High-order Tetrahedral Elements Research Articles

Large deformation analysis of functionally graded elastoplastic materials via solid tetrahedral finite elements

In this paper, a solid finite element formulation applied to the analysis of functionally graded materials (FGMs) under finite elastoplastic deformation with mixed hardening is presented.The main novelty of this paper is the use of gradually variable material coefficients in finite elastoplastic strain regime.The numerical simulations are performed with the same constitutive models but with different variations of the material coefficients. Full integration and high order tetrahedral elements are used. Results show that high order elements and mesh refinement avoids general locking problems. Finally, the differences (regarding final results) between the homogeneous and the FG cases are depicted.

Higher-Order DG-FETD Modeling of Wideband Antennas With Resistive Loading

A discontinuous Galerkin finite-element time-domain (DG-FETD) method with higher-order tetrahedral elements is developed to model wideband antennas with resistive loading. To fully characterize the wideband fundamental parameters of the antennas with multiscaled structures, several schemes are adopted to effectively model resistive loading and accurately calculate return loss, directivity, and radiation pattern. Successful simulation of interesting antennas using the proposed DG-FETD method demonstrates its capability of modeling wideband antennas without or with resistive loading.

Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements

In this paper, the discontinuous Galerkin (DG) finite-element time-domain (FETD) method is developed to model electromagnetic (EM) structures with waveguide excitations. Several specific issues about the DG-FETD modeling are addressed. First, the higher order tetrahedral elements are employed to accurately model the geometry of EM structures and effectively reduce the dispersion error so that the efficiency of the FETD method is increased. To further increase the efficiency of the DG-FETD method, the local time-stepping scheme is applied. Secondly, the conformal perfect matching layer (PML) is applied to terminate the waveguide. The formulation of the conformal PML is presented in this paper. Thirdly, a novel approach is proposed to extract the S-parameters of waveguide structures. This approach applies the surface magnetic current to excite the EM fields in the waveguide structures. Taking advantage of the relationship between the excitation current and excited fields in the uniform waveguide, one can readily obtain the incident electric fields that are required for calculating the S-parameters. This approach avoids the pre-simulation of the uniform waveguide. Finally, the numerical results are given to validate the DG-FETD modeling.

Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green–Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant–Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials.

Higher Order Finite Element Analysis of Finite-by-Infinite Arrays

This paper describes a finite element analysis of finite-by-infinite arrays with arbitrary composition. The analysis employs higher order tetrahedral elements for discretization and imposes appropriate boundary conditions on the unit cell boundaries. The radiation boundary condition imposed on the array aperture is derived through a spectral- and a mixed-domain formulation. The two formulations are found to produce consistent numerical results. In addition to a general code using tetrahedral elements, a special code is also developed based on brick element discretization, which utilizes the conjugate gradient fast Fourier transform (CG-FFT) method. Both computer codes are applied to the analysis of several finite-by-infinite arrays and numerical examples are presented to demonstrate their accuracy and capability.