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  • Open Access

    ARTICLE

    Higher-Order Stress-Strain Theory for Damage Modeling Implemented in an Element-free Galerkin Formulation

    Yang Yang1, Anil Misra2

    CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.1, pp. 1-36, 2010, DOI:10.3970/cmes.2010.064.001

    Abstract Gradient theories have found wide applications in modeling of strain softening phenomena. This paper presents a higher order stress-strain theory to describe the damage behavior of strain softening materials. In contrast to most conventional gradient approaches for damage modeling, the present higher order theory considers strain gradients and their conjugate higher-order stress such that stable numerical solutions may be achieved. We have described the derivation of the required constitutive relationships, the governing equations and its weak form for this higher-order theory. The constitutive coefficients were obtained from a granular media approach such that the internal length scale parameter reflects the… More >

  • Open Access

    ARTICLE

    3D Higher-OrderX-FEM Model for the Simulation of Cohesive Cracks in Cementitious Materials Considering Hygro-Mechanical Couplings

    C. Becker1, S. Jox2, G. Meschke3

    CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.3, pp. 245-278, 2010, DOI:10.3970/cmes.2010.057.245

    Abstract A three-dimensional numerical model based on the Extended Finite Element Method (X-FEM) is presented for the simulation of cohesive cracks in cementitious materials, such as concrete, in a hygro-mechanical framework. Enhancement functions for the small scale resolution of the displacement jump across cracks in the context of the X-FEM is used in conjunction with a higher order family of hierarchical shape functions for the representation of the large scale displacement field of the investigated structure. Besides the theoretical and computational formulation in a multiphase context, aspects of the implementation, such as integration and crack tracking algorithms, are discussed. Representative numerical… More >

  • Open Access

    ARTICLE

    Free and Forced Vibrations of Thick Rectangular Plates using Higher-Order Shear and Normal Deformable Plate Theory and Meshless Petrov-Galerkin (MLPG) Method

    L. F. Qian1,2, R. C. Batra3, L. M. Chen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 519-534, 2003, DOI:10.3970/cmes.2003.004.519

    Abstract We use a meshless local Petrov-Galerkin (MLPG) method to analyze three-dimensional infinitesimal elastodynamic deformations of a homogeneous rectangular plate subjected to different edge conditions. We employ a higher-order plate theory in which both transverse shear and transverse normal deformations are considered. Natural frequencies and the transient response to external loads have been computed for isotropic and orthotropic plates. Computed results are found to agree with those obtained from the analysis of the 3-dimensional problem either analytically or by the finite element method. More >

  • Open Access

    ARTICLE

    Elastostatic Deformations of a Thick Plate by using a Higher-Order Shear and Normal Deformable Plate Theory and two Meshless Local Petrov-Galerkin (MLPG) Methods

    L. F. Qian1,3, R. C. Batra2, L. M. Chen3

    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 161-176, 2003, DOI:10.3970/cmes.2003.004.161

    Abstract We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the three-dimensional analysis of the problem by the finite element method. More >

  • Open Access

    ARTICLE

    New insights in nonlinear static stability analysis by the FEM

    B. Pichler1, H.A. Mang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 43-55, 2000, DOI:10.3970/cmes.2000.001.345

    Abstract In order to avoid a fully nonlinear analysis to obtain stability limits on nonlinear load-displacement paths, linear eigenvalue problems may be used to compute estimates of such limits. In this paper an asymptotic approach for assessment of the errors resulting from such estimates is presented. Based on the consistent linearization of the geometrically nonlinear static stability criterion – the so-called consistently linearized eigenvalue problem – higher-order estimation functions can be calculated. They are obtained from a scalar post-calculation performed after the solution of the eigenproblem. Different extensions of these higher-order estimation functions are presented. An ab initio criterion for the… More >

  • Open Access

    ARTICLE

    Higher-Order Line Element Analysis of Potential Field with Slender Heterogeneities

    H.-S. Wang1,2, H. Jiang3,4, B. Yang2

    CMC-Computers, Materials & Continua, Vol.51, No.3, pp. 145-161, 2016, DOI:10.3970/cmc.2016.051.145

    Abstract Potential field due to line sources residing on slender heterogeneities is involved in various areas, such as heat conduction, potential flow, and electrostatics. Often dipolar line sources are either prescribed or induced due to close interaction with other objects. Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect. In the present work, we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities. In a benchmark example of two parallel rods, we compare the line element solution with the boundary element solution to show… More >

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