Finite Element Mesh Superposition Research Articles

K-0921 重合メッシュ法による織物複合材料の局所的損傷進展解析(J05-2 強度・破壊機構解析(1))(J05 複合材料の加工と評価)

There have been many reports on the numerical analysis of damage propagation in woven fabric composite materials. However, most of them studied the behaviors under in-plane loading conditions including tension, compression and shearing. Because composite materials are often used as plates and shells, their out-of-plane bending behaviors are important. To study the micro- or mesoscopic damage propagation under bending, the consideration of micro-macro coupling is a critical issue. A small region to consider the microscopic behavior is subject to macroscopic non-uniform strain field under bending. Therefore, the conventional homogenizing technique is not applicable. In this paper, we propose a new computational method named finite element mesh superposition method to solve this problem. A two-dimensional example of plain woven fabric composites is shown in this paper.

Microscopic Stress Analysis of Heterogeneous Media by Finite Element Mesh Superposition Method.

Microscopic Stress Analysis of Heterogeneous Media by Finite Element Mesh Superposition Method.

Global/Local Modelling of Structures with Local Heterogeneity.

For the numerical simulation of mechanical behaviors of structures with local heterogeneity, a global/local modelling technique using the finite element mesh superposition technique and shell-solid connection is proposed. Not only the global deformation but also three-dimensional stresses nearby the local heterogeneity can be analyzed precisely with less efforts than conventional methods. The finite element mesh superposition technique makes it possible to overlay local fine solid mesh which considers the local heterogeneity on global rough solid mesh which neglects the local heterogeneity. Aplate structure that contains dissimilar material in a local portion is analyzed by the proposed modelling technique. The results agreed well with those calculated using the conventional three-dimensional fine mesh model.

706 重合メッシュ法による局所的き裂を有する不均質材料のミクロ応力解析

706 重合メッシュ法による局所的き裂を有する不均質材料のミクロ応力解析

Multi-scale computational method for elastic bodies with global and local heterogeneity

A multi-scale computational method using the homogenization theory and the finite element mesh superposition technique is presented for the stress analysis of composite materials and structures from both micro- and macroscopic standpoints. The proposed method is based on the continuum mechanics, and the micro–macro coupling effects are considered for a variety of composites with very complex microstructures. To bridge the gap of the length scale between the microscale and the macroscale, the homogenized material model is basically used. The classical homogenized model can be applied to the case that the microstructures are periodically arrayed in the structure and that the macroscopic strain field is uniform within the microscopic unit cell domain. When these two conditions are satisfied, the homogenization theory provides the most reliable homogenized properties rigorously to the continuum mechanics. This theory can also calculate the microscopic stresses as well as the macroscopic stresses, which is the most attractive advantage of this theory over other homogenizing techniques such as the rule of mixture. The most notable feature of this paper is to utilize the finite element mesh superposition technique along with the homogenization theory in order to analyze cases where non-periodic local heterogeneity exists and the macroscopic field is non-uniform. The accuracy of the analysis using the finite element mesh superposition technique is verified through a simple example. Then, two numerical examples of knitted fabric composite materials and particulate reinforced composite material are shown. In the latter example, a shell-solid connection is also adopted for the cost-effective multi-scale modeling and analysis.

Microscopic and Mesoscopic Evaluations of Materials. Hierarchical Modelling and Local Stress Analysis of Composite Materials and Structures.

In the numerical simulation of mechanical behaviors of composite materials and structures, a novel hierarchical modelling technique is proposed. Not only the global deformation but also the mesoscopic stresses are analyzed precisely with less human efforts than conventional methods. Four level hierarchy is defined for the textile composites, and the homogenization method and finite element mesh superposition technique are adopted. The latter technique makes it possible to overlay arbitrary local fine mesh on the global rough mesh. A panel with a rib made of knitted fabric composite material is analyzed by the proposed method. Three-dimensional modelling of the mesostructure of knitted fabric composite material is also shown. The validity of the proposed method was examined, and the mesoscopic stresses are calculated easily.

Theories and Computational Models for Composite Laminates

A review of equivalent–single–layer and layerwise laminated plate theories and their finite element models is presented. The layerwise theory advanced by the senior author is presented and a variable displacement finite element model and mesh superposition techniques are described. A simultaneous multiple model approach that is based on the variable kinematic theory and the mesh superposition method are also described. The objective of the simultaneous multiple model approach is to match the most appropriate mathematical model with each subregion based on the physical characteristics, applied loading, expected behavior, and level of solution accuracy desired in that subregion. Thus solution economy is maximized without sacrificing the solution accuracy.

On adaptive multilevel superposition of finite element meshes for linear elastostatics

A multilevel finite element mesh superposition technique aimed at hierarchically improving the quality of numerical solutions and mathematical models for a certain class of problems is developed. A posteriori error estimates, adaptive mesh overlay schemes, iterative solution procedures, data structures, and numerical experiments are described in the context of linear elastostatics.

An evaluation of equivalent-single-layer and layerwise theories of composite laminates

A review of equivalent-single-layer and layerwise laminate theories is presented and their computational models are discussed. The layerwise theory advanced by the author is reviewed and a variable displacement finite element model and the mesh superposition techniques are described. The variable displacement finite elements contain several different types of assumed displacement fields. By choosing appropriate terms from the multiple displacement field, an entire array of elements with different orders of kinematic refinement can be formed. The variable kinematic finite elements can be conveniently connected together in a single domain for global-local analyses, where the local regions are modeled with refined kinematic elements. In the finite element mesh superposition technique an independent overlay mesh is superimposed on a global mesh to provide localized refinement for regions of interest regardless of the original global mesh topology. Integration of these two ideas yields a very robust and economical computational tool for global-local analysis to determine three-dimensional effects (e.g. stresses) within localized regions of interest in practical laminated composite structures.