A study of breast motion using non-linear dynamic FE analysis

This paper presents a new method to simulate non-linear breast motion by using a three-dimensional (3D) dynamic finite element model (FEM). The model consists of a thorax with two breasts and three skin layers with specific mechanical properties. Using free breast vibration, the viscous damping ratios were ascertained to be 0.215 for an 80B size breast. The shear modulus for the breast was derived as the value that gave the minimum difference between the FEM-predicted results and the experimental data. A hyper-elastic neo-Hookean material model simulated the large deformation of breast tissue. The mode shapes of breast motions at different natural frequencies were established. The highest breast displacement amplitude ratio relative to the thorax was at 4 Hz. The study showed that FEM can predict breast displacement with sufficient accuracy and thereby provide the basis by which bras may be engineered more ergonomically in the future.

Practitioner Summary: To facilitate a theoretical analysis of breast motion to enable the design of more supportive bras, a dynamic FEM based on reliable non-linear properties of breast tissues has been developed. The methods and findings have potential widespread benefit for developing new products to promote women's health and comfort.     

Forced vibration analysis of piezoelectric quartz plates in resonance

Quartz is a widely used piezoelectric material and quartz resonators are the primary components in many industrial applications due to the piezoelectric effect. To have a thorough understanding on the vibration characteristics of quartz plates, the experimental measurement of resonant frequencies and mode shapes is indispensable. In this paper, two experimental techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), which are, respectively, full-field and point-wise displacement measurement methods, are used to obtain the out-of-plane vibration characteristics of AT-Cut quartz in real time. The resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time from AF-ESPI method. However, only the resonant frequencies of the out-of-plane vibration modes are determined by the LDV. The cantilever and completely free quartz plates are used in this study and the experimental results are verified by the finite element method (FEM) analysis. The cantilever quartz plates are excited from applying voltage and acoustic waves. Furthermore, three designs of electrode for a quartz plate with free-boundary condition are studied. Excellent agreement between the measured data from the optical method and the numerical results predicted by FEM are found for both resonant frequencies and mode shapes.     

Time-dependent gas flows through axisymmetrical porous heat-evolutional bodies

Gas motion in the gravity field through porous heat-evolutional bodies, which can result from natural or man-made disasters (such as the explosion of the reactor at the Chernobyl Nuclear Power Plant), is investigated. A mathematical model and an original numerical method based on a combination of explicit and implicit finite-difference schemes are proposed for studying time-dependent gas flows through axisymmetric porous heat-evolutional bodies. The cooling of axisymmetric porous elements of smoothly converging and stepwise converging shapes, as well as the effect of the geometry of a heat-evolutional element on its cooling process have been investigated. The axisymmetric and plane gas flows through porous heat-evolutional elements were compared and it has been found that the cooling mode of an axisymmetric body may differ from the cooling mode of a plane body not only in quantity but also in quality.     

Finite element modal analysis of a spinning flexible disk-spindle system in a HDD considering the flexibility of complicated supporting structure

The free vibration of a spinning flexible disk-spindle system in a HDD considering the flexibility of complicated supporting structure is analyzed by FEM and substructure synthesis. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The stationary shaft is also modeled by Timoshenko beam. The flexible supporting structure with a complex shape which includes the stator core, housing and base plate is modeled by using a four-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility at the interface node between the one-dimensional (1-D) beam element and the 3-D solid element. Rigid link constraint is imposed at the interface area between shaft and housing to describe the physical motion at this interface. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies and mode shapes with the experimental ones. This research shows that the flexible supporting structure as well as the rigid link constraint between shaft and housing play an important role in accurately predicting the natural frequencies.     

