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1.
A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.  相似文献   

2.
For the stability problem of homogeneous shear flows in sea straits of arbitrary cross section, a sufficient condition for stability is derived under the condition of inviscid flow. It is shown that there is a critical wave number, and if the wave number of a normal mode is greater than this critical wave number, the mode is stable.  相似文献   

3.
A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.  相似文献   

4.
For a non-linear system excited by a stochastic load which is expressed as a time series,a recursive method based on the Z-transform is presented.To identify the obtained response time series,a discrete wavelet transform (DWT) technique is proposed.  相似文献   

5.
The analytical solution to a Foppl-Hencky membrane with a rigidly clamped boundary condition under concentrated force is provided. Stability of a nonlinear circular membrane is investigated.  相似文献   

6.
Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quantity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invariance of the conserved quantity.  相似文献   

7.
All types of gradient systems and their properties are discussed. Two problems connected with gradient sys-tems and mechanical systems are studied. One is the direct problem of transforming a mechanical system into a gradi-ent system, and the other is the inverse problem, which is transforming a gradient system into a mechanical system.  相似文献   

8.
The effects of packing configurations on the phase transition of straight granular chute flow with two bottlenecks axe studied. The granular flow shows a dilute- to-dense flow transition when the channel width is varied, accompanied with a peculiar bistable phenomenon. The bistable phenomenon is induced by the initial packing config- uration of particles. When the packing is dense, the initial flux is small and will induce a dense flow. When the packing is loose, the initial flux is large and will induce a di- lute flow. The fabric network of granulax packing is analyzed from a complex network perspective. The degree distribution shows quantitatively different characteristics for the configurations. A two-dimensional (2D) packing clustering coefficient is defined to better quantify the fabric network.  相似文献   

9.
A systematic numerical integration method is applied to the absolute nodal coordinate formulation(ANCF)fully parameterized beam element with smooth varying and continuous cross section.Moreover,the formulation for the integration points and weight coefficients are given in the method which is used to model the multilayer beam with a circular cross section.To negate the effect of the bending stiffness for the element used to model the high-voltage electrical wire,the general continuum mechanical approach is adjusted.Additionally,the insulation cover for some particular types of the wire is described by the nearly incompressible Mooney-Rivlin material model.Finally,a static problem is presented to prove the accuracy and convergence properties of the element,and a dynamic problem of a flexible pendulum is simulated whereby the balance of the energy can be ensured.An experiment is carried out in which a wire is released as a pendulum and falls on a steel rod.The configurations of the wire are captured by a high-speed camera and compared with the simulation results.The feasibility of the wire model can therefore be demonstrated.  相似文献   

10.
Large eddy simulation of vertical turbulent jets under JONSWAP waves   总被引:1,自引:0,他引:1  
The effect of random waves on vertical plane turbulent jets is studied numerically and the mechanism behind the interaction of the jet and waves is analyzed. The large eddy simulation method is used and the σ-coordinate system is adopted. Turbulence is modeled by a dynamic coherent eddy model. The σ-coordinate transformation is introduced to map the irregular physical domain with a wavy free surface and an uneven bottom onto a regular computational domain. The fractional step method is used to solve the fil...  相似文献   

11.
The dynamic response of multiple coplanar interface cracks between two dissimilar piezoelectric strips subjected to mechanical and electrical impacts is investigated. Solutions to two kinds of electric boundary conditions on crack surfaces, i.e. electric impermeable and electric permeable, are obtained. Laplace and Fourier transforms and dislocation density functions are employed to reduce the mixed boundary value problem to Cauchy singular integral equations,which can be solved numerically. The effects of electrical load, geometry criterion of piezoelectric strips, relative location of cracks and material properties on the dynamic energy release rate are examined.  相似文献   

12.
徐燕  杨娟 《力学季刊》2022,43(1):149-158
基于线性磁电弹性理论,利用Schwarz-Christoffel(CS)变换技术和Stroth公式,首次系统研究了压电压磁复合材料中含带两个不对称裂纹的正六边形孔口问题在部分渗透磁电边界条件下的解析解.当忽略磁场时,磁电非渗透裂纹和磁电渗透裂纹两种极端情况下的解析解答可退化为文献已有研究结果.数值结果揭示了正六边形孔口尺寸、裂纹长度以及力电载荷和磁载荷对能量释放率的影响规律.研究结果表明:减小孔口边长和裂纹长度可以提高材料的可靠性;机械载荷总是促进裂纹扩展;在磁电非渗透和磁电部分渗透边界条件下,负电场和负磁场会延缓裂纹的扩展,而正电场可以增强或阻碍裂纹的扩展,这取决于所施加的电场和磁场的强度以及机械载荷的水平;在磁电渗透边界条件下,电场和磁场对裂纹的扩展没有影响.  相似文献   

13.
先分析理想裂纹面电边界条件(包括导通型裂纹和不导通型裂纹),然后分析缺陷的厚度及其对尖端场的影响,用封闭形式的解表示出了缺陷厚度的影响.结果指出,裂纹长厚比对计算结果是有影响的,除非裂纹极扁,不可通裂纹边界条件可以给出合理的结果,而可通边界条件只有在一些限制条件下才适用。  相似文献   

14.
The plane problem of a Griffith crack steadily propagating in an anisotropic piezoelectric medium is investigated through an analytical approach which is new in this topic. Complete solutions are provided in the subsonic regime under permeable and impermeable boundary conditions and the combined effects of mechanical and electrical far-fields are pointed out.  相似文献   

