Energy balance method for modelling of soft tissue deformation

This paper presents a novel methodology for modelling of soft tissue deformation, from the standpoint of work–energy balance based on the law of conservation of energy. The work done by an external force is always balanced against the strain energy due to the internal force of the object. A position-based incremental approach is established, in which the work–energy balance is achieved via an iterative position increment process for the new equilibrium state of the object. The position-based incremental approach is further combined with non-rigid mechanics of motion to govern the dynamics of soft tissue deformation. The proposed method employs nonlinear geometric and material formulations to account for the nonlinear soft tissue deformation. Soft tissue material properties can be accommodated by specifying strain energy density functions. Integration with a haptic device is also achieved for soft tissue deformation with haptic feedback for surgical simulation. Experimental results demonstrate that the deformations by the proposed method are in good agreement with those by a commercial package of finite element analysis. Isotropic and anisotropic deformations, as well as soft tissue viscoelastic behaviours, can be accommodated by the proposed methodology via strain energy density functions.     

The verification of the quantities of interest based on energy norm of solutions by node-based smoothed finite element method

Verification of the quantities of interest computed with the finite element method (FEM) requires an upper bound on the strain energy, which is half of the energy norm of displacement solutions. Recently, a modified finite element method with strain smoothing, the node-based smoothed finite element method (NS-FEM), has been proposed to solve solid mechanics problems. It has been found in some cases that the energy norm formed by the smoothed strain of NS-FEM solutions bounds the energy norm of exact displacements from above. We analyze the bounding property of this method, give three kind of energy norms of solutions computed by FEM and NS-FEM, and extend them to the computation of an upper bound and a lower bound on the linear functional of displacements. By examining the bounding property of NS-FEM with different energy norms using some linear elastic problems, the advantages of NS-FEM over the traditional error estimate based methods is observed.     

Materially and geometrically nonlinear analysis of laminated anisotropic plates by p-version of FEM

A p-version finite element model based on degenerate shell element is proposed for the analysis of orthotropic laminated plates. In the nonlinear formulation of the model, the total Lagrangian formulation is adopted with moderately large deflections and small rotations being accounted for in the sense of von Karman hypothesis. The material model is based on the Huber-Mises yield criterion and Prandtl-Reuss flow rule in accordance with the theory of strain hardening yield function, which is generalized for anisotropic materials by introducing the parameters of anisotropy. The model is also based on the equivalent-single layer laminate theory. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. Gauss-Lobatto numerical quadrature is used to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed p-version finite element model is demonstrated through several comparative points of view in terms of ultimate load, convergence characteristics, nonlinear effect, and shape of plastic zone.     

膜结构找形分析中的混合法

在膜结构设计过程中一个很重要也是不可或缺的过程就是找形分析.常用的找形方法有力密度法、动力松弛法和非线性有限元法.力密度法原理简单但找形结果往往不能满足精度要求;非线性有限元法结果精度高但存在确定初始坐标问题和非线性系统的收敛问题.针对力密度法和非线性有限元法的不足,在综合以上两种方法后得到了混合法对膜结构进行找形,并在Matlab和Ansys中编写了相应的程序模拟实现了混合法找形.结合两个实际工程说明了混合法找形可以应用于大型复杂柔性体系的找形,同时证明了混合法找形的先进性和可行性.     

基于 h 型自适应有限元法在薄板冲压 成型中的应用

在对薄板冲压成型这一过程进行有限元仿真分析时,难以精确分析场变量发生剧烈变化的应力 集中及应变梯度大的区域,如何平衡精度和效率间的关系是冲压成型仿真的关键。因此,基于非线性有限元大 变形的相关理论,针对动态仿真的网格自适应关键技术,建立了自适应分析模式下的薄板冲压成型算法。为了 提高计算精度,提出基于单元应变能增量的能量误差准则以及基于板料成型几何特征的几何误差准则,并结合 2 类误差准则,建立了基于自适应分析算法的误差判断准则;为了提高计算效率,引入阻尼因子提出了阻尼子 循环算法,将自适应加密后的板料单元按时间步长划分为若干个区域,并按照不同时间步长分别求解。结果表 明,该算法有效提高了薄板冲压成型有限元仿真的精度与效率。     

