Finite Element Mesh Superposition Research Articles

Numerical Characterization of Mixing in a Kneading Element Channel of Dual‐Speed Corotating Non‐Twin Screws Using Lagrangian Statistics Method

Front Cover: Symmetry break is introduced by a novel non-twin kneading element. The self-cleaning still remains where one-tip rotor engaged with two-tip one replaces two identical two-tip rotors of conventional twin screws. The numerical simulation is performed using finite element method and mesh superposition technique. A Lagrangian statistics method reveals that the non-twin geometry offers equivalent distributive mixing and better dispersive mixing. This is reported by Baiping Xu, Ruifeng Liang, Shuping Xiao, Lingcao Tan, Jian Song, and Huiwen Yu in article number 2200052.

Effects of global / local setting on analysis results in s-version finite element mesh superposition method with the local mesh exceeding

Effects of global / local setting on analysis results in s-version finite element mesh superposition method with the local mesh exceeding

2D Numerical Simulation of Flow and Mixing Performances in Novel Four-screw Extruders

Two kinds of novel four screw extruders, namely square-layout four screw extruder (SFSE) and rhombic-layout four screw extruder (RFSE), were selected to study their flow and mixing performances. Based on the finite element method and mesh superposition technique (MST), two-dimensional flow characteristics in the SFSE and RFSE at cross sections were studied by using Polyflow software. Moreover, the measurements of mixing efficiency, such as the mixing index, time-averaged efficiency, instantaneous efficiency and logarithm stretching rate, were calculated in the SFSE and RFSE, respectively. The comparisons of mixing efficiencies in the SFSE and RFSE were employed in order to better understand the effect of screw layout on the mixing performances in four screw extruders. The results show that the mixing efficiency of RFSE is higher than that of the SFSE. For the square-layout of four screws, the counter-rotating SFSE has higher mixing efficiency than the co-rotating SFSE.

Development of High Accuracy Numerical Integration Technique for Finite Element Mesh Superposition Analysis with Curved Lines or Surfaces

Development of High Accuracy Numerical Integration Technique for Finite Element Mesh Superposition Analysis with Curved Lines or Surfaces

Multiscale stress analysis of trabecular bone around acetabular cup implant by finite element mesh superposition method

Multiscale stress analysis of trabecular bone around acetabular cup implant by finite element mesh superposition method

曲線境界を含む重合メッシュ解析における連成項の高精度数値積分法

本稿では,重合メッシュ法の連成項の計算において曲線境界を有する数値積分を効率よく実行するための手法を提案する.積分範囲に含まれる曲線境界は,曲線の由来となっている高次要素のヤコビアンを用いて評価した.本提案手法を用いた解析結果を,折れ線近似に基づく評価法と比較したところ,両者の解析結果とほぼ同一となった,

Study on Appropriate Decomposition Procedure of Integral Domain for High Accurate Numerical Integration of Interactive Terms in Finite Element Mesh Superposition Method by Auto-Mesh Generation

Study on Appropriate Decomposition Procedure of Integral Domain for High Accurate Numerical Integration of Interactive Terms in Finite Element Mesh Superposition Method by Auto-Mesh Generation

Structural strength prediction for porous titanium based on micro-stress concentration by micro-CT image-based multiscale simulation

For the design of porous titanium component, differently from its use as functional materials, structural strength prediction algorithm is proposed based on the micro-stress concentration analyzed by the multiscale simulation. The modeling of real microstructure is carried out by the image-based technique with X-ray micro-CT. The multiscale computational method consists of asymptotic homogenization and finite element mesh superposition (FEMS) techniques. A criterion is proposed to predict the nonlinearity initiation point in the load and displacement curve by means of micro-stress distribution expressed by histogram. Only the constituent's yield strength is referred regardless of the microscopic morphology. The originality of this paper lies in the validation of the homogenization process, the modeling guideline of micro-mesh superposition onto macro-mesh in FEMS, and the strength prediction algorithm. L-shaped components with different pore diameter were discussed in both experiment and simulation.

Reduction of Finite Element Mesh and Model Order for Fast Dynamic Analysis of Global/Local Problem

MEMS structures and machines fabricated by photolithography and/or etching have often repeated unit microstructure. We need to design not only the global parameters but also microscopic and local parameters. In pursuit of this, a dynamic analysis of global/local problem is essential, and especially fast computational method and convenient modeling technique are both required for the MEMS design. Hence, this paper presents the application of model order reduction (MOR) for fast dynamic analysis combined with the finite element mesh superposition (FEMS) technique for practical and convenient modeling of the above-mentioned microstructures. Through two examples, the accuracy is carefully investigated for both global and local responses associated with the base vectors in MOR algorithm. The first example is analyzed by a kind of homogenization technique and MOR. The number of DOFs was finally reduced by a factor of approximately 1/6 (47,362/296,268). In addition, MOR enabled us to reduce the coefficient matrix size to only 300. The second example is analyzed by both FEMS and MOR, and it was found that MOR is also applicable to an unusual matrices generated by FEMS.

