Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTechnical Report: Modeling of Composite Piezoelectric Structures with the Finite Volume Method
تقرير فني: النمذجة للهياكل البيزوالكترية المركبة باستخدام طريقة الحجم المحدود
726
0
0.0
(
0
)
Added by
Valentin Bolborici
Publication date
2011
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
الأجهزة البيزي الكهربائية، مثل محركات الصوت المتحركة المتنقلة البيزي الكهربائية، لها بنيات بيزي الكهربائية مركبة. بنية بيزي الكهربائية مركبة تتألف من مجموعة من المواد المربوطة لها، حيث أن واحداً منها على الأقل هو محول بيزي الكهربائي. تم عمل التحليل الرقمي للبنيات البيزي الكهربائية في الماضي بشكل أساسي باستخدام طريقة العنصر المحدود. بديلاً، يقدم النهج المستند إلى الحجم المحدود المزايا التالية: (أ) يمكن تفسير المعادلات التفاضلية العادية الناتجة من عملية التقطيع مباشرة كدوائر مقابلة و (ب) يمكن معالجة الظواهر التي تحدث في الحدود بدقة. يوسع هذا التقرير العمل المنشور في المجلة العلمية IEEE Transactions on UFFC 57 (2010) 7: 1673-1691 بإعطاء طريقة لتنفيذ الشروط الحدودية بين المواد المربوطة في البنيات البيزي الكهربائية المركبة. ينتهي التقرير بمثال واحد لتحليل البنية الأحادية.
Piezoelectric devices, such as piezoelectric traveling wave rotary ultrasonic motors, have composite piezoelectric structures. A composite piezoelectric structure consists of a combination of two or more bonded materials, where at least one of them is a piezoelectric transducer. Numerical modeling of piezoelectric structures has been done in the past mainly with the finite element method. Alternatively, a finite volume based approach offers the following advantages: (a) the ordinary differential equations resulting from the discretization process can be interpreted directly as corresponding circuits and (b) phenomena occurring at boundaries can be treated exactly. This report extends the work of IEEE Transactions on UFFC 57(2010)7:1673-1691 by presenting a method for implementing the boundary conditions between the bonded materials in composite piezoelectric structures. The report concludes with one modeling example of a unimorph structure.
rate research
Read More
The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce computational costs of a classical high fidelity code based on Finite Element Method (FEM), Finite Volume (FVM) or Spectral methods. The efficient implementation of most of these RBM requires to modify this high fidelity code, which cannot be done, for example in an industrial context if the high fidelity code is only accessible as a black-box solver. The Non Intrusive Reduced Basis method (NIRB) has been introduced in the context of finite elements as a good alternative to reduce the implementation costs of these parameter-dependent problems. The method is efficient in other contexts than the FEM one, like with finite volume schemes, which are more often used in an industrial environment. In this case, some adaptations need to be done as the degrees of freedom in FV methods have different meenings. At this time, error estimates have only been studied with FEM solvers. In this paper, we present a generalisation of the NIRB method to Finite Volume schemes and we show that estimates established for FEM solvers also hold in the FVM setting. We first prove our results for the hybrid-Mimetic Finite Difference method (hMFD), which is part the Hybrid Mixed Mimetic methods (HMM) family. Then, we explain how these results apply more generally to other FV schemes. Some of them are specified, such as the Two Point Flux Approximation (TPFA).
Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce the Extended Finite Element Method (XFEM) to solve fluid-structure interaction problems involving sharp edges on structures. Four different FEM solvers, including conventional linear and quadratic FEMs as well as their corresponding XF
Recently developed concept of dissipative measure-valued solution for compressible flows is a suitable tool to describe oscillations and singularities possibly developed in solutions of multidimensional Euler equations. In this paper we study the convergence of the first-order finite volume method based on the exact Riemann solver for the complete compressible Euler equations. Specifically, we derive entropy inequality and prove the consistency of numerical method. Passing to the limit, we show the weak and strong convergence of numerical solutions and identify their limit. The numerical results presented for the spiral, Kelvin-Helmholtz and the Richtmyer-Meshkov problem are consistent with our theoretical analysis.
We present a (partial) historical summary of the mathematical analysis of finite differences and finite volumes methods, paying a special attention to the Lax-Richtmyer and Lax-Wendroff theorems. We then state a Lax-Wendroff consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates a recent generalization of the flux consistency notion designed to cope with general discrete functions.
We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent arbitrary crack geometry without an explicit function or basis enrichment, and (2) it does not require an algorithm for imposing contact constraints. The first feature, which is common in phase-field models of fracture, is attained by regularizing a sharp interface geometry using a surface density functional. The second feature, which is a unique advantage for contact problems, is achieved by a new approach that calculates the stress tensor in the regularized interface region depending on the contact condition of the interface. Particularly, under a slip condition, this approach updates stress components in the slip direction using a standard contact constitutive law, while making other stress components compatible with stress in the bulk region to ensure non-penetrating deformation in other directions. We verify the proposed phase-field method using stationary interface problems simulated by discrete methods in the literature. Subsequently, by allowing the phase field to evolve according to brittle fracture theory, we demonstrate the proposed methods capability for modeling crack growth with frictional contact.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
