8-node and 12-node plane elements based on assumed stress quasi-conforming method immune to distorted mesh

2017 ◽  
Vol 34 (8) ◽  
pp. 2731-2751 ◽  
Author(s):  
Changsheng Wang ◽  
Yang Wang ◽  
Caixia Yang ◽  
Xiangkui Zhang ◽  
Ping Hu
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Element Mesh ◽  
Content Type ◽  
Mesh Model ◽  
Distorted Mesh ◽  
New Strategy ◽  
Discrete Methods ◽  
Element Boundary ◽  
Fundamental Analytical Solutions

Purpose Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties. Design/methodology/approach First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration. Findings The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy. Originality/value New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.

An Efficient CAD-Integrated Multi-Dimensional Model for Microfluidic Simulations

2007 ◽  
Author(s):  
Josh Danczyk ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Analytical Solutions ◽  
Cross Flow ◽  
Reduction Process ◽  
Microfluidic Devices ◽  
Element Mesh ◽  
Narrow Channels ◽  
Artificial Boundary Conditions ◽  
Weighted Residuals

Microfluidic devices exhibit high-aspect ratio in that their channel-widths are much smaller than their overall lengths. High-aspect geometry leads to an unduly large finite element mesh, making the (otherwise popular) finite-element method (FEM) a poor choice for modeling microfluidic devices. An alternate computational strategy is to exploit well-known analytical solutions for fluid flow over the narrow-channels of a device, and then either: (a) assume the same analytical solutions for the (wider) cross-flow regions, or (b) exploit these solutions to set-up artificial boundary conditions over the cross-flow regions. Such simplified models are computationally far superior to FEM, but do not support the generality or flexibility of FEM. In this paper, we propose a third strategy for exploiting the analytical solutions: (c) directly incorporate them into standard FE-based analysis via model reduction techniques. The advantages of the proposed strategy are: (1) designers can use standard CAD/CAE environments to model, analyze and post-process microfluidic simulation, (2) well-established dual-weighted residuals can be used to estimate modeling errors, and (3), if desired, one can eliminate the dependency on possibly inaccurate analytical solutions over selected regions. The simplicity and generality of the proposed method is inherited from the model reduction process, so are its theoretical properties, while simultaneously its computational efficiency is inherited from the use of analytical solutions.

Multistage topology optimization of induction heating apparatus in time domain electromagnetic field with magnetic nonlinearity

2019 ◽  
Vol 38 (3) ◽  
pp. 1009-1022
Author(s):  
Hiroshi Masuda ◽  
Yoshifumi Okamoto ◽  
Shinji Wakao
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Induction Heating ◽  
Time Domain ◽  
Computation Time ◽  
Design Domain ◽  
Element Mesh ◽  
Content Type ◽  
Actual Application ◽  
Application Model

Purpose The purpose of this paper is to solve efficiently the topology optimization (TO) in time domain problem with magnetic nonlinearity requiring a large-scale finite element mesh. As an actual application model, the proposed method is applied to induction heating apparatus. Design/methodology/approach To achieve TO with efficient computation time, a multistage topology is proposed. This method can derive the optimum structure by repeatedly reducing the design domain and regenerating the finite element mesh. Findings It was clarified that the structure derived from proposed method can be similar to the structure derived from the conventional method, and that the computation time can be made more efficient by parameter tuning of the frequency and volume constraint value. In addition, as a time domain induction heating apparatus problem of an actual application model, an optimum topology considering magnetic nonlinearity was derived from the proposed method. Originality/value Whereas the entire design domain must be filled with small triangles in the conventional TO method, the proposed method requires finer mesh division of only the stepwise-reduced design domain. Therefore, the mesh scale is reduced, and there is a possibility that the computation time for TO can be shortened.

scholarly journals AN INVESTIGATION OF IRREGULAR CRACK PATH EFFECTS ON FRACTURE MECHANICS PARAMETERS USING A GRAIN MICROSTRUCTURE MESHING TECHNIQUE

2012 ◽  
Vol 04 (01) ◽  
pp. 1250001 ◽  
Author(s):  
A. MEHMANPARAST ◽  
F. BIGLARI ◽  
C. M. DAVIES ◽  
K. M. NIKBIN
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Crack Path ◽  
Crack Tip ◽  
Grain Structure ◽  
Element Mesh ◽  
Mesh Structure ◽  
Crack Paths

A sub-grain size finite element modelling approach is presented in this paper to investigate variations in fracture mechanics parameters for irregular crack paths. The results can be used when modelling intergranular and transgranular crack growth where creep and fatigue are the dominant failure mechanisms and their crack paths are irregular. A novel method for sub-grain scale finite element mesh consisting of multiple elements encased in ~50–150 μm-sized grains has been developed and implemented in a compact tension, C(T), mesh structure. The replicated shapes and dimensions were derived from an isotropic metallic grain structure using representative random sized grain shapes repeated in sequence ahead of the crack tip. In this way the effects of crack tip angle ahead of the main crack path can be considered in a more realistic manner. A comprehensive sensitivity analysis has been performed for elastic and elastic-plastic materials using ABAQUS and the stress distributions, the stress intensity factor and the J-integral have been evaluated for irregular crack paths and compared to those of obtained from analytical solutions. To examine the local and macroscopic graph path effects on fracture mechanics parameters, a few extreme cases with various crack-tip angles have been modelled by keeping the macroscopic crack path parallel to the axis of symmetry. The numerical solutions from these granular mesh structures have been found in relatively good agreement with analytical solutions.

