模拟三维裂纹问题的自适应多尺度扩展有限元法

为了在大型结构分析中考虑小裂纹或以小的代价提高裂纹附近求解精度,该文建立了分析三维裂纹问题的自适应多尺度扩展有限元法。基于恢复法评估三维扩展有限元后验误差,大于给定误差值的单元进行细化。所有尺度单元采用八结点六面体单元,采用六面体任意结点单元连接不同尺度单元。采用互作用积分法计算三维应力强度因子。三维I 型裂纹和I-II 复合型裂纹算例分析表明了该方法的正确性和有效性。     

基于单位分解法的实体壳广义单元模型

基于单位分解的广义有限元法的逼近空间由单位分解函数和局部覆盖函数构成,采用传统有限元形函数作为单位分解函数,其局部覆盖函数的定义不依赖于有限元网格.以十六结点六面体等参单元形函数作为单位分解函数,采用一阶多项式局部覆盖函数建立了十六结点六面体广义单元.在此基础上利用广义有限元法可以灵活构造各向异性逼近空间的特点,根据薄壳的变形特性,对壳体法向挠度和切向位移分别采用一阶和零阶多项式局部覆盖函数,构造了实体薄壳广义单元.计算结果表明:十六结点六面体广义单元和实体薄壳广义单元用于板壳结构分析时具有比相应的常规实体单元更高的收敛性和求解效率,且实体薄壳广义单元比十六结点六面体广义单元具有更高的求解效率.     

基于隔离非线性的实体单元模型与计算效率分析

实体有限元模型计算中往往需要较多的计算单元与结点数量,且这些单元状态判定以及大规模的刚度矩阵分解将消耗大量的计算资源,计算效率低。该文基于隔离非线性法理论建立了线性四面体与六面体等参单元分析模型,采用直接积分格式的6积分点替代六面体等参单元的8高斯点作为非线性应变插值点,能够在保证计算精度的同时提高单元状态判定效率。控制方程采用Woodbury公式与组合近似法联合求解,使得整个求解过程只有矩阵回代以及矩阵与向量的乘积,进一步提高了求解效率。基于时间复杂度的计算效率分析表明:随着结点自由度数目的增加,该文方法的计算效率相对传统变刚度法显著提高,数值算例验证了实体单元模型的正确性以及算法的高效性。     

旋转叶片模态分析的有限单元选择与实验研究

为进行压气机旋转叶片模态分析的精确数值计算,在研究叶片模型四面体单元和六面体单元网格划分模态数值计算结果收敛性的基础上,重点研究了采用实体单元和变厚度壳单元在叶片模态分析数值计算中的区别,通过与叶片的实验模态进行对比,得出了采用实体四面体单元进行旋转叶片模态数值计算的精度明显高于变厚度壳单元的结论.采用叶片实物进行三维扫描建模的方法,又通过数值分析与实验进行对比验证了结论,为变厚度预扭旋转叶片模态分析进行精确的数值计算奠定了基础.     

木托盘有限元分析精度的影响因素

目的研究有限元软件模拟木托盘抗弯性能时各因素对其分析精度的影响。方法对木托盘的抗弯性能进行理论分析和有限元模拟。通过计算铺板力学模型得到理论变形值;将Creo软件建立的托盘模型导入Ansys Workbench进行分析,得到有限元模拟值。采用控制变量法,改变单元类型和网格划分方式,并将结果与理论计算值进行对比分析。结果采用软件默认的单元类型和经网格划分方式等得到的整体位移结果与理论值的误差为2.97%。通过对各影响因素的调整,顶铺板的位移结果与理论值的误差为0.02%。结论单元数量相同的情况下,高阶单元的分析精度优于低阶单元,六面体单元优于四面体单元。保持其他设置条件不变,细化网格可提高分析精度。     

一种有限元结构动态计算的过渡元──9节点板壳－实体元

本文利用三维八节点实体元和八节点由壳超参数单元构造出一种９节点板壳－实体过渡元。该元具有三维实体和曲壳的双重属性。可用于一些板壳－实体结构的动态计算。由于该元要求与之相联的实体，板壳元网络划分简单，单元结点数较少，动态计算精度能满足工程精度要求，所以该元具有一定的实用价值。     

一种有限元结构动态计算的过渡元—9节点板壳—实体元

本文利用三维八节点实体元和八节点曲壳超参数单元构造出一种９节点板壳－实体过渡元，该元具有三维实体和曲壳的双重属性，可用于一些板壳－实体结构的动态计算，由于该元要求与的实体，板壳元各划分简单，单元结点数较少，动态计算精度能满足工程精度要求，所以该元具有一定的实用价值。     

