A new strain smoothing method for triangular and tetrahedral finite elements

ABSTRACTThe evaluation of the accuracy and performance of a higher‐order curl‐conforming triangular prismatic finite element is carried out in this article. The triangular prismatic finite element proposed by the authors is tested by simulating real microwave devices in planar technology. The results obtained using this prismatic element are compared with those obtained using the finite element method reference commercial software HFSS that makes use of higher‐order tetrahedral finite elements. Conclusions about the use of this prismatic element for the analysis of planar microwave devices are given. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:1794–1801, 2016

The purpose of this study is to develop a computer code for accurate prediction of the mechanical behavior of hyperelastic solids under large deformation and finite strains. It is used, in the present work, the Lagrangian positional version of the Finite Element Method, in which the degrees of freedom are current positions instead of displacements. The main mechanical variables are the Green-Lagrange strain and the second Piola-Kirchhoff stress tensors. Isoparametric tetrahedral solid finite element of any approximation degree is employed with full integration in order to obtain accuracy. In order to be general, it is developed a numerical strategy to determine the shape functions coefficients of any order, following tetrahedral basis. The solid equilibrium is achieved at the current position by means of the Minimal Potential Energy Principle regarding positions and is solved by the Newton-Raphson iterative scheme. It is important to mention that the adopted constitutive laws are nonlinear, isotropic and homogeneous hyperelastic, normally used in mechanical analysis of elastomers, with the near compressibility assumption. It is applied the Flory decomposition, i.e., the multiplicative split of the deformation gradient into a volumetric and an isochoric part. A parallel processing strategy is used to increase the simulation speed and memory capacity, justifying the use of high order elements for solid analysis. Results confirm that the developed computer code is capable of predicting the static behavior of complex problems, such as Cook's membrane and partially loaded block. The shape functions generator code exhibits simplicity and, thus, it may be easily implemented in other finite elements. The increase in the order of approximation and the mesh refinement improve accuracy and, therefore, the proposed methodology together with parallel computing indicate a safe way for further developments in plasticity and damage mechanics for large strain and deformations.

An efficient multiphysics solid shell based finite element approach for modeling thin sheet metal forming processes

Purpose In order to avoid the problem of volumetric locking often encountered when using constant strain tetrahedral finite elements, the purpose of this paper is to present a new composite tetrahedron element which is especially designed for the combined finite-discrete element method (FDEM). Design/methodology/approach A ten-noded composite tetrahedral (COMPTet) finite element, composed of eight four-noded low order tetrahedrons, has been implemented based on Munjiza’s multiplicative decomposition approach. This approach naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. The problem of volumetric locking is avoided via a selective integration approach that allows for different constitutive components to be evaluated at different integration points. Findings A number of validation cases considering different loading and boundary conditions and different materials for the proposed element are presented. A practical application of the use of the COMPTet finite element is presented by quantitative comparison of numerical model results against simple theoretical estimates and results from acrylic fracturing experiments. All of these examples clearly show the capability of the composite element in eliminating volumetric locking. Originality/value For this tetrahedral element, the combination of “composite” and “low order sub-element” properties are good choices for FDEM dynamic fracture propagation simulations: in order to eliminate the volumetric locking, only the information from the sub-elements of the composite element are needed which is especially convenient for cases where re-meshing is necessary, and the low order sub-elements will enable robust contact interaction algorithms, which maintains both relatively high computational efficiency and accuracy.

In this paper, a modified method of characteristics in combination with integral identities of triangular and tetrahedral linear elements is used to prove a uniform optimal-order error estimate that depends only on the initial data and right-hand side, but not on a scaling parameter ɛ, for multidimensional time-dependent advection-diffusion equations.

This paper describes the development of a software to perform three-dimensional crack propagation analyses. The software is based on the conventional finite element method with second order tetrahedral element and an automatic mesh generation software. Hexahedral finite elements have historically been used in fracture analyses and methodologies to compute the crack parameters have been developed for the hexahedral elements. In present research, the authors have developed a VCCM (virtual crack closure-integral method) for the second order tetrahedral finite element. Use of the tetrahedral element allows us to utilize an automatic mesh generation software. The direction and rate of crack propagation are predicted based on the stress intensity factors and the shape of crack is updated. Hence, a software package containing the modules for mesh generation, for finite element analysis, for stress intensity factor evaluation, for predicting the rate and the direction of crack propagation and for updating crack configuration, can be developed.

Meshfree-enriched simplex elements with strain smoothing for the finite element analysis of compressible and nearly incompressible solids

The structure of rubber‐like materials is characterized through chain‐like macromolecules which are linked together at certain points. This special design leads to a completely random three‐dimensional network. There exist several ways to specify rubber‐like material behaviour. Many scientists use the tool of statistical mechanics to transfer the information from the micro level to the macro level. In this context, one should mention e.g. the work of Treolar & Riding [1979] (full network theory) or the eight‐chain model suggested by Arruda & Boyce [1]. In the present contribution, the step from the micro level to the macro level is done by means of the finite element method. For this purpose, we derive a unit cell consisting of one three‐dimensional tetrahedral finite element and six truss elements lying on every edge of the tetrahedron. The truss elements represent the material behaviour of a certain group of polymer chains, whereas the tetrahedral elements ensure incompressibility. So, using a finite element model with a sufficiently high number of unit cells, we are able to model the well‐known macro‐mechanical material behaviour of rubber‐like polymers.

