A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
The spatial stability equation of moving jet containing dense suspended solid particles was derived out by means of the continuum phase-coupled model. The stability curves of moving jet far different downstream distan...The spatial stability equation of moving jet containing dense suspended solid particles was derived out by means of the continuum phase-coupled model. The stability curves of moving jet far different downstream distances, Reynolds number of flow-field, particle properties and velocities of jetting device are got by the finite difference method based on the asymptotic method and the Eulerian conservative difference scheme. Founded on the analysis of the obtained stability curves it is found that the positive velocity of jetting device widens the unstable frequency range of flow-field hut the effect of the negative one is contrary. In addition, particles existing in the flow-field curb the instability of flow-field and the effect enhances with the decrease of Reynolds number of flow-field. These conclusions benefit learning the development of moving two-phase jet.展开更多
In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. ...In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.展开更多
This paper deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid continuum with uniaxial or triaxial anisotropy. The anisotropic solid continuum consists o...This paper deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid continuum with uniaxial or triaxial anisotropy. The anisotropic solid continuum consists of anisotropic spherical particles periodically distributed in an anisotropic infinite matrix. The particles are or are not embedded in an anisotropic spherical envelope, and the infinite matrix is imaginarily divided into identical cubic cells with central particles. The thermal stresses are thus investigated within the cubic cell. This mulfi-particle-（envelope）-matrix system based on the cell model is applicable to two- and three-component materials of precipitate-matrix and precipitate-envelope-matrix types, respectively. Finally, an analysis of the determination of the thermal stresses in the multi-par- ticle-（envelope）-matrix system which consists of isotropic as well as uniaxial- and/or triaxial-anisotropic components is presented. Additionally, the thermal-stress induced elastic energy density for the anisotropic components is also derived. These analytical models which are valid for isotropic, anisotropic and isotropic-anisotropic multi-particle- （envelope）-matrix systems represent the determination of important material characteristics. This analytical determination includes： （1） the determination of a critical particle radius which defines a limit state regarding the crack initiation in an elastic, elastic-plastic and plastic components; （2） the determination of dimensions and a shape of a crack propagated in a ceramic components; （3） the determination of an energy barrier and micro-/macro-strengthening in a component; and （4） analytical-（experimental）-computational methods of the lifetime prediction. The determination of the thermal stresses in the anisotropic components presented in this paper can be used to determine these material characteristics of real two- and three-component materials with anisotropic components or with anisotropic and isotropic components.展开更多
为了抑制连续体结构拓扑优化结果中的灰度单元,在实体各向同性材料惩罚密度法(Solid isotropic microstructures with penalization,SIMP)的基础上提出一种双重SIMP方法。首先利用含有灵敏度过滤的SIMP方法对设计变量进行迭代和优化,将...为了抑制连续体结构拓扑优化结果中的灰度单元,在实体各向同性材料惩罚密度法(Solid isotropic microstructures with penalization,SIMP)的基础上提出一种双重SIMP方法。首先利用含有灵敏度过滤的SIMP方法对设计变量进行迭代和优化,将优化结果作为中间变量,然后用不含有灵敏度过滤的SIMP方法对中间变量进行优化迭代,得到最终优化结果。以简支梁的结构柔顺度最小为例,将双重SIMP方法用于柔性结构的优化设计中并与标准SIMP算法相比;结果表明,双重SIMP方法得到清晰的拓扑分布结构,有效抑制了灰度单元,并且双重SIMP方法可以得到更小的结构柔顺度,证明了该方法的有效性;双重SIMP算法的灰度单元对惩罚因子的依赖性很小,可以选用较小的惩罚因子;针对不同的网格划分模型,双重SIMP算法得到的优化目标和灰度单元数更稳定,体现出了很好的网格依赖性。说明该方法具有很好的适用性和稳定性。展开更多
基金Project supported by the National Basic Research Program of China (973Project) (No.2002CB412709) and the National Natural Science Foundation of China (Nos.50278012,10272027,19832010)
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
文摘The spatial stability equation of moving jet containing dense suspended solid particles was derived out by means of the continuum phase-coupled model. The stability curves of moving jet far different downstream distances, Reynolds number of flow-field, particle properties and velocities of jetting device are got by the finite difference method based on the asymptotic method and the Eulerian conservative difference scheme. Founded on the analysis of the obtained stability curves it is found that the positive velocity of jetting device widens the unstable frequency range of flow-field hut the effect of the negative one is contrary. In addition, particles existing in the flow-field curb the instability of flow-field and the effect enhances with the decrease of Reynolds number of flow-field. These conclusions benefit learning the development of moving two-phase jet.
文摘In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.
文摘This paper deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid continuum with uniaxial or triaxial anisotropy. The anisotropic solid continuum consists of anisotropic spherical particles periodically distributed in an anisotropic infinite matrix. The particles are or are not embedded in an anisotropic spherical envelope, and the infinite matrix is imaginarily divided into identical cubic cells with central particles. The thermal stresses are thus investigated within the cubic cell. This mulfi-particle-（envelope）-matrix system based on the cell model is applicable to two- and three-component materials of precipitate-matrix and precipitate-envelope-matrix types, respectively. Finally, an analysis of the determination of the thermal stresses in the multi-par- ticle-（envelope）-matrix system which consists of isotropic as well as uniaxial- and/or triaxial-anisotropic components is presented. Additionally, the thermal-stress induced elastic energy density for the anisotropic components is also derived. These analytical models which are valid for isotropic, anisotropic and isotropic-anisotropic multi-particle- （envelope）-matrix systems represent the determination of important material characteristics. This analytical determination includes： （1） the determination of a critical particle radius which defines a limit state regarding the crack initiation in an elastic, elastic-plastic and plastic components; （2） the determination of dimensions and a shape of a crack propagated in a ceramic components; （3） the determination of an energy barrier and micro-/macro-strengthening in a component; and （4） analytical-（experimental）-computational methods of the lifetime prediction. The determination of the thermal stresses in the anisotropic components presented in this paper can be used to determine these material characteristics of real two- and three-component materials with anisotropic components or with anisotropic and isotropic components.
文摘为了抑制连续体结构拓扑优化结果中的灰度单元,在实体各向同性材料惩罚密度法(Solid isotropic microstructures with penalization,SIMP)的基础上提出一种双重SIMP方法。首先利用含有灵敏度过滤的SIMP方法对设计变量进行迭代和优化,将优化结果作为中间变量,然后用不含有灵敏度过滤的SIMP方法对中间变量进行优化迭代,得到最终优化结果。以简支梁的结构柔顺度最小为例,将双重SIMP方法用于柔性结构的优化设计中并与标准SIMP算法相比;结果表明,双重SIMP方法得到清晰的拓扑分布结构,有效抑制了灰度单元,并且双重SIMP方法可以得到更小的结构柔顺度,证明了该方法的有效性;双重SIMP算法的灰度单元对惩罚因子的依赖性很小,可以选用较小的惩罚因子;针对不同的网格划分模型,双重SIMP算法得到的优化目标和灰度单元数更稳定,体现出了很好的网格依赖性。说明该方法具有很好的适用性和稳定性。
