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Development of an Adaptive Model for Coupling the Meshfree Peridynamics to the Finite Element Method
Nikpayam, Jaber | 2021
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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 54351 (45)
- University: Sharif University of Technology
- Department: Aerospace Engineering
- Advisor(s): Kouchakzadeh, Mohammad Ali
- Abstract:
- The presence of spatial partial derivatives in the equations of classical continuum mechanics has led to the fact that methods based on this theory are not valid in displacement discontinuities (such as cracks). The peridynamic theory is a nonlocal formulation of solid mechanics which is most suited to model discontinuities and dynamic fractures in continuous or discrete media. By substituting integral expressions instead of partial differentials in the equations of motion, peridynamics provides an integrated model that is valid and the same in continuous, discontinuous, and discrete media.The capability of the peridynamic theory in modeling discontinuities and cracks has been demonstrated in numerous studies. However, the nonlocal nature of the theory restricts its application in large domains due to its prohibitive computational costs. On the other hand, local methods based on classical continuum mechanics, such as finite element method (FEM), are relatively fast and produce accurate results in the absence of discontinuities. But these methods are incapable in dealing with fracture problems. Thus, in order to take advantages of both techniques, it is desired to couple peridynamics with classical theory so that the fracture-prone regions are described by meshfree peridynamics and the remaining modeled with FEM.The purpose of this study is to provide an adaptive model for coupling of meshfree peridynamics with finite element method to investigate the possibility of crack formation and growth in materials. For this purpose, by introducing a new concept called co-family, the peridynamic equations of motion are changed in such a way that in domains with variable horizon, the formation of ghost forces is reduced. Then, by developing an intermediate element called morakkab, a new method for coupling finite element and meshfree peridynamic models is proposed. The new coupling method is used to simulate the formation and growth of cracks adaptively. Adaptivity means that at first the whole domain is modeled by the finite element method and then, whenever necessary (e.g. at the onset of crack formation), the fracture-prone parts of the finite element model automatically convert to the meshfree peridynamic model
- Keywords:
- Fracture Mechanics ; Coupling ; Finite Element Method ; Peridynamics ; Adaptive Method ; Variable Horizon ; Co-Family Method
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- فهرست تصاویر
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- مقدمه
- نظریه پریدینامیک
- ماده الاستیک
- پریدینامیک در مسائل با افق متغیر
- جفتسازی پریدینامیک بدون شبکه و روش اجزای محدود
- نکات مهم پیادهسازی عددی در روش پریدینامیک بدون شبکه
- خلاصه و جمعبندی
- پیشنهادهایی برای ادامه پژوهش
- پیوست مشتق فرشه
- پیوست چگالی انرژی کرنشی الاستیک دوبعدی در نظریه کلاسیک
- پیوست فرمولبندی المان چهارگرهی دوبعدی در روش اجزای محدود
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