The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES...The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.展开更多
In this two_part paper, a thorough investigation is made on Fourier expansions with irreducible tensorial coefficients for orientation distribution functions (ODFs) and crystal orientation distribution functions (CODF...In this two_part paper, a thorough investigation is made on Fourier expansions with irreducible tensorial coefficients for orientation distribution functions (ODFs) and crystal orientation distribution functions (CODFs), which are scalar functions defined on the unit sphere and the rotation group, respectively. Recently it has been becoming clearer and clearer that concepts of ODF and CODF play a dominant role in various micromechanically_based approaches to mechanical and physical properties of heterogeneous materials. The theory of group representations shows that a square integrable ODF can be expanded as an absolutely convergent Fourier series of spherical harmonics and these spherical harmonics can further be expressed in terms of irreducible tensors. The fundamental importance of such irreducible tensorial coefficients is that they characterize the macroscopic or overall effect of the orientation distribution of the size, shape, phase, position of the material constitutions and defects. In Part (Ⅰ), the investigation about the irreducible tensorial Fourier expansions of ODFs defined on the N_dimensional (N_D) unit sphere is carried out. Attention is particularly paid to constructing simple expressions for 2_ and 3_D irreducible tensors of any orders in accordance with the convenience of arriving at their restricted forms imposed by various point_group (the synonym of subgroup of the full orthogonal group) symmetries. In the continued work -Part (Ⅱ), the explicit expression for the irreducible tensorial expansions of CODFs is established. The restricted forms of irreducible tensors and irreducible tensorial Fourier expansions of ODFs and CODFs imposed by various point_group symmetries are derived.展开更多
New superconvergent structures are proposed and analyzed for the finite volume element(FVE)method over tensorial meshes in general dimension d(for d≥2);we call these orthogonal superconvergent structures.In this fram...New superconvergent structures are proposed and analyzed for the finite volume element(FVE)method over tensorial meshes in general dimension d(for d≥2);we call these orthogonal superconvergent structures.In this framework,one has the freedom to choose the superconvergent points of tensorial k-order FVE schemes(for k≥3).This flexibility contrasts with the superconvergent points(such as Gauss points and Lobatto points)for current FE schemes and FVE schemes,which are fixed.The orthogonality condition and the modified M-decomposition(MMD)technique that are developed over tensorial meshes help in the construction of proper superclose functions for the FVE solutions and in ensuring the new superconvergence properties of the FVE schemes.Numerical experiments are provided to validate our theoretical results.展开更多
The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models u...The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models used are derived from Carrera’s Unified Formulation(CUF)and they permit the vibration modes along the thickness to be accurately described.The finite-element method is employed and the plate element implemented has nine nodes,and the mixed interpolation of tensorial component(MITC)method is used to contrast the membrane and shear locking phenomenon.The related governing equations are derived from the principle of virtual displacement,extended to the analysis of electromechanical problems.An isotropic plate with piezoelectric patches is analyzed,with clamped-free boundary conditions and subjected to open-and short-circuit configurations.The results,obtained with different theories,are compared with the higher-order type solutions given in the literature.The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.展开更多
This paper present electrical networks, with topological modelisations, generalized cross talked functions implemented in a Kron＇s formalism; Coupling functions are called chords and give a powerful extension to the ...This paper present electrical networks, with topological modelisations, generalized cross talked functions implemented in a Kron＇s formalism; Coupling functions are called chords and give a powerful extension to the method. Applied in electromagnetic compatibility, it has proven its efficiency in time computation and accuracy. The paper review the Kron＇s formalism, a mathematical modelisation of currents by tensorial analysis and topologie, the string principles, and an application, at the end, we propose power-chopper modeling.展开更多
基金funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 107.02-2019.330。
文摘The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.
文摘In this two_part paper, a thorough investigation is made on Fourier expansions with irreducible tensorial coefficients for orientation distribution functions (ODFs) and crystal orientation distribution functions (CODFs), which are scalar functions defined on the unit sphere and the rotation group, respectively. Recently it has been becoming clearer and clearer that concepts of ODF and CODF play a dominant role in various micromechanically_based approaches to mechanical and physical properties of heterogeneous materials. The theory of group representations shows that a square integrable ODF can be expanded as an absolutely convergent Fourier series of spherical harmonics and these spherical harmonics can further be expressed in terms of irreducible tensors. The fundamental importance of such irreducible tensorial coefficients is that they characterize the macroscopic or overall effect of the orientation distribution of the size, shape, phase, position of the material constitutions and defects. In Part (Ⅰ), the investigation about the irreducible tensorial Fourier expansions of ODFs defined on the N_dimensional (N_D) unit sphere is carried out. Attention is particularly paid to constructing simple expressions for 2_ and 3_D irreducible tensors of any orders in accordance with the convenience of arriving at their restricted forms imposed by various point_group (the synonym of subgroup of the full orthogonal group) symmetries. In the continued work -Part (Ⅱ), the explicit expression for the irreducible tensorial expansions of CODFs is established. The restricted forms of irreducible tensors and irreducible tensorial Fourier expansions of ODFs and CODFs imposed by various point_group symmetries are derived.
基金This work is supported in part by the National Natural Science Foundation of China under grants 11701211,11871092,12131005the China Postdoctoral Science Foundation under grant 2021M690437。
文摘New superconvergent structures are proposed and analyzed for the finite volume element(FVE)method over tensorial meshes in general dimension d(for d≥2);we call these orthogonal superconvergent structures.In this framework,one has the freedom to choose the superconvergent points of tensorial k-order FVE schemes(for k≥3).This flexibility contrasts with the superconvergent points(such as Gauss points and Lobatto points)for current FE schemes and FVE schemes,which are fixed.The orthogonality condition and the modified M-decomposition(MMD)technique that are developed over tensorial meshes help in the construction of proper superclose functions for the FVE solutions and in ensuring the new superconvergence properties of the FVE schemes.Numerical experiments are provided to validate our theoretical results.
文摘The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models used are derived from Carrera’s Unified Formulation(CUF)and they permit the vibration modes along the thickness to be accurately described.The finite-element method is employed and the plate element implemented has nine nodes,and the mixed interpolation of tensorial component(MITC)method is used to contrast the membrane and shear locking phenomenon.The related governing equations are derived from the principle of virtual displacement,extended to the analysis of electromechanical problems.An isotropic plate with piezoelectric patches is analyzed,with clamped-free boundary conditions and subjected to open-and short-circuit configurations.The results,obtained with different theories,are compared with the higher-order type solutions given in the literature.The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.
文摘This paper present electrical networks, with topological modelisations, generalized cross talked functions implemented in a Kron＇s formalism; Coupling functions are called chords and give a powerful extension to the method. Applied in electromagnetic compatibility, it has proven its efficiency in time computation and accuracy. The paper review the Kron＇s formalism, a mathematical modelisation of currents by tensorial analysis and topologie, the string principles, and an application, at the end, we propose power-chopper modeling.