338 多孔質チタン部材の内部ミクロ応力に基づく強度設計手法に関する研究(新機能多孔質材料の創製と評価)

For the design of porous titanium component, differently from its use as functional materials, structural strength prediction algorithm is proposed based on the micro-stress concentration analyzed by the multiscale simulation. The modeling of real microstructure is carried out by the image-based technique with X-ray micro-CT. The multiscale computational method consists of asymptotic homogenization and finite element mesh superposition (FEMS) techniques. A criterion is proposed to predict the nonlinearity initiation point in the load and displacement curve by means of micro-stress distribution expressed by histogram. Only the constituent's yield strength is referred regardless of the microscopic morphology. The originality of this paper lies in the validation of the homogenization process, the modeling guideline of micro-mesh superposition onto macro-mesh in FEMS, and the strength prediction algorithm. L-shaped components with different pore diameter were discussed in both experiment and simulation.

OS0619 重合メッシュ法によるポーラスチタン部材のミクロ応力基準強度予測(先進複合材料の強度・特性評価,オーガナイズドセッション)

OS0619 重合メッシュ法によるポーラスチタン部材のミクロ応力基準強度予測(先進複合材料の強度・特性評価,オーガナイズドセッション)

Multiscale analysis of stress distribution in teeth under applied forces

Objectives The present study aimed to clarify stress distribution in teeth under an external applied load using microindentation and multiscale simulation. Methods Anisotropic material properties of enamel and dentin were measured using a microindentation method with a dynamic ultra microhardness tester. The numerical model was constructed using the finite element mesh superposition method with a microscale (enamel rods), mesoscale (teeth), and macroscale (bone). Multiscale simulation was used to analyze different scale structures. A concentrated load (10 N) was applied to the labial surface of the central incisor. Results The results revealed stresses of 5 MPa (normal stress) and 6.5 MPa (shear stress) in the enamel sheath at the center of the labial region compared to 1.4 MPa (normal stress) and 21.4 MPa (shear stress) in the cervical region. Significance These results suggest that shear stresses in the enamel sheath may play significant roles in stress transmission.

Adaptive superposition of finite element meshes in non‐linear transient solid mechanics problems

AbstractAn s‐adaptive finite element procedure is developed for the transient analysis of 2‐D solid mechanics problems with material non‐linearity due to progressive damage. The resulting adaptive method simultaneously estimates and controls both the spatial error and temporal error within user‐specified tolerances. The spatial error is quantified by the Zienkiewicz–Zhu error estimator and computed via superconvergent patch recovery, while the estimation of temporal error is based on the assumption of a linearly varying third‐order time derivatives of the displacement field in conjunction with direct numerical time integration. The distinguishing characteristic of the s‐adaptive procedure is the use of finite element mesh superposition (s‐refinement) to provide spatial adaptivity. Mesh superposition proves to be particularly advantageous in computationally demanding non‐linear transient problems since it is faster, simpler and more efficient than traditional h‐refinement schemes. Numerical examples are provided to demonstrate the performance characteristics of the s‐adaptive method for quasi‐static and transient problems with material non‐linearity. Copyright © 2007 John Wiley & Sons, Ltd.

A Multi-Scale Analysis for an Evaluation of the Mechanical Properties of Composite Materials

Fiber reinforced composite materials have been applied widely to many structures, because they have some advantages like easy handling, high specific strength, etc. The numerical method like finite element method has been applied to design and to evaluate the material properties and behavior as the development of Computer Aided Engineering. It is very difficult to calculate with accuracy not only in structural scale but also in detail material scale (for example, the order of fiber diameter) by the traditional FEM, becausecompositematerials like woven fabric composites have the geometrical complexityand the large difference between above mentioned scales. The development of multi-scale analysis method is one of the major topics in computational mechanics. Mesh superpositionis one of multi-scale analysis methods and is an effective method to solve the problems which have the large difference between the structure scale and the reinforcement scale. We have expanded the finite element mesh superposition method with 3 scales and have defined as M3 (Macro-Meso-Micro) method. In this paper, we have proposed a new approach method combined with M3 method and homogenized method to obtain the mechanical properties and to simulate the behavior of woven fabric composites. In addition, the elastic-plastic mechanics and the damage mechanics have been introduced into M3 method to investigate the effects of matrix-crack on the structural and material properties. From the numerical results, it is revealed that it is very useful for the evaluation of mechanical properties of composite materials.

Image-based multi-scale modelling strategy for complex and heterogeneous porous microstructures by mesh superposition method

This study is focused on the multi-scale modelling strategy for complex and heterogeneous microstructures of real materials by automatic image-based modelling and finite element mesh superposition method. The synergetic application of the conventional asymptotic homogenization method and the authors' mesh superposition method has been proposed to obtain the microscopic responses under high gradient of macroscopic fields at the macroscopic crack tip and/or interface, for instance. For complex and random microstructures, automatic image-based voxel meshing by means of x-ray CT is commonly required; however, it cannot always adapt to the mathematical theory of microscopic modelling in the mesh superposition method. Therefore, a modelling technique for mesh refinement is proposed in this paper using additional elements for insulation in consideration of the theoretical background of the mesh superposition method.In this paper, we provide the modelling procedure and its theoretical consideration of mesh refinement for flexible modelling of real materials. To demonstrate the technique, a numerical example of a porous ceramic component with random microstructure and macroscopic crack is illustrated.

