单步辛算法的相位误差分析及修正

若一个算法的幅值误差和相位误差都不累加,则该算法就是最理想的算法, 但这样的算法难以构造. 辛几何算法解决了幅值误差的累加问题,但相位误差累加问题仍然 存在. 给出了单步隐式辛算法相位误差的精确估计公式,提出了简单而实用的修正方法. 以 Euler中点隐式辛差分格式为例,针对几个线性动力学系统,对相位误差进行了数值分析和 修正.     

直剪实验剪切面积的修正及误差分析

针对现行直剪实验没有考虑剪切面积不断减小对实验结果的影响,本文从理论上推导了计算有效剪切面积的公式,然后通过实验并采用最小二乘法对数据进行处理.结果表明,土体的抗剪强度误差随着环刀面积的增大而减小,当环刀面积为30 cm2时,随着剪切位移的增大,土体的抗剪强度误差增大;当剪切位移达到4 mm和6 mm时,抗剪强度误差可达8.2%和12.38%.现行方法测得的黏聚力和内摩擦角均比真实值小,低估了土体的抗剪强度,因而需要修正.     

应变损伤材料I型动态扩展裂纹尖端场的渐近分析

研究了应变损伤材料Ｉ型动态扩展的裂纹尖端场。假定材料服从Ｊ２流动理论，且损伤规律以幂律应变软化的规律给出。对于塑性区引进了应力函数φ，ψ０借助于动力学方程的分析，给出了渐近方程及数值解。结果表明，对于可压缩材料Ｉ型平面应变尖端场是完全由塑性区组成，没有弹性卸载区。在裂纹尖端附近，应力和应变分别具有如下的奇异性：σ￣（ｌｎＲ／ｒ）＾－ｎ／ｎ＋１，ε￣（ｌｎＲ／ｒ）＾１／ｎ＋１。     

幂硬化材料Ⅲ型裂纹问题的塑性区修正

在工程实际中大量韧性较好的中低强度钢材的广泛应用,高温环境引起材料的蠕变以及构件工艺历史等原因引起的残余应变,使得构件中存在有塑性变形.在此情况下,对于含裂纹构件的线弹性断裂分析理论已受到了限制,因此,必须用弹塑性力学的分析方法来描述裂纹的启裂和扩展规律。在一般情况下,对于含裂纹构件的弹塑性分析在数学上求解是复杂的。人 ...     

方位引出装置框架误差分析与修正

炮兵指挥车通过方位引出装置实现对目标方向和位置的测量。采用两环结构的方位引出装置存在着框架误差,影响对目标位置和方位角的测量精度。通过应用方向余弦矩阵法,研究了框架误差的产生机理,推导了框架误差的补偿公式。通过数学分析和仿真,验证了方位引出框架误差补偿的正确性。实验结果证明:该补偿方案能够对方位引出两环结构带来的框架误差进行实时修正,补偿后的精度(PE)≤0.3 mil,满足战技指标要求,实现对目标位置和方位角的准确测量。     

梁变形实验主要误差分析和修正

引言材料力学梁变形实验多数采用图1(a)所示细长矩形截面悬臂梁,用千分表测定挠度以验证理论.具体做法是:在 B 截面加载荷 P,同时用千分表测其挠度(?)_B(图1(a));再将千分表移到 C 截面测得在 B 截 ...     

I型定常扩展裂纹尖端的弹黏塑性场

考虑材料在扩展裂纹尖端的黏性效应，假设黏性系数与塑性应变率的幂次成反比，对幂硬化材料中平面应变扩展裂纹尖端场进行了弹黏塑性渐近分析，得到了不含间断的连续解，并讨论了I型裂纹数值解的性质随各参数的变化规律. 分析表明应力和应变均具有幂奇异性，并且只有在线性硬化时，尖端场的弹、黏、塑性才可以合理匹配. 对于I型裂纹，裂尖场不含弹性卸载区. 当裂纹扩展速度趋于零时，动态解趋于准静态解，表明准静态解是动态解的特殊形式；如果进一步考虑硬化系数为零的极限情况，便可退化为Hui和Riedel的非线性黏弹性解.     