Fracture mechanics analysis using the finite element method has been one of the key methodologies to evaluate structural integrity for aging infrastructures such as aircraft, ship, power plants, etc. However, three-dimensional crack analyses for structures with highly complex three-dimensional shapes have not widely been used, because of many technical difficulties such as the lack of enough computational power. The authors have been developing a fracture mechanics analysis system that can deal with arbitrary shaped cracks in three-dimensional structures. The system consists of mesh generation software, a finite element analysis program and a fracture mechanics module. In our system, a Virtual Crack Closure-Integral Method (VCCM) for the quadratic tetrahedral finite elements is adopted to evaluate the stress intensity factors. This system can perform the three-dimensional fracture analyses. Fatigue and SCC crack propagation analyses with more than one cracks of arbitrary complicated shapes and orientations. The rate and direction of crack propagation are predicted by using appropriate formulae based on the stress intensity factors. When the fracture mechanics analysis system is applied to the complex shaped aging structures with the cracks which are modeled explicitly, the size of finite element analysis tends to be very large. Therefore, a large scale parallel structural analysis code is required. We also have been developing an open-source CAE system, ADVENTURE. It is based on the hierarchical domain decomposition method (HDDM) with the balancing domain decomposition (BDD) pre-conditioner. A general-purpose parallel structural analysis solver, ADVENTURE_Solid is one of the solver modules of the ADVENTURE system. In this paper, we combined VCCM for the tetrahedral finite element with ADVENTURE system and large-scale fracture analyses are fully automated. They are performed using the massively parallel super computer ES2 (Earth Simulator 2) which is owned and run by JAMSTEC (Japan Agency for Marine-Earth Science and Technology).

Algebraic mesh quality metrics for unstructured initial meshes

A parallel LES technique for viscous incompressible flow with heat transfer based on the finite-element method using tetrahedral elements has been developed. It uses an algorithm based on the SIMPLER method to solve the Navier-Stokes equations, in which a BTD term is introduced to ensure computational stability. In this technique, the Crank-Nicholson method is used as a time integration scheme to improve the accuracy to solve both the Navier-Stokes equations and the energy equation. Moreover, the Smagorinsky model is applied to approximate the Reynolds stress term and the zero-equation model is applied to solve the energy equation. The code based on this technique is parallelized by using mesh partitioning by finite elements in order to carry out the element-based calculations and by using row-based domain decomposition of the global matrix to solve the linear equations. The developed LES technique was verified by simulating natural convection problems in a cubic cavity at Ra=103 to 1010. Numerical results at Ra=103 to 108 agree well with those computed by other researchers and successfully demonstrated the stable prediction of the unsteadiness and the heat transfer at Ra=109 to 1010. It was also applied to a realistic heat transfer probelm in a rotating cavity. Computed heat transfer coefficients at Ra=1.09×109 and 2.18×109 were found to be within 15% of those measured experimentally. This acceptable error means that the new LES technique can be applited to solve heat tranfer problems in a rotating flow -field.

A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well‐known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three‐dimensional electroelasticity.

The linear tetrahedral (solid) element is a three-dimensional finite element with both local and global coordinates. It is characterized by linear shape functions. It is also called the constant strain tetrahedron. The linear tetrahedral element has modulus of elasticity E and Poisson’s ratio v.

The problem of calculating the stress-strain state and solving the problem of weight optimization of a single-engine transport aircraft nacelle fasteners is relevant In connection with the development of aircraft construction. One of the fastening elements is the brace, which is under the action of static loads.. The method of calculation of the transport aircraft nacelle brace, which is based on the finite element method, is considered in the work. A tetrahedral finite element was chosen as the element. The stresses and strains of the brace were determined, the stress-strain state was analyzed and recommendations for optimization of structural elements were given.

Background and aimsAlthough studies on the relation between arrhythmias and the action potential duration (APD) have been carried out, most of them are based only on electrophysiological factors of the heart and lack experiments that consider cardiac mechanical and electromechanical characteristics. Therefore, we conducted this study to clarify the relevance of the shortening of APD of a cell in relation to the mechanical contraction activity of the heart and the associated risk of arrhythmia.MethodsThe human ventricular model used in this study has two dynamic characteristics: electrophysiological conduction and mechanical contraction. The model simulating electrophysiological characteristics was consisted of lumped parameter circuit that can mimic the phenomenon of ion exchange through the cell membrane of myocyte and consisted of 214,319 tetrahedral finite elements. In contrast, the model simulating mechanical contraction characteristics was constructed to mimic cardiac contraction by means of the crossbridge of a myofilament and consisted of 14,720 hermite-based finite elements to represent a natural 3D curve of the cardiac surface. First, we performed a single cell simulation and the electrophysiological simulation according to the change of the APD by changing the electrical conductivity of the IKs channel. Thus, we confirmed the correlation between APD and intracellular Ca2+ concentration. Then, we compared mechanical response through mechanical simulation using Ca2+ data from electrical simulation.ResultsThe APD and the sum of the intracellular Ca2+ concentrations showed a positive correlation. The shortened APD reduced the conduction wavelength of ventricular cells by shortening the plateau and early repolarization in myocardial cells. The decrease in APD reduced ventricular pumping efficiency by more than 60% as compared with the normal group (normal conditions). This change is caused by the decline of ventricular output owing to reduced ATP consumption during the crossbridge of myofilaments and decreased tension.ConclusionThe shortening of APD owing to increased electrical conductivity of a protein channel on myocardial cells likely decreases the wavelength and the pumping efficiency of the ventricles. Additionally, it may increase tissue sensitivity to ventricular fibrillation, including reentry, and cause symptoms such as dyspnea and dizziness.