A novel numerical method for the solution of nonlinear equations with applications to heat transfer

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
J.N. Reddy ◽  
Matthew Martinez ◽  
Praneeth Nampally
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Mixed Boundary ◽  
Salient Feature ◽  
Two Dimensions ◽  
Element Mesh ◽  
Content Type ◽  
Linear Differential

Purpose The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions. Design/methodology/approach In the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM). Findings Numerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM. Originality/value To the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not.

A Four-Node Hybrid-Trefftz Plane Elasticity Element with Fundamental Analytical Solutions

2011 ◽  
Vol 279 ◽  
pp. 194-199
Author(s):  
Ke Yong Wang
Keyword(s):  
Analytical Solutions ◽  
Displacement Field ◽  
Plane Elasticity ◽  
Element Formulation ◽  
Airy Stress Function ◽  
Numerical Examples ◽  
Variational Functional ◽  
Elasticity Problems ◽  
Element Boundary ◽  
Fundamental Analytical Solutions

A new four-node hybrid-Trefftz element is developed for plane elasticity problems. From the Airy stress function, the fundamental analytical solutions of the governing equation are derived as Trefftz functions for the intra-element (Trefftz) displacement field. Together with an independent frame displacement field along the element boundary, the element formulation is then constructed following the modified variational functional. Several numerical examples indicate that the proposed element exhibits good performance.

Design optimization of key components’ spatial position of unilateral axle counting sensor

Sensor Review ◽  
2018 ◽  
Vol 38 (3) ◽  
pp. 261-268
Author(s):  
Weiming Tong ◽  
Yanlong Liu ◽  
Xianji Jin ◽  
Zhongwei Li ◽  
Jian Guan
Keyword(s):  
Finite Element ◽  
Design Optimization ◽  
Operation Time ◽  
Spatial Location ◽  
Optimization Method ◽  
Element Mesh ◽  
Content Type ◽  
Sensor Structure ◽  
Excitation Coil ◽  
Railway Signal Device

PurposeThe unilateral axle counting sensor is an important railway signal device that detects a train. For efficient and stable detection, the amplitude of induced electromotive force and its changes must be big enough. Therefore, the purpose of this study is to find a way to design and optimize the sensor structure quickly and accurately.Design/methodology/approachWith the help of extensive electromagnetic field calculations, the study puts forward a modified model based on the finite element method, establishes an independent air domain around the sensor, wheel and the railway and adopts a unique grid division method. It offers a design optimization method of the induction coil angles and its spatial location with respect to the excitation coil by using the combination weighting algorithm.FindingsThe modified modeling method can greatly reduce the number of finite element mesh and the operation time, and the method can also be applied to other areas. The combination weighting algorithm can optimize the structure of the sensor quickly and accurately.Originality/valueThis study provides a way to design and optimize the structure of the sensor and a theoretical basis for the development. The results can improve and expand the technology of the axle counting sensor.

Anderson acceleration for electromagnetic nonlinear problems

2019 ◽  
Vol 38 (5) ◽  
pp. 1493-1506
Author(s):  
Mattia Filippini ◽  
Piergiorgio Alotto ◽  
Alessandro Giust
Keyword(s):  
Finite Element ◽  
Fixed Point ◽  
Nonlinear Problems ◽  
Test Case ◽  
Test Cases ◽  
Content Type ◽  
Restarted Gmres ◽  
Acceleration Method ◽  
Anderson Acceleration ◽  
Element Boundary

Purpose The purpose of this paper is to implement the Anderson acceleration for different formulations of eletromagnetic nonlinear problems and analyze the method efficiency and strategies to obtain a fast convergence. Design/methodology/approach The paper is structured as follows: the general class of fixed point nonlinear problems is shown at first, highlighting the requirements for convergence. The acceleration method is then shown with the associated pseudo-code. Finally, the algorithm is tested on different formulations (finite element, finite element/boundary element) and material properties (nonlinear iron, hysteresis models for laminates). The results in terms of convergence and iterations required are compared to the non-accelerated case. Findings The Anderson acceleration provides accelerations up to 75 per cent in the test cases that have been analyzed. For the hysteresis test case, a restart technique is proven to be helpful in analogy to the restarted GMRES technique. Originality/value The acceleration that has been suggested in this paper is rarely adopted for the electromagnetic case (it is normally adopted in the electronic simulation case). The procedure is general and works with different magneto-quasi static formulations as shown in the paper. The obtained accelerations allow to reduce the number of iterations required up to 75 per cent in the benchmark cases. The method is also a good candidate in the hysteresis case, where normally the fixed point schemes are preferred to the Newton ones.

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