Adaptive superposition of finite element meshes in elastodynamic problems

An adaptive finite element procedure is developed for modelling transient phenomena in elastic solids, including both wave propagation and structural dynamics. Although both temporal and spatial adaptivity are addressed, the novel feature of the formulation is the use of mesh superposition to produce spatial refinement (referred to as s-adaptivity) in transient problems. Spatial error estimation is based on superconvergent patch recovery of higher-order accurate stresses and is used to guide mesh adaptivity, while the temporal error estimation is based on the assumption of linearly varying third-order time derivatives of the displacement field and is used to adjust the time step size for the HHT-α variant of the Newmark direct numerical integration method. Spatial adaptivity of the mesh is performed using a hierarchical h-refinement scheme that is efficiently implemented using a structured version of finite element mesh superposition. This particular spatial adaptivity scheme is extremely fast and consequently makes it feasible to repeatedly update both the mesh and the time increment as required in an adaptive transient analysis. This work represents the initial effort in applying this type of spatial adaptivity to transient problems. Three example problems are given to demonstrate the performance characteristics of the s-adaptive procedure. Copyright © 2005 John Wiley & Sons, Ltd.

Multi-scale finite element analysis of porous materials and components by asymptotic homogenization theory and enhanced mesh superposition method

To analyse the macroscopic and microscopic behaviours of heterogeneous materials and components, a multi-scale computational method is studied. Although asymptotic homogenization theory has been the main tool during the last decade to solve various multi-scale problems, the assumption of the periodicity of the microscopic unit cell and the incapability of considering the scale effect have resulted in the limitations to this theory's applications. These problems should be overcome because advanced materials are often used as joint or laminated components and the interface crack problem must be analysed. For this sake, a novel multi-scale finite element method is proposed that uses the enhanced mesh superposition method together with the asymptotic homogenization theory. The finite element mesh superposition method uses the global mesh and the local mesh that is superimposed arbitrarily onto the global mesh. The enhanced method allows the adoption of different constitutive laws for the two meshes. The advantage of the homogenization theory to predict the homogenized material model accurately based on the complex microstructure is still utilized. The homogenized material model is used for the global mesh, whilst the microscopic heterogeneity and the crack are considered in the local mesh with the material properties of the constituents. The formulation, modelling strategy, implementation and numerical accuracy of the proposed method is described. A porous ceramic is studied in the numerical example.

OS08W0015 Multi-scale modeling and analysis of heterogeneity in ceramics

To understand the correlation between the microstructure and the macroscopic properties and behaviors, novel digital image-based multi-scale analysis techniques are presented. They include the mathematical homogenization method, enhanced finite element mesh superposition method and statistical evaluation and visualization of the microscopic morphology of porous ceramics.

界面き裂を有する不均質接合体のマルチスケール有限要素解析

In the last decade, a multi-scale computational method using the asymptotic homogenization method with the help of the finite element method has been intensively studied and applied to various advanced materials such as fiber reinforced composite materials and porous materials. It enables us to analyze the overall behaviors of structures considering the microscopic heterogeneity, where there is a large gap between the macro-scale and the micro-scale within the framework of continuum mechanics. However, no literature can be found that studied the joint or laminated members of heterogeneous dissimilar materials with interface crack. Due to the non-periodic condition at the interface and the existence of crack, the homogenized material modeling is of no use. Hence, an enhanced finite element mesh superposition method is employed to solve the two-scale problem. Two independent meshes, i. e., the global mesh and the local mesh, are used. The global mesh represents the joint or laminated members from the macroscopic viewpoint using the homogenized model. The local mesh is used to consider the heterogeneous microstructure of the material as well as the crack and superimposed onto the global mesh. The formulation, numerical accuracy and effectiveness of the proposed multi-scale method are presented in this paper.

Novel Development and Applications in Finite Element Technologies. Efficient Modeling of Microscopic Heterogeneity and Local Crack in Composite Materials by Finite Element Mesh Superposition Method.

The finite element mesh superposition method is applied to the two-dimensional crack problem of composite materials. The microscopic heterogeneity involved in the composite materials is modeled by the fixed grid model. On this global mesh, a local mesh that considers the local crack is superimposed without taking care of the matching of nodes and elements of both meshes. The use of the fixed grid model for the global mesh can reduce the time and efforts for the mesh generation to express the complex heterogeneous microstructures. Also it makes the computation and the implementation of the finite element mesh superposition method very easy. The accuracy was verified by comparing with the theory and the calculation by the conventional fine mesh.