In-plane vibration of plates by continuous mass matrix method

The continuous mass matrix method derived for frameworks is extended to the analysis of in-plane vibration of plates. A continuous mass distribution which is the same as the actual mass distribution of the plate is considered over each rectangular finite element. Taking into account that the rigid body movement produces inertial forces in dynamic analysis for a rectangular plate element eight independent conditions are provided to satisfy eight independent freedoms. Each condition is obtained from an independent displacement distribution satisfying the equations of motion at any point of the element and not only at the nodes of the rectangle. The dynamic element stiffness matrix thus obtained is a function of the natural circular frequency. The limit of the dynamic element stiffness matrix when the value of the natural circular frequency tends to zero is the static, stress compatible element stiffness matrix. The analysis of plates under forcing forces is performed by modal analysis after the natural circular frequencies and the corresponding modal shapes have been obtained from the free vibrations, for all the forcing forces are assumed to be function of the same time variation. Otherwise one must recur to a numerical analysis. The effect of the sizes, number of the meshes, the additional static load on the plate and the rigidity of the boundaries on the vibration of the plate is discussed. Few example problems are solved in order to illustrate the above mentioned effects. The numerical results obtained by continuous mass matrix method are compared with those of consistent mass matrix method. The convergence in terms of the sizes of meshes and the limit of convergence are examined.     

Characterization of delamination effect on composite laminates using a new generalized layerwise approach

A dynamic analysis method has been developed to investigate and characterize the effect due to presence of discrete single and multiple embedded delaminations on the dynamic response of composite laminated structures with balanced/unbalanced and arbitrary stacking sequences in terms of number, placement, mode shapes and natural frequencies. A new generalized layerwise finite element model is developed to model the presence of multiple finite delamination in laminated composites. The new theory accurately predicts the interlaminar shear stresses while maintaining computational efficiency.     

航空相机的模态分析及轴承模型的修改

为了研究航空相机的动态结构刚度,运用有限元分析和试验相结合的模态分析法获得系统的固有频率和模态振型.应用大型通用有限元软件MSC.Nastran/Patran建立了航空相机的有限元模型,分析得出该相机的固有频率和模态.利用有限元分析结果中的模态振型指导试验模态分析中测点位置的选择,通过试验测得相机系统固有频率的实际值,并与有限元分析结果进行比较,验证了有限元分析的合理性,确定相机结构达到了设计性能指标.在有限元建模中采用改进的线性轴承模型后,降低了系统的计算难度,使有限元分析结果与试验值更加接近.     

基于稳定节点光滑有限元法的纯电动汽车电磁场仿真

针对纯电动汽车电磁场数值分析时传统有限元法（finite element method, FEM）因数值“过硬”而计算精度低的问题，在传统FEM的基础上引入梯度光滑技术和稳定项修正，采用基于稳定节点的光滑有限元法（stable node based smoothed FEM, SNS FEM）对长直接地金属槽和纯电动汽车整车电磁场算例进行仿真分析。结果表明，SNS FEM可显著降低前处理网格划分难度，在一定程度上软化数值模型，具有计算效率高、精度高、收敛速度快和抗网格畸变能力强等优点，在工业应用中具有较大潜力。     

Coupling of finite element method with material point method by local multi-mesh contact method

As a Lagrangian particle method, the material point method (MPM) has the potential to model extreme deformation of materials, where the traditional finite element method (FEM) often encounters mesh distortion and element entanglement which lead to numerical difficulties. However, FEM is more accurate and efficient than MPM for problems with small deformation. It is therefore desirable to model the body with extreme deformation by MPM and the body with small deformation by FEM, respectively. In this paper, a method to handle the contact interaction between the MPM body and the FEM body is proposed, which is implemented on the background grid of MPM. By this method, FEM is coupled with MPM and a hexahedral element is incorporated into our 3D explicit MPM code MPM3D®. Several numerical examples, including plate impact, sphere rolling, perforation of thick plate, and fluid–structure interaction problems, are studied and the numerical results are in good agreement with analytical solution and results available in the literature. The coupling of FEM and MPM offers advantages of both FEM and MPM.     

