The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform

Chongmin Song - One of the best experts on this subject based on the ideXlab platform.

  • an improved continued fraction based high order transmitting boundary for time domain analyses in unbounded domains
    International Journal for Numerical Methods in Engineering, 2012
    Co-Authors: Carolin Birk, Suriyon Prempramote, Chongmin Song
    Abstract:

    SUMMARY A high-order local transmitting boundary to model the propagation of acoustic or elastic, scalar or vectorvalued waves in unbounded domains of arbitrary geometry is proposed. It is based on an improved continuedfraction solution of the dynamic stiffness matrix of an unbounded medium. The coefficient matrices of the continued-fraction expansion are determined recursively from the scaled boundary Finite Element Equation in dynamic stiffness. They are normalised using a matrix-valued scaling factor, which is chosen such that the robustness of the numerical procedure is improved. The resulting continued-fraction solution is suitable for systems with many DOFs. It converges over the whole frequency range with increasing order of expansion and leads to numerically more robust formulations in the frequency domain and time domain for arbitrarily high orders of approximation and large-scale systems. Introducing auxiliary variables, the continued-fraction solution is expressed as a system of linear Equations in i! in the frequency domain. In the time domain, this corresponds to an Equation of motion with symmetric, banded and frequency-independent coefficient matrices. It can be coupled seamlessly with Finite Elements. Standard procedures in structural dynamics are directly applicable in the frequency and time domains. Analytical and numerical examples demonstrate the superiority of the proposed method to an existing approach and its suitability for time-domain simulations of large-scale systems. Copyright © 2011 John Wiley & Sons, Ltd. Received 6 January 2011; Revised 29 March 2011; Accepted 20 April 2011

  • the scaled boundary Finite Element method in structural dynamics
    International Journal for Numerical Methods in Engineering, 2009
    Co-Authors: Chongmin Song
    Abstract:

    The scaled boundary Finite Element method is extended to solve problems of structural dynamics. The dynamic stiffness matrix of a bounded (Finite) domain is obtained as a continued fraction solution for the scaled boundary Finite Element Equation. The inertial effect at high frequencies is modeled by high-order terms of the continued fraction without introducing an internal mesh. By using this solution and introducing auxiliary variables, the Equation of motion of the bounded domain is expressed in high-order static stiffness and mass matrices. Standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain. Numerical examples for modal and direct time-domain analyses are presented. Rapid convergence is observed as the order of continued fraction increases. A guideline for selecting the order of continued fraction is proposed and validated. High computational efficiency is demonstrated for problems with stress singularity.

  • a continued fraction based high order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry
    International Journal for Numerical Methods in Engineering, 2008
    Co-Authors: Mohammad Bazyar, Chongmin Song
    Abstract:

    A high-order local transmitting boundary is developed to model the propagation of elastic waves in unbounded domains. This transmitting boundary is applicable to scalar and vector waves, to unbounded domains of arbitrary geometry and to anisotropic materials. The formulation is based on a continued-fraction solution of the dynamic-stiffness matrix of an unbounded domain. The coefficient matrices of the continued fraction are determined recursively from the scaled boundary Finite Element Equation in dynamic stiffness. The solution converges rapidly over the whole frequency range as the order of the continued fraction increases. Using the continued-fraction solution and introducing auxiliary variables, a high-order local transmitting boundary is formulated as an Equation of motion with symmetric and frequency-independent coefficient matrices. It can be coupled seamlessly with Finite Elements. Standard procedures in structural dynamics are directly applicable for evaluating the response in the frequency and time domains. Analytical and numerical examples demonstrate the high rate of convergence and efficiency of this high-order local transmitting boundary. Copyright © 2007 John Wiley & Sons, Ltd.

  • a boundary condition in pade series for frequency domain solution of wave propagation in unbounded domains
    International Journal for Numerical Methods in Engineering, 2007
    Co-Authors: Chongmin Song, Mohammad Bazyar
    Abstract:

    A boundary condition satisfying the radiation condition at infinity is frequently required in the numerical simulation of wave propagation in an unbounded domain. In a frequency domain analysis using Finite Elements, this boundary condition can be represented by the dynamic stiffness matrix of the unbounded domain defined on its boundary. A method for determining a Pade series of the dynamic stiffness matrix is proposed in this paper. This method starts from the scaled boundary Finite-Element Equation, which is a system of ordinary differential Equations obtained by discretizing the boundary only. The coefficients of the Pade series are obtained directly from the ordinary differential Equations, which are not actually solved for the dynamic stiffness matrix. The high rate of convergence of the Pade series with increasing order is demonstrated numerically. This technique is applicable to scalar waves and elastic vector waves propagating in anisotropic unbounded domains of irregular geometry. It can be combined seamlessly with standard Finite Elements. Copyright © 2006 John Wiley & Sons, Ltd.

