基于整体位移模式的平面裂纹结构数值模拟方法

对于平面裂纹问题,针对扩展有限元法和无网格伽辽金法的不足,从结构的整体位移模式出发,提出了一种新的数值模拟方法。在整个求解域内构造其试探函数,并引入裂纹修正项描述裂尖处的奇异性和裂纹面的强间断特性;同时,提出了一种新的强制边界条件施加方法,通过引入位移边界水平集函数,将位移边界条件包含在近似位移场的表达式中,有效地解决了位移边界条件问题,减小了刚度矩阵的阶数,非常方便地消除了刚度矩阵的奇异性,降低了线性方程组的求解难度。含裂纹矩形平板结构的数值算例验证了该方法的有效性。     

Numerical analysis of quasi-static crack branching in brittle solids by a modified displacement discontinuity method

Mechanism of quasi-static crack branching in brittle solids has been analyzed by a modified displacement discontinuity method. It has been assumed that the pre-existing cracks in brittle solids may propagate at the crack tips due to the initiation and propagation of the kink (or wing) cracks. The originated wing cracks will act as new cracks and can be further propagated from their tips according to the linear elastic fracture mechanics (LEFM) theory. The kink displacement discontinuity formulations (considering the linear and quadratic interpolation functions) are specially developed to calculate the displacement discontinuities for the left and right sides of a kink point so that the first and second mode kink stress intensity factors can be estimated. The crack tips are also treated by boundary displacement collocation technique considering the singularity variation of the displacements and stresses near the crack tip. The propagating direction of the secondary cracks can be predicted by using the maximum tangential stress criterion. An iterative algorithm is used to predict the crack propagating path assuming an incremental increase of the crack length in the predicted direction (straight and curved cracks have been treated). The same approach has been used for estimating the crack propagating direction and path of the original and wing cracks considering the special crack tip elements. Some example problems are numerically solved assuming quasi-static conditions. These results are compared with the corresponding experimental and numerical results given in the literature. This comparison validates the accuracy and applicability of the proposed method.     

A methodology for an accurate evaluation of the linearization procedures in nonlinear mean field homogenization

A systematic methodology for the evaluation of the linearization procedures sustaining mean field homogenization theories for nonlinear composite materials is proposed and applied as an illustration to various recently proposed ‘affine’ and ‘second-order’ formulations for nonlinear elasticity. It relies on the analysis of composites for which both the exact nonlinear homogenization problem and the homogenization problem associated with the ‘linear comparison material’ defined by the linearization procedure can be solved numerically with the same accuracy and for the same microstructure. The comparison of the results then provides a rigorous evaluation of the effects of the sole linearization method. To cite this article: A. Rekik et al., C. R. Mecanique 333 (2005).     

A higher resolution edge‐based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

In this article, we present a higher‐order finite volume method with a ‘Modified Implicit Pressure Explicit Saturation’ (MIMPES) formulation to model the 2D incompressible and immiscible two‐phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median‐dual vertex‐centered finite volume method with an edge‐based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re‐compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge‐based implementation of the MIMPES method of Hurtado and co‐workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two‐step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge‐based implementation of a modified second‐order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation for 2D double-diffusive convection (DDC) in rectangular enclosures based on a high resolution upwind compact streamfunction model I: numerical method and code validation

Applied Mathematics and Mechanics - A high resolution upwind compact streamfunction numerical algorithm for two-dimensional (2D) double-diffusive convection (DDC) is developed. The unsteady...     

锥形端部弹体在岩石(混凝土)介质层中侵彻实用计算方法

采用刚塑性不可压缩的介质模型 ,用极限分析理论的上限方法 ,通过建立动力学许可速度场得到介质对弹体侵彻的静阻力分量 ,通过破碎介质动量守恒条件得到弹体侵彻的动阻力分量 ,在模型中还考虑了介质的尺度关系和弹体的弹头形状两种影响因素。侵彻过程中的速度、加速度、阻力和经历时间通过弹体的运动方程增量计算得到。通过与几种常用经验公式比较说明了本文方法的实用和可靠性。     

BEHAVIOR OF OBSTRUCTED SQUARE BUOYANT VERTICAL JETS IN STATIC AMBIENT （Ⅰ）—— VERIFICATION OF MATHEMATICAL MODEL AND NUMERICAL METHOD

Some experiments were made for the buoyant jet from a square orifice with a square disc placed on it in static ambient and concentration along the axis in self-similar area behind disc was measured. And at the same time a three-dimensional mathematical model was established to simulate the whole flowing under different conditions. All the results predicted by the numerical calculation were substantiated by the experiments. The results were compared with experiential formula for obstructed round buoyant vertical jets in static ambient and it was found that the two concentration distributions had good accordance. Star shape of temperature isolines on cross-sections in the near areas from the disc was found and it was a very special figure for obstructed square buoyant vertical jets with a square disc. The shape will transform to concentric circles gradually alike to the round buoyant vertical jet in self-similar area with increasing of the distance from the disc.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite-element-displacement-perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander’s nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper, three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip. of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program. The results reveal that the constraints along the thickness direction are obviously separated into two parts: the keeping similar high constraint field (Z₁) and rapid reducing constraints one (Z₂). The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively. So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively. The distribution of the Crack Tip Opening Displacement (CTOD) along the thickness direction and the three dimensional distribution of the void growth ratio (V_g) near the crack tip are also obtained. The two fracture parameters are in similar trends along the thickness direction, and both of them can reflect the effect of thickness and that of the loading level to a certain degree.