层合板层间断裂分析的组合界面单元及其特性

提出了一种由刚性元和零厚度的内聚力单元组合而成的新型界面单元,该界面单元嵌在板壳结构界面之间,可用来模拟界面损伤的起始和演化,能考虑板壳的平动和转动对分层损伤的作用。该界面单元具有有限厚度,八个结点,每个结点有五个自由度,通过刚性元将板壳单元结点的位移和结点力转换到内部零厚度的内聚力单元上,界面损伤通过内聚力单元的损伤演化体现出来。采用板壳单元和新型界面单元建立有限元模型,对混合弯曲(MMB)试验和双悬臂梁(DCB)弯曲试验进行了计算模拟,计算结果能很好地模拟结构的界面损伤过程。相比传统的用内聚力单元和三维实体单元组成的模型,建模方便,在精度相当的前提下,可以使单元尺寸增大一倍,减少裂尖内聚力区域(cohesive zone)内的单元数量,缩小计算规模,提高计算效率。     

一种高效的FE-PSBFE耦合方法及在岩土工程弹塑性分析中的应用

针对复杂岩土工程结构建模困难、耗时费力的难题,结合八叉树网格离散技术,对网格中的六面体采用等参单元,对于非六面体采用多面体比例边界有限单元（PSBFE）,建立了一种快速、高效的FE-PSBFE弹塑性耦合数值分析方法。采用实现的PSBFE对标准土石坝进行数值模拟,验证了其正确性和计算精度;通过典型复杂心墙坝对提出FE-PSBFE耦合方法的灵活性、通用性和高效性进行了研究,研究结果表明:与传统FEM相比,该耦合方法可大幅加速模型前处理进程,解决了复杂三维空间河谷形状、水平分层填筑和材料分区导致的网格剖分难题,几十万单元的网格划分一般仅需几分钟;与PSBFE相比,显著提高了岩土结构弹塑性分析的效率,FE-PSBFE可减少超过80%的求解时间。FE-PSBFE耦合方法对其他复杂几何条件的工程问题也具有良好的实用性,为快速精细化抗震分析提供了技术手段。     

半圆孔板承受拉伸和弯曲时的三维应力集中

根据Hellinger-Reissner原理建立了具有一个无外力圆柱表面三维8节点杂交应力元,元内假定应力场满足以柱坐标表示的三维平衡方程及无外力圆柱面上的外力边界条件,当元退化为二维时也满足协调方程。单元位移场选取与相邻元协调。用这种特殊杂交应力元,在相当粗的网格下即能准确地分析具有半圆孔厚(薄)板的三维(二维)应力集中。     

波形钢腹板-混凝土组合箱梁截面变形的拟平截面假定及其应用研究

为使波形钢腹板-混凝土组合箱梁的正截面弯曲应力计算能够应用平截面假定,根据该组合箱梁模型试验在弹性阶段的应变实测数据和空间有限元计算结果,忽略波形钢腹板的抗弯贡献,假设上、下翼板的混凝土纵向正应变在弹性阶段符合“拟平截面假定”,并运用变分法理论进行了证明。算例表明据“拟平截面假定”计算的翼板应力计算值与有限元法计算结果吻合。“拟平截面假定”为波形钢腹板-混凝土组合箱梁的弯曲应力计算及抗弯承载力计算在理论上提供了必要的变形协调条件。     

Automatic three-dimensional finite element mesh generation via modified ray casting

Three-dimensional (3-D) finite element mesh generation has been the target of automation due to the complexities associated with generating and visualizing the mesh. A fully automatic 3-D mesh generation method is developed. The method is capable of meshing CSG solid models. It is based on modifying the classical ray-casting technique to meet the requirements of mesh generation. The modifications include the utilization of the element size in the casting process, the utilization of 3-D space box enclosures, and the casting of ray segments (rays with finite length). The method begins by casting ray segments into the solid. Based on the intersections between the segments and the solid boundary, the solid is discretized into cells arranged in a structure. The cell structure stores neighbourhood relations between its cells. Each cell is meshed with valid finite elements. Mesh continuity between cells is achieved via the neighbourhood relations. The last step is to process the boundary elements to represent closely the boundary. The method has been tested and applied to a number of solid models. Sample examples are presented.     

有限元网格自动剖分的分区直接法

本文提出了一种灵活、方便、输入信息量少的分区直接剖分方法。可以对各种具有复杂结点布置要求的空间有限元网格进行剖分,自动生成不同形式的单元信息、结点坐标以及各种所需的计算信息。     

A FORMULATION OF THE QS6 ELEMENT FOR LARGE ELASTIC DEFORMATIONS

The numerical simulation of processes undergoing finite deformations requires robust elements. For a broad range of applications these elements should have a good performance in bending dominated situations as well as in the case of incompressibility. The element should be insensitive against mesh distortions which frequently occurs during finite deformations. Furthermore, due to efficiency reasons a good coarse mesh accuracy in required in non-linear analysis. The QS6 element, developed in this paper, tries to fulfil the above-mentioned requirements. The performance is depicted by means of numerical examples.     

