Finite element simulation and modeling of 2-D arrays for 3-D ultrasonic imaging

Issues of modeling and design of 2-D arrays in three dimensions with finite element code are discussed. These ultrasonic arrays are used for real time dynamic imaging of the heart. Topics include optimization, sensitivity, and performance and methods to speed up the run times required for computer simulations of large three-dimensional models. Empirical results from 45×45 2-D arrays are also presented     

MICROSTRUCTURAL MODELING AND NUMERICAL ANALYSIS FOR THE SUPERPLASTIC FORMING PROCESS

Superplastic forming is a manufacturing process during which a sheet is blow formed into a die to produce lightweight and strong components. In this paper, the microstructural mechanism of grain growth during superplastic deformation is studied. A new model, which considers grain growth, is proposed and applied to conventional superplastic materials. The relationships among the strain, strain rate, test temperature, initial grain size, and grain growth in superplastic materials are discussed. According to the proposed model, theoretical predictions for superplastic forming processes are presented, and comparison with experimental data is given. The new constitutive equation of superplasticity is introduced into a finite element method program to study superplastic blow forming. The effects of the geometric shape parameters of the die on the superplastic blow forming process are investigated, and the inhomogeneity in the thickness distribution of the specimen is analyzed.     

2-D multiplane finite element technique for solving a class of 3-D problems

A finite element technique, for efficient solution of a class of 3-D elasticity problems, is presented. In this method, standard 2-D finite elements are used along with a ‘connector’ element. An element, previously used to model material interfaces, is shown to provide the properties for use as a ‘connector’ element, if input variables are redefined. The accuracy of the technique is illustrated with a sample solution.     

Electro-Quasistatic High Voltage Field Simulations of Large Scale Insulator Structures Including 2-D Models for Nonlinear Field-Grading Material Layers

Resistive field-grading material is applied to nonceramic insulators. For the design of insulator structures, these resistive field-dependent and thus nonlinear material layers are considered as 2-D layers within 3-D transient finite element method (FEM) simulations of electro-quasistatic fields. The 2-D layer modeling approach is validated and compared to conventional 3-D layer modeling for various layer thicknesses. Numerical results for realistic structures are shown herein.      

A 2-D mesoscopic model coupling mechanical and diffusion for electromigration in thin films

Electromigration is an important mechanism of deformation and failure in miniaturized electronics materials. In this paper, a 2-D mesoscopic simulation method is developed for analyzing electromigration-induced stress in thin films and finite element method is implemented for solution. Numerical simulations are compared with theoretical result and comparisons validate the model. The method has advantage in describing boundary conditions for constrained diffusion when focusing on creep process of thin films.     

粗网格划分下的箱梁三维实体有限元分析方法

针对现有箱梁分析方法普遍存在的计算精度与计算效率之间矛盾的问题,提出了粗网格划分下的箱梁三维实体有限元分析方法。在充分考虑箱梁受力变形特点的基础上,以修正的Hellinger-Reissner变分原理为基础,通过合理引入非协调位移插值项,构造出直角坐标系下的六面体八结点杂交应力单元8N21β和柱坐标系下的六面体八结点杂交应力单元8N21βc,分别用于粗网格划分下的直箱梁和曲线箱梁的三维实体有限元分析。数值算例表明:8N21β单元和8N21βc单元在粗网格划分下具有较高的计算精度,能有效提高箱梁三维实体有限元分析的计算效率。     

三维有限元并行EBE方法

采用Jacobi预处理,推导了基于EBE方法的预处理共轭梯度算法,给出了有限元EBE方法在分布存储并行机上的计算过程,可以实现整个三维有限元计算过程的并行化。编制了三维有限元求解的PFEM(ParallelFiniteElementMethod)程序,并在网络机群系统上实现。采用矩形截面悬臂梁的算例,对PFEM程序进行了数值测试,对串行计算和并行计算的效率进行了分析,最后将PFEM程序应用于二滩拱坝-地基系统的三维有限元数值计算中。结果表明,三维有限元EBE算法在求解过程中不需要集成整体刚度矩阵,有效地减少了对内存的需求,具有很好的并行性,可以有效地进行三维复杂结构的大规模数值分析。     