求解I型裂纹构元J积分的半解析方法

表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量. 目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务. 以J积分为参量的材料断裂测试中应用最广的是I型裂纹试样的断裂韧性测试. 本文在平面应变条件下,针对断裂韧性测试中使用的6种I型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数. 分析表明,6种I型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好. 新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值. 应用新方法可便于获得各类I型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.      

虚拟裂纹闭合法在结构断裂分析中的应用

基于三维虚拟裂纹技术(3DVCCT),利用ABAQUS用户单元子程序(UEL)编写裂纹界面单元,使3DVCCT集成于ABAQUS软件中,直接计算出裂纹的断裂参数.采用此方法对连杆杆身表面裂纹进行研究,得到了连杆裂纹的应力强度因子的分布规律.     

A new method for the analysis and assessment of fatigue crack closure. I: modeling

In this paper of a two-paper series a new method is proposed for the analysis and assessment of fatigue crack closure phenomena. Based on the proposed model, the combined effect of residual plastic stretch, asperity mismatch, and corrosion debris on the closure behavior of a fatigue crack can be simulated by a hypothetical rigid insert located in an ideal crack wake. The formulation of the model results in a set of equations which can predict the closure load as well as the load-CMOD characteristics using the residual CMOD at zero load as a unique experimental input. The model is verified using different sets of experimental data reported in the literature.     

Theoretical analysis of crack front instability in mode I+III

This paper focusses on the theoretical prediction of the widely observed crack front instability in mode I+III, that causes both the crack surface and crack front to deviate from planar and straight shapes, respectively. This problem is addressed within the classical framework of fracture mechanics, where the crack front evolution is governed by conditions of constant energy-release-rate (Griffith criterion) and vanishing stress intensity factor of mode II (principle of local symmetry) along the front. The formulation of the linear stability problem for the evolution of small perturbations of the crack front exploits previous results of Movchan et al. (1998) (suitably extended) and Gao and Rice (1986), which are used to derive expressions for the variations of the stress intensity factors along the front resulting from both in-plane and out-of-plane perturbations. We find exact eigenmode solutions to this problem, which correspond to perturbations of the crack front that are shaped as elliptic helices with their axis coinciding with the unperturbed straight front and an amplitude exponentially growing or decaying along the propagation direction. Exponential growth corresponding to unstable propagation occurs when the ratio of the unperturbed mode III to mode I stress intensity factors exceeds some “threshold” depending on Poisson's ratio. Moreover, the growth rate of helical perturbations is inversely proportional to their wavelength along the front. This growth rate therefore diverges when this wavelength goes to zero, which emphasizes the need for some “regularization” of crack propagation laws at very short scales. This divergence also reveals an interesting similarity between crack front instability in mode I+III and well-known growth front instabilities of interfaces governed by a Laplacian or diffusion field.     

Numerical study of contact forces for crack closure analysis

Plasticity induced crack closure (PICC) has been widely studied using numerical models. Different numerical parameters can be considered to quantify the opening level, namely one based on the analysis of contact stresses at minimum load. A modified version of this parameter is proposed here, based on nodal contact forces instead of contact stresses. The predictions were found to be similar to those obtained from the contact status of 2nd node behind crack tip. The PICC_contact parameter was also found to be very consistent and adequate for parametric studies of the influence of different physical parameters. The contributions to the opening stress intensity factor of different points along crack flank were found to strongly decrease with distance to crack tip. The cumulative K_open between the crack tip and a distance of 0.1 mm was found to vary from 30% to 100%, increasing with stress ratio, R. Finally, a K solution was developed for punctual forces applied on crack flank and compared with a literature solution for infinite plates. A good agreement was found for plane strain state but significant differences of about 10% were found for plane stress state.     