基于边光滑有限元法的剪切变形板几何非线性分析

为改善在计算板的几何非线性问题时有限元法系统过硬的数值缺陷,提高计算精度,在考虑剪切变形的yon Karman假设下,基于全拉格朗日描述方法,将边光滑有限元法应用于板的几何非线性分析.计算公式基于1阶剪切变形理论,并采用离散剪切间隙有效地消除剪切自锁.在三角形单元的基础上进一步形成边界光滑域,在每个光滑域内对应变进行光...     

互信息驱动的有限元医学图像配准方法

针对医学图像中软组织形变复杂多样的特点,在配准过程中以离散化的有限单元为基本单位模拟和预测整个弹性体产生的形变,将配准过程视为有限元求解二维平面应力问题并对有限元能量函数进行改进,选取高精度和鲁棒性良好的互信息(MI)为测度应用到方程求解中。为提高算法效率,在配准过程中采用多分辨率策略进行优化。通过对放疗中医学图像进行配准实验并与已有方法进行比较,得到的配准结果更优,对刚体位移更敏感并提高了速度,表明该方法是一种具有高精度和高效率的配准方法。     

温度冲击下倒装芯片的热应力数值模拟研究

由于几何材料的复杂性,倒装芯片封装中的热应力分布很难用解析的方法求解,而数值方法,如有限元法,已被广泛用于热应力应变的研究.二维有限元模型建模简单,模型的单元数和节点数较小,便于反复计算,微系统焊接中采用二维有限元模拟可提高数值模拟效率.本文对使用和未使用填充剂两种情况下的倒装芯片,采用有限元模拟方法研究了在温度载荷下整个结构的热应力、应变分布,并对结构可能造成的破坏性影响进行了定性和定量的分析.     

不确定性转子系统的随机有限元建模及响应分析

随机特性和随机载荷会引起转子系统动力响应的不确定性,是转子动力学分析中的重要影响因素.本文基于Timosheke梁理论,把转轴的材料和几何随机特性表示为一维随机场函数,推导出随机转轴有限元列式,建立转子系统随机动力学模型,并给出随机载荷作用下随机转子系统动力响应统计量的分析方法.分别对线性和非线性涡轮泵转子系统进行了随机动力响应分析,并同Monte Carlo仿真结果进行对比,结果表明所建立的随机有限元动力学模型和给出的随机响应分析方法是合理可行的,可以有效应用于实际转子系统随机动力学分析和设计中.     

平膜片式压力传感器有限元分析

本文用有限元方法分析平膜片式压力传感器弹性元件表面径向应变及切向应变与薄膜应变片阻值变化的联系后,根据电桥原理得到与其输出电压之间的关系,最终并分析了传感器之非线性精度。     

PANDA的功能可扩展性设计与应用

针对有限元分析软件功能的可扩展性需求,介绍面向对象有限元并行计算框架PAN DA的单元设计和单元类的扩充方法.在PANDA中,单元分析被抽象成单元算法和材料本构模式,并提供单元类型、材料模型的接口服务,用户可以根据不同的应用需求构成并实例化不同的C++抽象基类来解决实际问题.单元类的扩展步骤为:在ElementList...     

