Peridynamic Formulation for Higher-Order Plate Theory
- PDF / 1,460,103 Bytes
- 26 Pages / 439.37 x 666.142 pts Page_size
- 53 Downloads / 169 Views
Peridynamic Formulation for Higher-Order Plate Theory Zhenghao Yang 1 & Erkan Oterkus 1
& Selda Oterkus
1
Received: 30 September 2020 / Accepted: 17 November 2020/ # The Author(s) 2020
Abstract
In this study, a new peridynamic model is presented for higher-order plate theory. The formulation is derived by using Euler-Lagrange equation and Taylor’s expansion. The formulation is verified by considering two benchmark problems including simply supported and clamped plates subjected to transverse loading. Moreover, mixed (simply supportedclamped) boundary conditions are also considered to investigate the capability of the current formulation for mixed boundary conditions. Peridynamic results are compared with finite element analysis results and a very good agreement was obtained between the two approaches. Keywords Peridynamics . Higher-order . Plate . Non-local
1 Introduction Classical continuum mechanics (CCM) developed by Cauchy has been widely used for the analysis of deformation behaviour of materials and structures. Although CCM has been very successful in dealing with numerous complex problems of engineering, it encounters difficulties if the displacement field is discontinuous. This situation mainly arises when cracks occur inside the solution domain. In this case, the partial derivatives in the governing equations of CCM become invalid along the crack surfaces. Moreover, as the technology advances and nanoscale structures become a significant interest, accurate material characteristic at such a small scale cannot always be captured by CCM since CCM does not have a length scale parameter. To overcome the aforementioned issues related with CCM, a new continuum mechanics formulation, peridynamics, was proposed by Silling [1]. The governing equations of peridynamics (PD) are in the form of integro-differential equations and do not contain any spatial derivatives. Therefore, they are always valid even if the displacement field is discontinuous. Moreover, it has a length scale parameter, horizon, which can be utilized to model structures at nanoscale. According to dell’Isola et al. [2], the origins of peridynamics go back
* Erkan Oterkus [email protected]
1
Department of Naval Architecture, Ocean and Marine Engineering, PeriDynamics Research Centre, University of Strathclyde, 100 Montrose Street, Glasgow G4 0LZ, UK
Journal of Peridynamics and Nonlocal Modeling
to Piola. Since its introduction, there has been rapid development in peridynamics research especially during the last years. PD has been applied to analyze different material systems including metals [3], composites [4, 5], concrete [6] and graphene [7]. Moreover, it is not limited to elasticity behaviour and PD-based plasticity [8], viscoelasticity [9] and viscoplasticity [10] formulations are available. In addition, PD equations have been extended to other fields to perform heat transfer [11], diffusion [12], porous flow [13] and fluid flow [14] analyses. An extensive review on peridynamics is given in Javili et al. [15]. Simplied struct
Data Loading...