The lowest order solution of the crack–inhomogeneity interaction for mode I crack

The lowest order solution to crack–inhomogeneity interaction is derived for mode I crack. The basic solution evaluates the variation of near-tip stress intensity factors induced by an inhomogeneity of arbitrary shape. A set of simplified forms of the basic solution is also obtained for several special inhomogeneity shapes. As validated by numerical examples, the approximate solutions have good accuracy.     

Dynamic mode I perturbation solution for a moving crack unsteadily

Rice et al. (Journal of Mechanics and Physics of Solids42, 813–843) analyze the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of Willis et al. (Journal of the Mechanics and Physics of Solids43, 319–341), of dynamic mode I weight functions for a moving crack, we address that problem solved by Rice et al. in the 3D context of elastodynamic theory. Oscillatory crack tip motion results from constructive-destructive interference of stress intensity waves. Those waves, including system of the dilatational, shear and Rayleigh waves, interact on each other and with moving edge of crack, can lead to continuing fluctuations of the crack front and propagation velocity.     

Pseudo plane stress plastic field for mode I crack growth

The pseudo plane stress field for a mode I crack growth is analyzed for both perfectly plastic and power law hardening plastic materials. When finite strain is taken into account, it is found that for perfectly plastic materials, the plastic domain is a narrow strip ahead of the crack tip. For power law hardening plastic material, the plastic domain contains a strip and a region ahead of the strip. The fracture criterion is discussed. The energy dissipated in the plastic strip is found to be proportional to the square of the thickness. Singular solutions to the field are ruled out by analysis.     

Fracture analysis of mode III crack problems for the piezoelectric bimorph

In this paper, a symplectic method based on the Hamiltonian system is proposed to analyze the interfacial fracture in the piezoelectric bimorph under anti-plane deformation. A set of Hamiltonian governing equations is derived from the Hamiltonian function by introducing dual variables of generalized displacements and stresses which can be expanded in series in terms of the symplectic eigensolutions. With the aid of the adjoint symplectic orthogonality, coefficients of the series are determined by the boundary conditions along the crack faces and along the external geometry. The stress\electric displacement intensity factors and energy release rates (G) directly relate to the first few terms of the nonzero eigenvalue solutions. The two ideal crack boundary conditions, namely the electrically impermeable and permeable crack assumptions, are considered. Numerical examples including the complex mixed boundary conditions are considered to show fracture behaviors of the interface crack and discuss the influencing factors.     

Optimizing energy input for fracture by analysis of the energy required to initiate dynamic mode I crack growth

A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values minimum energy required for initiation of crack growth increases rapidly. Results received indicate a possibility to optimize energy consumption of different industrial processes connected with fracture. Much could be gained in for example drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e., frequency and amplitude of impacts, for industrial devices, e.g., bores, grinding machines, etc. and hence significantly reduce the process cost. The prediction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).     

An error analysis of the dynamic mode decomposition

Dynamic mode decomposition (DMD) is a new diagnostic technique in fluid mechanics which is growing in popularity. A powerful analysis tool, it has great potential for measuring the spatial and temporal dynamics of coherent structures in experimental fluid flows. To aid interpretation of experimental data, error-bars on the measured growth rates are needed. In this article, we undertake a massively parallel error analysis of the DMD algorithm using synthetic waveforms that are shown to be representative of the canonical instabilities observed in shear flows. We show that the waveform of the instability has a marked impact on the error of the measured growth rate. Sawtooth and square waves may have an order of magnitude larger error than sine waves under the same conditions. We also show that the effects of data quantity and quality are of critical importance in determining the error in the growth or decay rate, and that the effect of the key parametric variables are modulated by the growth rate itself. We further demonstrate methods by which ensemble and orthogonal data may be introduced to improve the noise response. With regard for the important variables, precise measurement of the growth rates of instabilities may be supplemented with an accurately estimated uncertainty. This opens many new possibilities for the measurement of coherent structure in shear flows.