A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations

Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other.     

Error Estimates for Semidiscrete Finite Element Approximations of the Stokes Equations Under Minimal Regularity Assumptions

Semidiscrete (spatially discrete) finite element approximations of the Stokes equations are studied in this paper. Properties of L ², H ¹ and H ^–1 projections onto discretely divergence-free spaces are discussed and error estimates are derived under minimal regularity assumptions on the solution.     

Optimal design of butterfly-shaped linear ultrasonic motor using finite element method and response surface methodology

A new method for optimizing a butterfly-shaped linear ultrasonic motor was proposed to maximize its mechanical output. The finite element analysis technology and response surface methodology were combined together to realize the optimal design of the butterfly-shaped linear ultrasonic motor. First, the operation principle of the motor was introduced. Second, the finite element parameterized model of the stator of the motor was built using ANSYS parametric design language and some structure parameters of the stator were selected as design variables. Third, the sample points were selected in design variable space using latin hypercube Design. Through modal analysis and harmonic response analysis of the stator based on these sample points, the target responses were obtained. These sample points and response values were combined together to build a response surface model. Finally, the simplex method was used to find the optimal solution. The experimental results showed that many aspects of the design requirements of the butterfly-shaped linear ultrasonic motor have been fulfilled. The prototype motor fabricated based on the optimal design result exhibited considerably high dynamic performance, such as no-load speed of 873 mm/s, maximal thrust of 27.5 N, maximal efficiency of 43%, and thrust-weight ratio of 45.8.     

载流导体的二维温度场的分析

为分析机电设备导体中电流引起的热分布问题,建立了机电设备的简化有限元模型,对导体进行了自适应网格划分,采用有限元方法求解热导微分方程,得到导体中热分布情况,可以估算导体的形状和尺寸,为机电设备选择合适的导体提供了一种有效的设计方法。     

Measurement of piezoelectric modulus by pulsed excitation of piezoelectric ceramic elements

The possibility of measuring the piezoelectric modulus by exciting piezoelectric ceramic components with a radio pulse is considered. It is shown that there is a relation between the piezoelectric modulus and the rate of change of the current envelope at the beginning of the transient. Theoretical relations are derived. __________ Translated from Izmeritel’naya Tekhnika, No. 10, pp. 71–72, October, 2006.     

Light composite elliptic springs for vehicle suspension

For composites to compete in vehicle suspension applications, it is essential to control their failure by utilising their strength in principal direction instead of shear. This can be achieved efficiently by employing a new configuration instead of existing one. This study marries between an elliptical configuration and the woven roving composites.

In this paper, the influence of ellipticity ratio on performance of woven roving wrapped composite elliptical springs has been investigated both experimentally and numerically. A series of experiments was conducted for composite elliptical springs with ellipticity ratios (a/b) ranging from one to two. Typical failure histories of their failure mechanism are presented and discussed. In general, this study demonstrated that composites elliptical spring can be used for light and heavy trucks and meet the requirements, together with substantial weight saving. The results showed that the ellipticity ratio significantly influenced the spring rate and failure loads. Composite elliptic spring with ellipticity ratios of a/b 2.0 displayed the highest spring rate.     

The perturbation method and the extended finite element method. An application to fracture mechanics problems

The extended finite element method has been successful in the numerical simulation of fracture mechanics problems. With this methodology, different to the conventional finite element method, discretization of the domain with a mesh adapted to the geometry of the discontinuity is not required. On the other hand, in traditional fracture mechanics all variables have been considered to be deterministic (uniquely defined by a given numerical value). However, the uncertainty associated with these variables (external loads, geometry and material properties, among others) it is well known. This paper presents a novel application of the perturbation method along with the extended finite element method to treat these uncertainties. The methodology has been implemented in a commercial software and results are compared with those obtained by means of a Monte Carlo simulation.     

Numerical evaluation of the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests

Nonlinear finite element analyses are used to examine the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests. Energy release rates are first determined by a recently developed direct energy balance approach. It is shown that the finite diameter loading rollers that are typically used in practical test set-ups cause both tests to be inherently nonlinear. The effect of these nonlinearities on the energy release rate is shown to be larger in the four point than the three point test and to increase with increasing roller diameter, increasing coefficient of friction along the crack plane, and decreasing supporting span length. For the four point test, the effect of these nonlinearities is also shown to increase with increasing ratio of inner to outer span length. Next, energy release rates at the onset of crack advance are determined by a simulated compliance calibration technique. This “perceived toughness” is compared with predictions of the “true toughness” given by the direct energy balance approach at the same load. It is shown that perceived toughnesses from this simulated compliance calibration procedure are larger than previously reported results that were obtained in a similar fashion using linear theory. In addition, the perceived toughness is shown to strongly depend upon the range used for fitting the load versus deflection data to obtain compliance. These findings are used to make some general recommendations regarding use of the two test methods and their associated data reduction techniques.     

新型横向磁场电机的标量磁位三维磁场分析与参数计算

提出了一种新型横向磁场电机（TFM），定子采用E型铁心，可以大大降低加工难度和制造成本。但是，该电机磁路复杂，需采用三维场场进行分析。在三维有限元磁场中，如果对电流区域进行适当处理，采用标量磁位进行分析，与采用矢量磁位相比，可大大提高计算速度。对电流区域在三维磁场计算中的处理方法进行了推导，根据所推导的原理编制三维有限元软件，利用该软件对样机磁场进行计算。试验结果表明了该方法的正确性。