  • a matrix function solution for the scaled boundary Finite Element Equation in statics
    Computer Methods in Applied Mechanics and Engineering, 2004
    Co-Authors: Chongmin Song
    Abstract:

    The scaled boundary Finite-Element method is a fundamental-solution-less boundary Element method based on Finite Elements. It leads to semi-analytical solutions for displacement and stress fields, which permits problems with singularities or in inFinite domains to be handled conveniently and accurately. However, the present eigenvalue method for solving the scaled boundary Finite-Element Equation requires additional treatments for multiple eigenvalues with parallel eigenvectors, which results from logarithmic terms in the solutions. A matrix function solution for the scaled boundary Finite-Element Equation in statics is presented in this paper. It is numerically stable for multiple or near-multiple eigenvalues as it is based on real Schur decomposition. Power functions, logarithmic functions and their transitions as occurring in fracture mechanics, composites and two-dimensional unbounded domains, are represented semi-analytically. No a priori knowledge on the types and orders of singularity are required when simulating stress singularities.

Bin Yan - One of the best experts on this subject based on the ideXlab platform.

  • the dynamic analysis of stochastic thin walled structures under thermal structural acoustic coupling
    Computational Mechanics, 2020
    Co-Authors: Bei Liu, Peter Wriggers, Wei Gao, Bin Yan
    Abstract:

    Random dynamic analysis of the thin-walled structure subjected to coupling loads from three fields is addressed in the frame of the Finite Element method. Based on the proposed dynamic Finite Element Equation of the deterministic structure under thermal–structural–acoustic coupling, when the randomness of structural physical parameters, temperature load and fatigue test data is fully considered, the dynamic responses of random structure subjected to coupling loads from three fields are dealt with by random factor method. The numerical characteristic values of the random temperature field and that of random dynamic responses are then derived through the moment method of random variables. Subsequently, the dynamic reliability of the stochastic structure under three-field coupling is evaluated using residual strength model, dynamic stress-intensity interference theory and the cumulative damage equal principle. Finally, the results from the methodology proposed are compared with that from Monte-carlo method for a case of numerical example, along with an inspection of the impacts of random variables on dynamic analysis results.

Mohammad Bazyar - One of the best experts on this subject based on the ideXlab platform.

  • a continued fraction based high order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry
    International Journal for Numerical Methods in Engineering, 2008
    Co-Authors: Mohammad Bazyar, Chongmin Song
    Abstract:

    A high-order local transmitting boundary is developed to model the propagation of elastic waves in unbounded domains. This transmitting boundary is applicable to scalar and vector waves, to unbounded domains of arbitrary geometry and to anisotropic materials. The formulation is based on a continued-fraction solution of the dynamic-stiffness matrix of an unbounded domain. The coefficient matrices of the continued fraction are determined recursively from the scaled boundary Finite Element Equation in dynamic stiffness. The solution converges rapidly over the whole frequency range as the order of the continued fraction increases. Using the continued-fraction solution and introducing auxiliary variables, a high-order local transmitting boundary is formulated as an Equation of motion with symmetric and frequency-independent coefficient matrices. It can be coupled seamlessly with Finite Elements. Standard procedures in structural dynamics are directly applicable for evaluating the response in the frequency and time domains. Analytical and numerical examples demonstrate the high rate of convergence and efficiency of this high-order local transmitting boundary. Copyright © 2007 John Wiley & Sons, Ltd.

  • a boundary condition in pade series for frequency domain solution of wave propagation in unbounded domains
    International Journal for Numerical Methods in Engineering, 2007
    Co-Authors: Chongmin Song, Mohammad Bazyar
    Abstract:

    A boundary condition satisfying the radiation condition at infinity is frequently required in the numerical simulation of wave propagation in an unbounded domain. In a frequency domain analysis using Finite Elements, this boundary condition can be represented by the dynamic stiffness matrix of the unbounded domain defined on its boundary. A method for determining a Pade series of the dynamic stiffness matrix is proposed in this paper. This method starts from the scaled boundary Finite-Element Equation, which is a system of ordinary differential Equations obtained by discretizing the boundary only. The coefficients of the Pade series are obtained directly from the ordinary differential Equations, which are not actually solved for the dynamic stiffness matrix. The high rate of convergence of the Pade series with increasing order is demonstrated numerically. This technique is applicable to scalar waves and elastic vector waves propagating in anisotropic unbounded domains of irregular geometry. It can be combined seamlessly with standard Finite Elements. Copyright © 2006 John Wiley & Sons, Ltd.

M S Gadala - One of the best experts on this subject based on the ideXlab platform.

