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Asymptotic Method

The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform

Tian Tang – 1st expert on this subject based on the ideXlab platform

  • Variational Asymptotic Method for Unit Cell Homogenization
    Solid Mechanics and Its Applications, 2009
    Co-Authors: Wenbin Yu, Tian Tang

    Abstract:

    This article presents an overview of a recently developed micromechanics theory, namely, the variational Asymptotic Method for unit cell homogenization along with its companion code VAMUCH. It is emerging as a general-purpose micromechanics tool for predicting not only the effective properties of heterogeneous materials but also the local fields within the microstructure. The differences between VAMUCH and other micromechanics approaches are articulated. A simple realistic example is used to demonstrate it application in practical situations.

  • Micromechanical modeling of the multiphysical behavior of smart materials using the variational Asymptotic Method
    Smart Materials and Structures, 2009
    Co-Authors: Tian Tang, Wenbin Yu

    Abstract:

    The primary objective of the present paper is to develop a micromechanics model for the prediction of the effective properties and the distribution of local fields of smart materials which are responsive to fully coupled electric, magnetic, thermal and mechanical fields. This work is based on the framework of the variational Asymptotic Method for unit cell homogenization (VAMUCH), a recently developed micromechanics modeling scheme. For practicle use of this theory, we implement this new model using the finite element Method into the computer program VAMUCH. For validation, several examples will be presented in the full paper to compare with existing models and demonstrate the application and advantages of the new model.

  • variational Asymptotic Method for unit cell homogenization of periodically heterogeneous materials
    International Journal of Solids and Structures, 2007
    Co-Authors: Wenbin Yu, Tian Tang

    Abstract:

    A new micromechanics model, namely, the variational Asymptotic Method for unit cell homogenization (VAMUCH), is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields. Considering the periodicity as a small parameter, we can formulate a variational statement of the unit cell through an Asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. In comparison to other approaches, VAMUCH does not rely on ad hoc assumptions, has the same rigor as MHT, has a straightforward numerical implementation, and can calculate the complete set of properties simultaneously without using multiple loadings. This theory is implemented using the finite element Method and an engineering program, VAMUCH, is developed for micromechanical analysis of unit cells. Many examples of binary composites, fiber reinforced composites, and particle reinforced composites are used to demonstrate the application, power, and accuracy of the theory and the code of VAMUCH.

Wenbin Yu – 2nd expert on this subject based on the ideXlab platform

  • Variational Asymptotic Method for Unit Cell Homogenization
    Solid Mechanics and Its Applications, 2009
    Co-Authors: Wenbin Yu, Tian Tang

    Abstract:

    This article presents an overview of a recently developed micromechanics theory, namely, the variational Asymptotic Method for unit cell homogenization along with its companion code VAMUCH. It is emerging as a general-purpose micromechanics tool for predicting not only the effective properties of heterogeneous materials but also the local fields within the microstructure. The differences between VAMUCH and other micromechanics approaches are articulated. A simple realistic example is used to demonstrate it application in practical situations.

  • Micromechanical modeling of the multiphysical behavior of smart materials using the variational Asymptotic Method
    Smart Materials and Structures, 2009
    Co-Authors: Tian Tang, Wenbin Yu

    Abstract:

    The primary objective of the present paper is to develop a micromechanics model for the prediction of the effective properties and the distribution of local fields of smart materials which are responsive to fully coupled electric, magnetic, thermal and mechanical fields. This work is based on the framework of the variational Asymptotic Method for unit cell homogenization (VAMUCH), a recently developed micromechanics modeling scheme. For practicle use of this theory, we implement this new model using the finite element Method into the computer program VAMUCH. For validation, several examples will be presented in the full paper to compare with existing models and demonstrate the application and advantages of the new model.

  • variational Asymptotic Method for unit cell homogenization of periodically heterogeneous materials
    International Journal of Solids and Structures, 2007
    Co-Authors: Wenbin Yu, Tian Tang

    Abstract:

    A new micromechanics model, namely, the variational Asymptotic Method for unit cell homogenization (VAMUCH), is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields. Considering the periodicity as a small parameter, we can formulate a variational statement of the unit cell through an Asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. In comparison to other approaches, VAMUCH does not rely on ad hoc assumptions, has the same rigor as MHT, has a straightforward numerical implementation, and can calculate the complete set of properties simultaneously without using multiple loadings. This theory is implemented using the finite element Method and an engineering program, VAMUCH, is developed for micromechanical analysis of unit cells. Many examples of binary composites, fiber reinforced composites, and particle reinforced composites are used to demonstrate the application, power, and accuracy of the theory and the code of VAMUCH.

Nicolae Herisanu – 3rd expert on this subject based on the ideXlab platform

  • The Optimal Homotopy Asymptotic Method
    , 2020
    Co-Authors: Vasile Marinca, Nicolae Herisanu

    Abstract:

    This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy Methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations.  The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation

  • the optimal homotopy Asymptotic Method
    , 2015
    Co-Authors: Vasile Marinca, Nicolae Herisanu

    Abstract:

    The homotopy continuation Method was known as early as in the 1930s. This Method was used by kinematicians in the 1960s in the US for solving mechanism synthesis problems [76]. The latest development was done by A.P. Morgan at General Motors [77]. We also have two important literature studies by Garcia [78] and Allgowar [79]. The continuation Method gives a set of certain answers and some iteration processes to obtain our solutions more exactly.

  • the optimal homotopy Asymptotic Method for solving blasius equation
    Applied Mathematics and Computation, 2014
    Co-Authors: Vasile Marinca, Nicolae Herisanu

    Abstract:

    Starting from the reality that many known Methods fail in the attempt to obtain analytic solutions of Blasius-type equations, in this work, a new procedure namely Optimal Homotopy Asymptotic Method (OHAM) is proposed to obtain an explicit analytical solution of the Blasius problem. Comparison with Howarth’s numerical solution, as well as the obtained residual, reveals that the proposed Method is highly accurate. This proves the validity and great potential of the proposed procedure (OHAM) as a new kind of powerful analytical tool for nonlinear problems.