3-D Spectral Stochastic Finite Element Method in Electromagnetism

Spectral stochastic finite element method (SSFEM), used in mechanics to take into account random aspects of input data, has been implemented, as an extended version, in the 3-D finite element method (FEM) software CARMEL dedicated to electromagnetic field computation. As a test case, this approach has been applied to a 3-D electrostatic problem and successfully validated by comparing with the Monte Carlo simulation method involving usual "deterministic" CARMEL resolutions     

考虑三维圆柱铰间隙碰撞的空间机构柔性多体动力学分析方法

三维圆柱铰的动态性能对空间机构的运动精度和动力学特性有着重要的影响。基于多体动力学方法和刚体有限元方法,提出考虑三维圆柱铰的间隙碰撞和动态接触作用的空间机构柔性多体接触动力学方法。采用圆柱-圆柱的线接触力学模型和切片法,计算圆柱-圆柱的接触变形量和接触力,建立三维圆柱铰的轴销与轴套之间的间隙碰撞作用和三维动态接触关系。以等效刚体单元和Timoshenko梁单元描述柔性杆件的刚性有限元模型,建立柔性连杆和三维圆柱铰的具有多刚体系统的统一形式的动力学方程。计算分析了含三维圆柱铰的空间机构的运动精度和动力学特性,获得空间机构的位移响应,三维圆柱铰的相对运动轨迹和动态作用力等动力学响应。采用三维圆柱-圆柱动态线接触方法,能有效地预测空间机构系统的三维圆柱铰持续接触、间隙碰撞状态和摩擦作用下的动力学特性。计算结果表明三维圆柱铰的间隙碰撞作用对空间机构的运动精度和动态特性的影响较为显著。动力学模型和计算结果对复杂工况下高精度多间隙的空间机构的动态设计和动力学研究具有重要的理论意义。     

超塑性充模胀形的有限元模拟

以跟踪最大应变速率单元并使之维持最佳应变速率的方法确定超塑性充模胀形的最佳加压规范；用大变形刚粘塑性有限元法模拟了恒压和最佳加压规范下的超塑性充模胀形过程，并对比二者的结果，同时分析了ｍ值对胀形的影响。     

三维四向编织复合材料力学性能的有限元分析

在已有研究的基础上,提出了一个新的三维编织复合材料单元胞体模型,该模型正确地反映了纤维束的交织方式,十分接近三维编织复合材料的真实结构,可用于三维四向编织复合材料有效模量的有限元数值预报,并合理确定复合材料内部全场应力分布。采用有限元软件对该模型进行了力学分析,得到了相关等效弹性性能参数。结果表明:有限元计算得到的三维编织复合材料的等效弹性性能与实验结果和理论预测值都吻合较好,从而验证了该模型的有效性。此外,基于新的单元胞体模型还确定了三维四向编织复合材料的应力场,为进一步的强度计算奠定了基础。      

Stability of collapsed 8-node 2-D and 20-node 3-D isoparametric finite elements

The collapse of ordinary finite elements to generate the desired strain singularity at the crack tip for fracture mechanics applications can lead to unwanted additional singularities in that area. Although neither the quarter-point nor the half-point 8-node two-dimensional (2-D) and 20-node three-dimensional (3-D) elements exhibit this behaviour, the present article proves that arbitrarily small deviations from the quarter-point element can be constructed which do have additional singularities. Since the general behaviour of the half-point element is not affected by small modifications, this element is better suited to match complex body geometries.     

Low-Velocity Impact Response and Finite Element Analysis of Four-Step 3-D Braided Composites

The low-velocity impact characters of 3-D braided carbon/epoxy composites were investigated from experimental and finite element simulation approaches. The quasi-static tests were carried out at a constant velocity of 2 mm/min on MTS 810.23 material tester system to obtain the indentation load–displacement curves and indentation damages. The low-velocity tests were conducted at the velocities from 1 m/s to 6 m/s (corresponding to the impact energy from 3.22 J to 116 J) on Instron Dynatup 9250 impact tester. The peak force, energy for peak force, time to peak force, and total energy absorption were obtained to determine the impact responses of 3-D braided composites. A unit cell model was established according to the microstructure of 3-D braided composites to derive the constitutive equation. Based on the model, a user-defined material subroutine (VUMAT) has been compiled by FORTRAN and connected with commercial finite element code ABAQUS/Explicit to calculate the impact damage. The unit cell model successfully predicted the impact response of 3-D braided composites. Furthermore, the stress wave propagation and failure mechanisms have been revealed from the finite element simulation results and ultimate damage morphologies of specimens.     