Modelling of flow-induced stresses in a Francis turbine runner

This study presents the results of large scale modelling of the water flow and the analysis flow-induced stresses in a Francis turbine runner. The modelling undergoes two stages. The first stage deals with the water flow that has been investigated by using Computational Fluid Dynamics (CFD) in order to identify the loads acting on the turbine blades. At the second stage, the finite element analysis of stresses has been performed based on the pressure distributions calculated from CFD modelling. The operational data recorded at Unit 2 of the Derbendikan power station have been used as input in the modelling. The results of calculations have revealed that the zones of high stress are situated at the trailing edge of the turbine runner, which explains observed fatigue cracks in these areas.     

An application of ADINA to the solution of fluid-structure interaction problems

ADINA is employed to solve the lowest natural frequencies and corresponding mode shapes of a plate and turbine blade when submerged in water. Finite element solution parameters such as integration order of elements, mass matrix, flow around edges, and other modelling considerations are reported. The performance of the present solution algorithms and comparisons with experimentally obtained results are also presented.

The experience reported can be useful for the analysis of problems involving an elastic structure immersed in an acoustic fluid (exterior problems) and problems involving an acoustic fluid within elastic structures (interior problems).     

Vibration of triangular plates of variable thickness

The problem of the natural frequencies and mode shapes of cantilevered triangular plates with variable thickness and arbitrary planform is solved using the finite element technique. This is done for various combinations of four non-dimensional geometric parameters, namely, the aspect ratio, the two thickness ratios along the two coordinate directions and the sweepback angle. The frequencies for the various cases are tabulated and a few typical mode shapes have been presented graphically.     

Mode shapes and frequencies by finite element method using consistent and lumped masses

The rate of convergence of the mode shapes and frequencies by the finite element method using consistent and lumped mass formulations has been established. Simple examples are given to demonstrate the results. It has been found that for a system of differential equations of second order such as the equations of equilibrium in terms of displacement in the theory of elasticity, membrane etc., a proper lumped mass formulation will not suffer any loss of rate of convergence utilizing simple elements. However, in the case of higher order differential equations or when the use of more complicated elements is required or desired, a consistent mass formulation often will provide a better rate of convergence.     

Multi-objective shape optimization of a hydraulic turbine runner using efficiency,strength and weight criteria

An approach for multi-discipline automatic optimization of the hydraulic turbine runner shape is presented. The approach accounts hydraulic efficiency, mechanical strength and the weight of the runner. In order to effectively control the strength and weight of the runner, a new parameterization of the blade thickness function is suggested. Turbine efficiency is evaluated through numerical solution of Reynolds-averaged Navier-Stokes equations, while the finite element method is used to evaluate the von Mises stress in the runner. An objective function, being the weighted sum of maximal stress and the blade volume, is suggested to account for both the strength and weight of the runner. Multi-objective genetic algorithm is used to solve the optimization problem. The suggested approach has been applied to automatic design of a Francis turbine runner. Series of three-objective optimization runs have been carried out. The obtained results clearly indicate that simultaneous account of stress and weight objectives accompanied by thickness variation allows obtaining high efficiency, light and durable turbine runners.     

混流式水轮发电机组主轴系统振动特性分析

针对混流式水轮发电机组振动现象严重影响水电站安全运行的问题,应用ANSYS建立主轴系统的有限元模型,分析主轴系统固有频率及振型变化的特点,研究主轴系统的振动特性,并分析主轴系统在激励影响下发生共振的可能性及其振型.研究结果表明,主轴系统在多种外激励作用下,除了产生强迫振动外,还可产生主共振、分数共振等复杂的振动现象.研究结果对进一步研究主轴系统动态特性有一定的参考价值.     

滚动转子压缩机转子组合结构振动特性分析与测试

为了避免压缩机转子系统在工作过程中的振动超标,需要对其开展系统化的动态优化设计,包括压缩机转子乃至整机的振动特性测试以及利用转子动力学对其建模与分析.本文以转子系统组合件(泵组件+外壳组件)为研究对象,首先创建了压缩机转子系统三维实体有限元分析模型.进一步,对转子系统的固有特性进行了分析,获得了前5阶固有频率与模态振型.最后,对该滚动转子压缩机进行了动力学实验,校验了上述分析模型的合理性.本文的研究可为压缩机系统的减振与降噪提供技术参考.     

