The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Tian Tang - One of the best experts on this subject based on the ideXlab platform.
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Variational Asymptotic Method for Unit Cell Homogenization
Solid Mechanics and Its Applications, 2009Co-Authors: Wenbin Yu, Tian TangAbstract: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.
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Micromechanical modeling of the multiphysical behavior of smart materials using the variational Asymptotic Method
Smart Materials and Structures, 2009Co-Authors: Tian Tang, Wenbin YuAbstract: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.
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variational Asymptotic Method for unit cell homogenization of periodically heterogeneous materials
International Journal of Solids and Structures, 2007Co-Authors: Wenbin Yu, Tian TangAbstract: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 - One of the best experts on this subject based on the ideXlab platform.
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Variational Asymptotic Method for Unit Cell Homogenization
Solid Mechanics and Its Applications, 2009Co-Authors: Wenbin Yu, Tian TangAbstract: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.
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Micromechanical modeling of the multiphysical behavior of smart materials using the variational Asymptotic Method
Smart Materials and Structures, 2009Co-Authors: Tian Tang, Wenbin YuAbstract: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.
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variational Asymptotic Method for unit cell homogenization of periodically heterogeneous materials
International Journal of Solids and Structures, 2007Co-Authors: Wenbin Yu, Tian TangAbstract: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 - One of the best experts on this subject based on the ideXlab platform.
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The Optimal Homotopy Asymptotic Method
2020Co-Authors: Vasile Marinca, Nicolae HerisanuAbstract: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
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the optimal homotopy Asymptotic Method
2015Co-Authors: Vasile Marinca, Nicolae HerisanuAbstract: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.
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the optimal homotopy Asymptotic Method for solving blasius equation
Applied Mathematics and Computation, 2014Co-Authors: Vasile Marinca, Nicolae HerisanuAbstract: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.
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accurate analytical solutions to oscillators with discontinuities and fractional power restoring force by means of the optimal homotopy Asymptotic Method
Computers & Mathematics With Applications, 2010Co-Authors: Nicolae Herisanu, Vasile MarincaAbstract:In this paper a new approach combining the features of the homotopy concept with an efficient computational algorithm which provides a simple and rigorous procedure to control the convergence of the solution is proposed to find accurate analytical explicit solutions for some oscillators with discontinuities and a fractional power restoring force which is proportional to sign(x). A very fast convergence to the exact solution was proved, since the second-order approximation lead to very accurate results. Comparisons with numerical results are presented to show the effectiveness of this Method. Four numerical applications prove the accuracy of the Method, which works very well for the whole range of initial amplitudes. The obtained results prove the validity and efficiency of the Method, which can be easily extended to other strongly nonlinear problems.
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determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy Asymptotic Method
Journal of Sound and Vibration, 2010Co-Authors: Vasile Marinca, Nicolae HerisanuAbstract:This paper deals with the nonlinear oscillations of a particle which moves on a rotating parabola. An analytic approximate technique, namely optimal homotopy Asymptotic Method (OHAM) is employed to propose an analytic approach to solve nonlinear oscillations. The validity of the OHAM is independent on whether or not there exist small or large parameters in the considered nonlinear equations. Our procedure provides us with a convenient way to optimally control the convergence of the approximate solutions. An example is given and the results reveal that this procedure is very effective, simple and accurate. This paper demonstrates the general validity and the great potential of the OHAM.
Vasile Marinca - One of the best experts on this subject based on the ideXlab platform.
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The Optimal Homotopy Asymptotic Method
2020Co-Authors: Vasile Marinca, Nicolae HerisanuAbstract: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
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the optimal homotopy Asymptotic Method
2015Co-Authors: Vasile Marinca, Nicolae HerisanuAbstract: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.
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the optimal homotopy Asymptotic Method for solving blasius equation
Applied Mathematics and Computation, 2014Co-Authors: Vasile Marinca, Nicolae HerisanuAbstract: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.
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accurate analytical solutions to oscillators with discontinuities and fractional power restoring force by means of the optimal homotopy Asymptotic Method
Computers & Mathematics With Applications, 2010Co-Authors: Nicolae Herisanu, Vasile MarincaAbstract:In this paper a new approach combining the features of the homotopy concept with an efficient computational algorithm which provides a simple and rigorous procedure to control the convergence of the solution is proposed to find accurate analytical explicit solutions for some oscillators with discontinuities and a fractional power restoring force which is proportional to sign(x). A very fast convergence to the exact solution was proved, since the second-order approximation lead to very accurate results. Comparisons with numerical results are presented to show the effectiveness of this Method. Four numerical applications prove the accuracy of the Method, which works very well for the whole range of initial amplitudes. The obtained results prove the validity and efficiency of the Method, which can be easily extended to other strongly nonlinear problems.