Mapped infinite elements for 3-D vector potential magnetic problems

Numerous engineering problems, especially those in electromagnetics, often require the treatment of the unbounded continua. Mapped infinite elements have been developed for the solution of 3-D magnetic vector potential equations in infinite domain that may be used in conjunction with the standard finite elements. The electromagnetic field equations are written in terms of the magnetic vector potential for the infinite domain, and 3-D mapped infinite eiement formulation based on these equations is presented in detail. A series of magnetostatics and eddy current problems are solved to demonstrate the validity and efficiency of the procedure. These numerical results indicate that the combined finite–infinite element procedure is computationally much more economical for the solution of unbounded electromagnetic problems, especially when using the vector potential formulation, as the number of system equations decreases substantially compared to the finite element only procedure. The present procedure shows promise for the treatment of large practical industrial 3-D eddy current problems with manageable computer resources.     

Numerical analysis of effect of material and processing parameters on thickness distribution during superplastic die bulging of cavity sensitive materials

Abstract

The superplastic bulging of circular sheets clamped against axisymmetrical cylindrical dies has been analysed numerically by means of a rigid–viscoplastic finite element method, in which four node quadrilateral isoparametric elements are used with a Newton–Raphson non­linear solution scheme. Both effects of normal anisotropy and strain hardening in the material are considered and a modified Coulomb friction law is adopted. At the same time, the yield criterion suited for the superplastic forming process and the cavity damage evolution model deduced from continuum damage mechanics are applied to a finite element formulation. The influences of material parameters (the strain rate sensitivity exponent m, the strain hardening exponent n, the coefficient of normal anisotropy R) and processing parameters (pressure cycle, lubrication condition, die geometry) on the inhomogeneity of the thickness distribution are studied and discussed. A selection of the simulated results is compared with the experimental results, with good agreement.     

Droplet Deformation and 2-D/3-D Marangoni Flow Phenomena in Droplets Levitated by Electric Fields

An integrated numerical model is presented for free surface phenomena and Marangoni fluid flows in electrically levitated droplets under both terrestrial and microgravity conditions. The model development is based on the boundary element solution of the Maxwell equations simplified for electrostatic levitation applications and the free surface deformation that is primarily caused from the surface Maxwell stresses resulting from the applied electric fields. The electric and free surface model is further integrated with a finite element model for the surface-tension-induced fluid flows in the levitated droplets. Both 2-D and 3-D fluid flow structures may be developed in the electrically levitated droplets depending on the applied laser heating sources. The integrated model is applied to study the electric field distribution, free surface deformation, and 2-D and 3-D internal fluid flow structures in normal and microgravity for single, symmetric two-beam, four-beam, and six-beam laser heating arrangements. Among these arrangements, the six-beam arrangement with equal heating intensity gives the smallest temperature difference and the smallest maximum velocity.     

Assessing and improving acoustic radiation force image quality using a 1.5-D transducer design

A 1.5-D transducer array was proposed to improve acoustic radiation force impulse (ARFI) imaging signal-to-noise ratio (SNRARFI) and image contrast relative to a conventional 1-D array. To predict performance gains from the proposed 1.5-D transducer array, an analytical model for SNRARFI upper bound was derived. The analytical model and 1.5-D ARFI array were validated using a finite element modelbased numerical simulation framework. The analytical model demonstrated good agreement with numerical results (correlation coefficient = 0.995), and simulated lesion images yielded a significant (2.92 dB; p < 0.001) improvement in contrast-tonoise ratio when rendered using the 1.5-D ARFI array.     

STRESS INTENSITY FACTORS FOR CORNER CRACKS AT A HOLE BY A 3-D WEIGHT FUNCTION METHOD WITH STRESSES FROM THE FINITE ELEMENT METHOD

Abstract— Stress intensity factors for quarter-elliptical corner cracks emanating from a circular hole are determined using a 3-D weight function method combined with a 3-D finite element method. The 3-D finite element method is used to analyze uncracked configurations and provide stress distributions in the region where a crack is likely to occur. Using this stress distribution as input, the 3-D weight function method is used to determine stress intensity factors. Three different loading conditions, i.e. remote tension, remote bending and wedge loading, are considered for a wide range of geometrical parameters. The significance of using 3-D uncracked stress distributions is studied. Comparisons are made with solutions available in the literature.