An unsymmetric 8‐node hexahedral element with high distortion tolerance

Among all 3D 8‐node hexahedral solid elements in current finite element library, the ‘best’ one can produce good results for bending problems using coarse regular meshes. However, once the mesh is distorted, the accuracy will drop dramatically. And how to solve this problem is still a challenge that remains outstanding. This paper develops an 8‐node, 24‐DOF (three conventional DOFs per node) hexahedral element based on the virtual work principle, in which two different sets of displacement fields are employed simultaneously to formulate an unsymmetric element stiffness matrix. The first set simply utilizes the formulations of the traditional 8‐node trilinear isoparametric element, while the second set mainly employs the analytical trial functions in terms of 3D oblique coordinates (R, S, T). The resulting element, denoted by US‐ATFH8, contains no adjustable factor and can be used for both isotropic and anisotropic cases. Numerical examples show it can strictly pass both the first‐order (constant stress/strain) patch test and the second‐order patch test for pure bending, remove the volume locking, and provide the invariance for coordinate rotation. Especially, it is insensitive to various severe mesh distortions. Copyright © 2016 John Wiley & Sons, Ltd.     

A new 3-D finite element model to evaluate added mass for analysis of fluid-structure interaction problems

The paper presents the results of investigations conducted to evaluate the added mass to represent fluid-structure interaction effects in vibration/dynamic analysis of floating bodies such as ship hulls. While the structural plating is idealized by 9-noded plate/shell finite elements, the fluid domain is modelled by 20-noded/21-noded 3-D finite elements in the investigations conducted. A new 8-noded element has been developed to model the interface between the structure and the fluid. An efficient computational methodology has been used for computation of added mass. The finite element models are validated by comparing the results with those given by analytical solution for a submerged sphere. The efficacy of the finite element model is demonstrated through convergence of the results obtained for a floating barge problem. A better convergence rate and distribution of added mass in three orthogonal directions have been obtained.     

A simple mesh deformation technique for fluid–structure interaction based on a submesh approach

This paper describes an improvement in techniques currently used for mesh deformations in fluid–structure calculations in which large body motions are encountered. The proposed approach moving submesh approach (MSA) is based on the assumption of a pseudo-material deformation applied on a triangular coarse mesh to significantly reduce the CPU time. The computation mesh is then updated using an interpolation technique similar to the finite element method. This method may be applied on structured as well as on unstructured meshes. An extension to complex boundaries undergoing large rigid-body motions is proposed combining the MSA and an encapsulation box. The influence of the coarse mesh on the quality mesh is discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

A refined global-local finite element analysis method

A refined global-local method was proposed to improve the efficiency of finite element analysis. The proposed method was based on the regular finite element method in conjunction with three basic step, i.e. the global analysis, the local analysis and the refined global analysis. In the first two steps, a coarse finite element mesh was used to analyse the entire structure to obtain the nodal displacements which were subsequently used as displacement boundary conditions for local regions of interest. These local regions with the prescribed boundary conditions were then analysed with refined meshes to obtain more accurate stresses. In the third step, a new global displacement distribution based on the results of the previous two steps was assumed for the analysis, from which much improved solutions for both stresses and displacements were produced. Numerical examples showed that the proposed method yielded accurate solutions with significant savings in computing time compared with the regular finite element method. Further, this method is suitable for parallel computation.     

准各向同性纤维增强复合材料层合板的开孔拉伸破坏模拟

建立了一种新的有限元三维模型,对准各向同性纤维增强复合材料层合板[45/0/-45/90]_s和[45/-45/90/0]_s进行了开孔拉伸的破坏模拟。每一层均采用三维实体单元(ABAQUS中的C3D8R单元),由于基体比纤维强度低,在很低的拉伸载荷下,圆孔周围基体受到剪切力会出现沿纤维方向的纵向劈裂或基体开裂,从而钝化圆孔,大大减小应力集中,提高材料承载能力。为了准确模拟层合板的破坏,在每层圆孔周围(90°层除外)沿纤维方向引入2组基于表面的内聚力接触来模拟层内纵向劈裂,同时用这种接触来模拟层间的分层特性。为了提高计算效率并且保证计算精度,在圆孔周围采用精细的网格,其余地方采用相对稀疏的网格。在内聚区保证足够的单元个数,这样既能准确刻画内聚区应力分布,又能缓解网格依赖性。与文献中实验结果的对照显示,取得了较好的一致性。      

An adaptive multigrid technique for three-dimensional elasticity

A program for finite element analysis of 3D linear elasticity problems is described. The program uses quadratic hexahedral elements. The solution process starts on an initial coarse mesh; here error estimators are determined by the standard Babu?ka-Rheinboldt method and local refinement is performed by partitioning of indicated elements, each hexahedron into eight new elements. Then the discrete problem is solved on the second mesh and the refinement process proceeds in the following way-on the ith mesh only the elements caused by refinement on the (i-1)th mesh can be refined. The control of refinement is the task of the user because the dimension of the discrete problem grows very rapidly in 3D. The discrete problem is being solved by the frontal solution method on the initial mesh and by a newly developed and very efficient local multigrid method on the refined meshes. The program can be successfully used for solving problems with structural singularities, such as re-entrant corners and moving boundary conditions. A numerical example shows that such problems are solved with the same efficiency as regular problems.