0LZ, United Kingdom

Received: 24 April 2024 Revised: 10 June 2024 Accepted: 19 June 2024 Published: 21 June 2024

In this study, a two-dimensional "double-horizon peridynamics" formulation was presented for membranes. According to double-horizon peridynamics, each material point has two horizons: inner and outer horizons. This new formulation can reduce the computational time by using larger horizons and smaller inner horizons. To demonstrate the capability of the proposed formulation, various different analytical and numerical solutions were presented for a rectangular plate under different boundary conditions for static and dynamic problems. A comparison of peridynamic and classical solutions was given for different inner and outer horizon size values.
- Peridynamics,
- double horizon,
- nonlocal,
- classical,
- membrane,
- two-dimensional
Citation: Zhenghao Yang, Erkan Oterkus, Selda Oterkus. Two-dimensional double horizon peridynamics for membranes[J]. Networks and Heterogeneous Media, 2024, 19(2): 611-633. doi: 10.3934/nhm.2024027

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Abstract

In this study, a two-dimensional "double-horizon peridynamics" formulation was presented for membranes. According to double-horizon peridynamics, each material point has two horizons: inner and outer horizons. This new formulation can reduce the computational time by using larger horizons and smaller inner horizons. To demonstrate the capability of the proposed formulation, various different analytical and numerical solutions were presented for a rectangular plate under different boundary conditions for static and dynamic problems. A comparison of peridynamic and classical solutions was given for different inner and outer horizon size values.

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