  • eulerian volume of solid vos approach in solid mechanics and metal forming
    Computer Methods in Applied Mechanics and Engineering, 2011
    Co-Authors: Khaled S Alathel, M S Gadala
    Abstract:

    Abstract The commonly known volume of fluids (VOF) method in fluid mechanics applications is extended to applications in solid mechanics. For this extension, we propose the name volume of solid (VOS) method in solid mechanics. The derivation of the Eulerian Finite Element Equation is highlighted for quasi-static analysis. The VOF method is adapted to solid mechanics to track the free solid surface in large strain metal forming problems. The theoretical development of the VOS method includes the calculation of the fractional volume value of the solid in each Element and defining a free surface directional vector to find the location and shape of the free surface. The method is presented for uniform and non-uniform Cartesian grids. All issues related to the use of Eulerian Finite Element (FE) formulation and VOF method such as the connectivity of the free surface, tracking material point properties and updating the values for newly added nodes during the analysis, are discussed in this paper. The implementation of the VOS method in metal forming applications is presented using two processes; compressions between wedge-shaped dies and backward extrusion.

Lamorena German Arnel - One of the best experts on this subject based on the ideXlab platform.

  • Finite calculus. A stabilized Finite Element method for solving the Navier-Stokes Equations. Application to ocean turbulence
    Universitat Politècnica de Catalunya, 2020
    Co-Authors: Lamorena German Arnel
    Abstract:

    Ocean turbulence is a classic example of turbulent motion and observations of turbulence in the ocean lack in regions of complex topography since in-situ and experimental data are complicated to obtain. As a result, ocean circulation and flow interaction with obstacles such as seamounts and submarine canyons rely heavily on modelling and numerical simulation such that these are the only tools that can provide insights and ideas which are essential to the scientific community. This research investigated the capability of a stabilized Finite Element method (SFEM) based on the Finite increment calculus (FIC) procedure, which is one of the most promising approaches to numerically simulate turbulent flows with particular interest in its application in simulating oceanic turbulence. The use of the FIC procedure allows solution of a wide range of fluid flow problems without the need of a turbulence model. The available numerical model was first validated through numerical simulations of various test cases such as Taylor-Couette flow, Ekman spiral, lock-exchange flow and circulation driven by oscillatory forcing over a theoretical submarine canyon model. Excellent qualitative agreement with available numerical and experimental data was obtained through minimal modification of the numerical model using TCL programming codes. To improve on modeling capabilities, which eventually allowed simulation of oceanic turbulence, a systematic modification of the numerical model was done by introducing additional paramaters on the governing Equation, which is the incompressible Navier-Stokes Equations. The resulting stabilized Finite Element Equation was subsequently implemented into the numerical model, and the modification produced a coastal ocean model version. It was validated through numerical simulations of flow in coastal areas affected by topography, upwelling flow and submarine canyon. These flows are particularly reliant on numerical simulation, as the extreme nature of their flow makes obtention of accurate and reliable experimental data difficult or nearly impossible. The FIC approach has shown the potential for providing a reliable, accurate and efficient method for numerical simulation of coastal processes. The various applications demonstrated the good performance of the numerical model, and the computational results agree well with the theoretical and experimental data.Postprint (published version

  • Finite calculus. A stabilized Finite Element method for solving the Navier-Stokes Equations. Application to ocean turbulence
    Universitat Politècnica de Catalunya, 2020
    Co-Authors: Lamorena German Arnel
    Abstract:

    Ocean turbulence is a classic example of turbulent motion and observations of turbulence in the ocean lack in regions of complex topography since in-situ and experimental data are complicated to obtain. As a result, ocean circulation and flow interaction with obstacles such as seamounts and submarine canyons rely heavily on modelling and numerical simulation such that these are the only tools that can provide insights and ideas which are essential to the scientific community. This research investigated the capability of a stabilized Finite Element method (SFEM) based on the Finite increment calculus (FIC) procedure, which is one of the most promising approaches to numerically simulate turbulent flows with particular interest in its application in simulating oceanic turbulence. The use of the FIC procedure allows solution of a wide range of fluid flow problems without the need of a turbulence model. The available numerical model was first validated through numerical simulations of various test cases such as Taylor-Couette flow, Ekman spiral, lock-exchange flow and circulation driven by oscillatory forcing over a theoretical submarine canyon model. Excellent qualitative agreement with available numerical and experimental data was obtained through minimal modification of the numerical model using TCL programming codes. To improve on modeling capabilities, which eventually allowed simulation of oceanic turbulence, a systematic modification of the numerical model was done by introducing additional paramaters on the governing Equation, which is the incompressible Navier-Stokes Equations. The resulting stabilized Finite Element Equation was subsequently implemented into the numerical model, and the modification produced a coastal ocean model version. It was validated through numerical simulations of flow in coastal areas affected by topography, upwelling flow and submarine canyon. These flows are particularly reliant on numerical simulation, as the extreme nature of their flow makes obtention of accurate and reliable experimental data difficult or nearly impossible. The FIC approach has shown the potential for providing a reliable, accurate and efficient method for numerical simulation of coastal processes. The various applications demonstrated the good performance of the numerical model, and the computational results agree well with the theoretical and experimental data