Phase change problems with free convection: fixed grid numerical simulation

A numerical and experimental study of unsteady natural convection during freezing of water is presented. The mathematical model for the numerical simulations is based on the enthalpy-porosity method in vorticity-velocity formulation, equations are discretised on a fixed grid by means of a finite volume technique. A fully implicit method has been adopted for the mass and momentum equations. Experiments are performed for water in a differentially heated cube surrounded by air. The experimental data for natural convection with freezing in the cavity are collected to create a reference for comparison with numerical results. The method of simultaneous measurement of the flow and temperature fields using liquid crystal tracers is used. It allows us to collect transient data on the interface position, and the temperature and velocity fields. In order to improve the capability of the numerical method to predict experimental results, a conjugate heat transfer problem was solved, with finite thickness and internal heat conductivity of the non-isothermal walls. These results have been compared with the simulations obtained for the idealised case of perfectly adiabatic side walls, and with our experimental findings. Results obtained for the improved numerical model shown a very good agreement with the experimental data only for pure convection and initial time of freezing process. As time passes the discrepancies between numerical predictions and the experiment became more significant, suggesting a necessity for further improvements of the physical model used for freezing water. Received: 30 April 1999 / Accepted: 17 June 1999     

Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations

This paper presents a finite element technique for determining the vibration characteristics of a uniform Timoshenko beam-column supported on a two-parameter elastic foundation. The beam-column is discretized into a number of simple elements with four degrees of freedom each. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into a finite element model. The matrix equation governing the free vibrations of the beam-column on the elastic foundation is derived from Hamilton's principle. The numerical results for the natural frequencies and the associated mode shapes of the classical Euler-Bernoulli and Timoshenko beam-columns on the elastic foundation are presented and compared with the exact or available solutions, wherever possible. It is shown that the present technique provides a unified approach for the vibration analysis of beam-columns with any end conditions, resting on the elastic foundation.     

A knowledge base for finite element mesh design

The finite element method (FEM) is the most successful numerical method, that is used extensively by engineers to analyse stresses and deformations in physical structures. These structures should be represented as a finite element mesh. Defining an appropriate geometric mesh model that ensures low approximation errors and avoids unnecessary computational overheads is a very difficult and time consuming task. It is the major bottleneck in the FEM analysis process. The inductive logic programming system GOLEM has been employed to construct the rules for deciding about the appropriate mesh resolution. Five cylindrical mesh models have been used as a source of training examples. The evaluation of the resulting knowledge base shows that conditions in the domain are well represented by the rules, which specify the required number of the finite elements on the edges of the structures to be analysed using FEM. A comparison between the results obtained by this knowledge base and conventional mesh generation techniques confirms that the application of inductive logic programming is an effective approach to solving the problem of mesh design.     

Polysilicon micro beams buckling with temperature-dependent properties

The suspended electrothermal polysilicon micro beams generate displacements and forces by thermal buckling effects. In the previous electro-thermal and thermo-elastic models of suspended polysilicon micro beams, the thermo-mechanical properties of polysilicon have been considered constant over a wide rang of temperature (20–900°C). In reality, the thermo-mechanical properties of polysilicon depend on temperature and change significantly at high temperatures. This paper describes the development and validation of theoretical and Finite element model (FEM) including the temperature dependencies of polysilicon properties such as thermal expansion coefficient and Young’s modulus. In the theoretical models, two parts of elastic deflection model and thermal elastic model of micro beams buckling have been established and simulated. Also, temperature dependent buckling of polysilicon micro beam under high temperature has been modeled by Finite element analysis (FEA). Analytical results and numerical results using FEA are compared with experimental data available in literature. Their reasonable agreement validates analytical model and FEM. This validation indicates the importance of including temperature dependencies of polysilicon thermo-mechanical properties such as Coefficient of thermal expansion (CTE) in the previous models.