Ziqiang Bai¹, Wenzhen Qu^2,*, Guanghua Wu^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.3, pp. 2955-2972, 2024, DOI:10.32604/cmes.2023.031474

Abstract In the past decade, notable progress has been achieved in the development of the generalized finite difference method (GFDM). The underlying principle of GFDM involves dividing the domain into multiple sub-domains. Within each sub-domain, explicit formulas for the necessary partial derivatives of the partial differential equations (PDEs) can be obtained through the application of Taylor series expansion and moving-least square approximation methods. Consequently, the method generates a sparse coefficient matrix, exhibiting a banded structure, making it highly advantageous for large-scale engineering computations. In this study, we present the application of the GFDM to numerically solve inverse Cauchy problems in two-… More >

Leilei Chen^2,3, Haozhi Li^3,4, Lu Meng⁵, Pan Chen³, Pei Li^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.26, No.4, pp. 1-2, 2023, DOI:10.32604/icces.2023.010584

Abstract In this paper, a Direct FE² method is proposed to simulate the electromechanical coupling problem of inhomogeneous materials. The theoretical foundation for the proposed method, downscaling and upscaling principles, is the same as that of the FE² method. The two-level simulation in the Direct FE² method may be addressed in an integrative framework where macroscopic and microscopic degrees of freedom (DOFs) are related by multipoint constraints (MPCs) [1]. This critical characteristic permits simple implementation in commercial FE software, eliminating the necessity for recurrent data transfer between two scales [2-4]. The capabilities of Direct FE² are validated using four numerical examples,… More >

Jan Sladek¹, Vladimir Sladek¹ and Choon-Lai Tan²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.1, pp. 109-111, 2019, DOI:10.32604/icces.2019.05685

Abstract In recent years, a special attention has been directed to the investigation of the relations between the macroscopic material behaviour and its microstructure. For most of the analyses of composite structures, effective or homogenized material properties are used, instead of taking into account the individual component properties and geometrical arrangements. The effective properties are usually difficult or expensive to measure and in the design stage the composition may vary substantially, making frequent measurements prohibitive. Hence a lot of effort has been devoted into the development of mathematical and numerical models to derive homogenized material properties directly from those of the… More >

H. Nguyen-Van¹, N.Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.1, pp. 65-96, 2008, DOI:10.3970/cmes.2008.036.065

Abstract A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated with a single node which is termed as node-based elements. The displacement fields of the element are approximated by the linear interpolation functions of the original mesh while the approximations of mechanical strains and electric potential fields are normalized using the stabilized conforming nodal… More >

H. Nguyen-Van¹, N. Mai-Duy², T. Tran-Cong³

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 209-222, 2008, DOI:10.3970/cmes.2008.023.209

Abstract This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated.… More >

G. Dziatkiewicz¹ and P. Fedelinski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 35-46, 2007, DOI:10.3970/cmes.2007.017.035

Abstract The aim of the present work is to show the formulation and application of the dual reciprocity boundary element method (BEM) to free vibrations of two-dimensional piezoelectric structures. The piezoelectric materials are modelled as homogenous, linear -- elastic, transversal isotropic and dielectric. Displacements and electric potentials are treated as generalized displacements and tractions and electric charge flux densities are treated as generalized tractions. The static fundamental solutions, which are required in the proposed approach, are derived using the Stroh formalism. The domain inertial integral is transformed to the equivalent boundary integral using the dual reciprocity method (DRM). The boundary quantities… More >