Peridynamics and its implementation in finite element framework

Student thesis: Master's Thesis

Abstract

Predicting crack propagation and fracture is still a challenging research area. There are various methods for this, and the finite element method (FE method) is the most popular approach. The FE method is a powerful technology that can be used across multiple problems. However, because it is based on classical continuum mechanics (CCM), there are several disadvantages. Since the governing equation of CCM is a partial differential equation with a differential term for space, it is impossible to find the exact solution of the governing equation when spatial discontinuities exist which is caused by a crack.As an alternative approach Peridynamics is a method introduced to overcome the drawbacks of CCM. The governing equation of Peridynamics is form of an integral equation without spatial differentiation. Therefore, it is possible to analyse structures with cracks in which discontinuity in space exists.Peridynamics is a mesh-free method in which each node interacts with other nodes in its vicinity. Because of this, researchers often use language-based programs that can easily calculate numerical values of parameters of interest. This feature make it difficult to attempt to apply peridynamics to various simulation fields. However, if a model is made by FE software based on peridynamic theory, it is possible to expand the simulation fields by utilizing functions of FE software.In this thesis, various analyses are performed by implementing peridynamics in FE software. From the most basic isotropic material to an orthotropic plate, the simulations of the crack propagation were carried out. In addition, a peridynamic structure based on beam and plate theory were also modelled, and this model was compared with the results of the referenced papers. Furthermore, the buckling and free vibration analyses are performed for several cases to consider the effect of each parameter of the crack geometries on characteristics and stiffness of the plate.
Date of Award5 Dec 2019
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SupervisorErkan Oterkus (Supervisor) & Selda Oterkus (Supervisor)

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