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determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy Asymptotic Method
Journal of Sound and Vibration, 2010Co-Authors: Vasile Marinca, Nicolae HerisanuAbstract:This paper deals with the nonlinear oscillations of a particle which moves on a rotating parabola. An analytic approximate technique, namely optimal homotopy Asymptotic Method (OHAM) is employed to propose an analytic approach to solve nonlinear oscillations. The validity of the OHAM is independent on whether or not there exist small or large parameters in the considered nonlinear equations. Our procedure provides us with a convenient way to optimally control the convergence of the approximate solutions. An example is given and the results reveal that this procedure is very effective, simple and accurate. This paper demonstrates the general validity and the great potential of the OHAM.
Sehar Iqbal - One of the best experts on this subject based on the ideXlab platform.
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numerical solutions of weakly singular volterra integral equations using the optimal homotopy Asymptotic Method
Computers & Mathematics With Applications, 2012Co-Authors: M S Hashmi, Nargis Khan, Sehar IqbalAbstract:The purpose of this paper is to apply a numerical technique namely the optimal homotopy Asymptotic Method (OHAM) for finding the approximate solutions of a class of Volterra integral equations with weakly singular kernels. This Method uses simple computations with quite acceptable approximate solutions, which has close agreement with exact solutions. Illustrative examples are included to demonstrate the validity and applicability of the present Method and a comparison has been made with existing results.
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optimal homotopy Asymptotic Method for solving nonlinear fredholm integral equations of second kind
Applied Mathematics and Computation, 2012Co-Authors: M S Hashmi, Nasir Khan, Sehar IqbalAbstract:Abstract The aim of this communication is to present the effectiveness of optimal homotopy Asymptotic Method (OHAM) for solving nonlinear Fredholm integral equations of second kind. Here, we consider the first, second and third order Fredholm integral equations of second kind. Comparisons are made with Adomian Decomposition Method, Discrete Adomian Decomposition Method, Homotopy Perturbation Method, Quasi Interpolation Method, Triangular Functions Method, Trapezoidal rule and Simpson rule. The results reveal that the OHAM is very effective, simple and has close agreement with exact solutions.
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use of optimal homotopy Asymptotic Method and galerkin s finite element formulation in the study of heat transfer flow of a third grade fluid between parallel plates
Journal of Heat Transfer-transactions of The Asme, 2011Co-Authors: Sehar Iqbal, A M Siddiqui, Ali R Ansari, A JavedAbstract:We investigate the effectiveness of the optimal homotopy Asymptotic Method (OHAM) in solving nonlinear systems of differential equations. In particular we consider the heat transfer flow of a third grade fluid between two heated parallel plates separated by a finite distance. The Method is successfully applied to study the constant viscosity models, namely plane Couette flow, plane Poiseuille flow, and plane Couette-Poiseuille flow for velocity fields and the temperature distributions. Numerical solutions of the systems are also obtained using a finite element Method (FEM). A comparative analysis between the semianalytical solutions of OHAM and numerical solutions by FEM are presented. The semianalytical results are found to be in good agreement with numerical solutions. The results reveal that the OHAM is precise, effective, and easy to use for such systems of nonlinear differential equations.
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application of optimal homotopy Asymptotic Method for the analytic solution of singular lane emden type equation
Applied Mathematics and Computation, 2011Co-Authors: Sehar Iqbal, A JavedAbstract:Abstract In this study, optimal homotopy Asymptotic Method is applied on singular initial value Lane–Emden type problems to check the effectiveness and performance of the Method. It is observed that the Method is easy to implement, quite valuable to handle singular phenomena and yield excellent results at minimum computational cost. Computational results of some of the test problems are presented to demonstrate the viability and practical usefulness of the Method.
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some solutions of the linear and nonlinear klein gordon equations using the optimal homotopy Asymptotic Method
Applied Mathematics and Computation, 2010Co-Authors: Sehar Iqbal, Muhammad Idrees, A M Siddiqui, Ali R AnsariAbstract:Abstract We investigate the effectiveness of the Optimal Homotopy Asymptotic Method (OHAM) in solving time dependent partial differential equations. To this effect we consider the homogeneous, non-homogeneous, linear and nonlinear Klein–Gordon equations with boundary conditions. The results reveal that the Method is explicit, effective, and easy to use.