15.
There are three types of cracks: impermeable crack, permeable crack and conducting crack, with different electric boundary conditions on faces of cracks in piezoelectric ceramics, which poses difficulties in the analysis of piezoelectric fracture problems. In this paper, in contrast to our previous FEM formulation, the numerical analysis is based on the used of exact electric boundary conditions at the crack faces, thus the common assumption of electric impermeability in the FEM analysis is avoided. The crack behavior and elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and coupled mechanical-electrical loads with different electric boundary conditions on crack faces are investigated. It is found that the dielectric medium between the crack faces will reduce the singularity of stress and electric displacement. Furthermore, when the permittivity of the dielectric medium in the crack gap is of the same order as that of the piezoelectric ceramic, the crack becomes a conducting crack, the applied electric field has no effect on the crack propagation. The project supported by the National Natural Science Foundation of China (19672026, 19891180)  相似文献   

16.
In this paper the dynamic anti-plane problem for a functionally graded magneto-electro-elastic strip containing an internal crack perpendicular to the boundary is investigated. The crack is assumed to be either magneto-electrically impermeable or permeable. Integral transforms and dislocation density functions are employed to reduce the problem to Cauchy singular integral equations. Numerical results show the effects of loading combination parameter, material gradient parameter and crack configuration on the dynamic response. With the magneto-electrically permeable assumption, both the magnetical and electrical impacts have no contribution to the crack tip field singularity. However, with the impermeable assumption, both the applied magnetical loads and electrical loads play a dominant role in the dynamic fracture behavior of crack tips. And for the two kinds of crack surface conditions, increasing the graded index can all retard the crack extension.  相似文献   

17.
The dynamic response of an interfacial crack between two dissimilar magnetoelectroelastic layers is investigated under magnetic, electrical and mechanical impact loadings. Four kinds of ideal crack-face assumptions, i.e., magnetoelectrically impermeable (Case 1), magnetically impermeable and electrically permeable (Case 2), magnetically permeable and electrically impermeable (Case 3) and magnetoelectrically permeable (Case 4), are adopted separately. The dynamic field intensity factors and energy release rates are derived. The effects of loading combinations and crack configurations especially for the former on the dynamic response are examined according to energy release rate criterion. The numerical results show that, among others, a negative magnetic (or electrical) loading is generally prone to inhibit the crack extension rather than a positive one for a magnetically (or electrically) impermeable interfacial crack. Results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures.  相似文献   

18.
In the present study, an I-integral method is established for solving the crack-tip intensity factors of ferroelectric single-crystals. The I-integral combined with the phase field model is successfully used to investigate crack-tip intensity factor variations due to domain switching in ferroelectricity subjected to electromechanical loadings, which exhibits several advantages over previous methods based on small-scale switching. First, the shape of the switching zone around a crack tip is predicted by the time-dependent Ginzburg–Landau equation, which does not require preset energy-based switching criterion. Second, the I-integral can directly solve the crack-tip intensity factors and decouple the crack-tip intensity factors of different modes based on superimposing an auxiliary state onto an actual state. Third, the I-integral is area-independent, namely, the I-integral is not affected by the integral area size, the polarization distributions, or domain walls. This makes the I-integral applicable to large-scale domain switching. To this end, the electro-elastic field intensity factors of an impermeable crack in PbTiO3 ferroelectric single crystals are evaluated under electrical, mechanical, and combined loading. The intensity factors obtained by the I-integral agree well with those obtained by the extrapolation technique. From numerical results, the following conclusions can be drawn with respect to fracture behavior of ferroelectrics under large-scale switching. Under displacement controlled mechanical loading, the stress intensity factors (SIFs) decrease monotonically due to the domain switching process, which means a crack tip shielding or effective switching-induced toughening occurs. If an external electric field is applied, the electric displacement intensity factor (EDIF) increases in all cases, i.e., the formed domain patterns enhance the electric crack tip loading. The energy release rate, expressed by the crack-tip J-integral, is reduced by the domain switching in all examples, which underlines the switching-induced-toughening effect. In contrast, under stress controlled load, the SIF evolves due to large-scale switching to a stable value, which is higher than the non-switching initial value, i.e., fracture is promoted in this case.  相似文献   

19.
This paper investigates the interaction problem between a dislocation and a finite crack in piezoelectric media. Analytical solutions for the generalized two-dimensional problem of a dislocation that is interacting with a finite crack in piezoelectric media are formulated via Stroh formalism. The analysis is conducted on the unified electrical crack boundary condition with the introduction of the electric crack condition parameter that can describe all the electric crack boundary conditions. The two ideal crack boundary conditions, namely, the electrically impermeable and permeable crack assumptions are obtained as two special cases for the current solutions. Based on the complex variable method and the perturbation technique, closed form solutions are obtained. The field intensity factors at the crack tip and the image forces on the dislocation due to the crack are computed and discussed.  相似文献   

20.
吉兵  崔元庆 《力学季刊》2019,40(2):274-282
基于文献中报道的试验结果,本文考虑非均匀的畴变过程区,它包含一个位于中心的饱和区和环绕饱和区的渐变区.为了描述外加应力引起的部分铁弹畴变,本文采用一个显式的基于最小能量原理的非均匀畴变准则.考虑离面极化的压电陶瓷,假设其初始极化矢量平行于离面方向.畴变后的电畴位于面内,具体方位由最大释放功来确定.基于非均匀畴变准则,本文给出了裂尖处非均匀畴变区几何及畴变体积分数的分布.并在静止裂纹和稳态扩展裂纹两种特殊情况下计算了铁弹畴变对裂尖处应力强度因子的影响.结果表明:(1) 静止裂纹尖端处的畴变减小了材料的起裂强度;(2) 准静态稳态裂纹附近的畴变增加了材料的断裂强度.且理论预测的R曲线渐近值与试验结果定量吻合.  相似文献   

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