Topology optimization in crashworthiness design

Topology optimization has developed rapidly, primarily with application on linear elastic structures subjected to static loadcases. In its basic form, an approximated optimization problem is formulated using analytical or semi-analytical methods to perform the sensitivity analysis. When an explicit finite element method is used to solve contact–impact problems, the sensitivities cannot easily be found. Hence, the engineer is forced to use numerical derivatives or other approaches. Since each finite element simulation of an impact problem may take days of computing time, the sensitivity-based methods are not a useful approach. Therefore, two alternative formulations for topology optimization are investigated in this work. The fundamental approach is to remove elements or, alternatively, change the element thicknesses based on the internal energy density distribution in the model. There is no automatic shift between the two methods within the existing algorithm. Within this formulation, it is possible to treat nonlinear effects, e.g., contact–impact and plasticity. Since no sensitivities are used, the updated design might be a step in the wrong direction for some finite elements. The load paths within the model will change if elements are removed or the element thicknesses are altered. Therefore, care should be taken with this procedure so that small steps are used, i.e., the change of the model should not be too large between two successive iterations and, therefore, the design parameters should not be altered too much. It is shown in this paper that the proposed method for topology optimization of a nonlinear problem gives similar result as a standard topology optimization procedures for the linear elastic case. Furthermore, the proposed procedures allow for topology optimization of nonlinear problems. The major restriction of the method is that responses in the optimization formulation must be coupled to the thickness updating procedure, e.g., constraint on a nodal displacement, acceleration level that is allowed.     

悬臂梁结构损伤检测仿真研究

以悬臂梁结构为研究对象,针对户外条件下结构损伤检测过程复杂、周期长、检测效果不理想的问题,提出了模态曲率变化率法.通过大型商用有限元软件ABAQUS,建立梁结构有限元模型,基于模态曲率变化率法构建损伤指标,对梁结构进行损伤检测定位,并与模态应变能法的损伤检测效果进行了对比.结果表明:模态曲率变化率法计算过程简单,能够准确快捷地对悬臂梁结构进行损伤识别定位.     

有限单元畸变度计算方法

应变能是弹性体变形程序的度量,而各向同性弹性材料的应变能又是应变张量不变量的函数,基于这一有限变形弹性理论,可以建立构造各种有限单元畸变度的统一方法。对于常见的几种常用单元。如三角形、四边形、四面体和六面体,利用有了元等参变换,导出了畸变度的计算公式,由于这些畸变的度量与真实的物理现象联系在一起,因此在理论上更具合理性。     

基于有限元方法的极小曲面造型

讨论极小曲面方程的求解。极小曲面方程是一个高度非线性的二阶椭圆偏微分方程，求解十分困难。该文基于有限元方法，使用一个简单而有效的线性化策略，将问题转化为一系列线性问题，从而大大简化了求解过程。数值结果表明该方法简单有效，能产生合理的结果。     

管桁架—索网混合钢结构的计算分析

为更好地对管桁架-索网混合钢结构进行找形,在SAP 2000和3D3S中应用两种不同的初始态找形方法以比较对计算结果的影响.在SAP 2000中采用非线性有限元分析方法找形,在3D3S中采用力密度法和有限元法进行混合找形,并进行初始态、动力以及载荷态分析.比较分析这两种找形方法的计算结果,发现二者的计算结果误差不大,均为可行的简化计算方法.     

基于优化法的金属材料应力-应变曲线反演

采用优化法反演金属材料的应力-应变曲线.建立与试验边界条件一致的有限元仿真模型,并用Abaqus进行有限元仿真.设计变量为给定应变下的应力参数,优化目标是使模拟的应力-位移曲线与试验曲线一致,采用自适应响应面法和序列二次规划法开展优化迭代.结果表明,反演参数能很好地表现材料行为特征,为下一步仿真分析提供材料数据基础.     

超磁致伸缩力传感器的模型研究

磁致伸缩逆效应是稀土超磁致伸缩材料的一个重要应用特性,应用磁致伸缩逆效应可以制作超磁致伸缩力传感器,基于能量变分原理,建立了超磁致伸缩力传感器的有限元模型。应用该模型计算了超磁致伸缩力传感器空气隙中的磁感应强度和磁致伸缩棒上施加力的关系,并与实验值进行了比较。计算结果与实验结果符合较好,表明建立的超磁致伸缩力传感器的有限元模型是有效的。     

机身壁板稳定性显式非线性分析

对6种不同构型的飞机机身下壁板薄壁结构试验件,进行显示有限元非线性屈曲分析,并与工程方法及试验得到的结果进行对比分析,可知有限元法比工程方法更精确,且与试验相比,误差更稳定.