Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method

Transient thermal dynamic analysis of stationary cracks in functionally graded piezoelectric materials (FGPMs) based on the extended finite element method (X-FEM) is presented. Both heating and cooling shocks are considered. The material properties are supposed to vary exponentially along specific direction while the crack-faces are assumed to be adiabatic and electrically impermeable. A dynamic X-FEM model is developed in which both Crank–Nicolson and Newmark time integration methods are used for calculating transient responses of thermal and electromechanical fields respectively. The generalized dynamic intensity factors for the thermal stresses and electrical displacements are extracted by using the interaction integral. The accuracy of the developed approach is verified numerically by comparing the calculated results with reference solutions. Numerical examples with mixed-mode crack problems are analyzed. The effects of the crack-length, poling direction, material gradation, etc. on the dynamic intensity factors are investigated. It shows that the transient dynamic crack behaviors under the cooling shock differ from those under the heating shock. The influence of the thermal shock loading on the dynamic intensity factors is significant.     

Crack patterns corresponding to the residual strength plateau of ceramics subjected to thermal shock

The formation mechanism of the residualstrength plateau of ceramics subjected to thermal shockis addressed.A set of thermal shock experimentsof 99Al2O3 are conducted,where the thin specimensof 1 mm × 10 mm × 50 mm exhibit parallel through edgecracks,and thus permit quantitative measurements of thecrack patterns.The cracks evolve with the severity of thermal shock.It is found that there is a correlation between thelength and density of the thermal shock cracks.The increaseof crack length weakens the residual strength,whereas theincrease of crack density improves it.In a considerably widetemperature range,the two contrary effects just counteracteach other;consequently a plateau appears in the variationcurve of the residual strength.A comparison between thenumerical and experimental results of the residual strengthis made,and they are found in good agreement.This work ishelpful to a deep understanding of the thermal shock failureof ceramics.     

Multi-cracks problem for piezoelectric materials strip subjected to dynamic loading

This paper analyses and models the dynamic interaction among permeable multi-cracks in a piezoelectric strip under anti-plane shear waves by the Schmidt method. The Fourier transform is applied and then two pairs of triple integral equations can be solved using the Schmidt method. The results show that the stress and the electric displacement intensity factors of cracks depend on not only the crack length and the piezoelectric coefficient, but also the thickness of the piezoelectric strip, the distance between multi-cracks and the frequency of incident wave.     

环形激波绕射、反射和聚焦流场的间断有限元模拟

采用间断有限元方法对环形激波在圆柱形激波管内绕射、反射和聚焦流场进行了数值模拟。将二维守恒方程的间断有限元方法发展到轴对称Euler方程,并对环形激波绕后台阶流动进行了数值计算。计算结果表明,采用间断有限元方法能够有效地捕捉运动激波在圆柱形激波管内传播的复杂流场结构;在聚焦点附近,数值解具有较大的梯度变化,表明该方法对间断解具有较强的捕捉能力,在聚焦点附近不会产生振荡或抹平间断现象。     

Dynamic effective property of fibrous piezoelectric composites with spring- or membrane-type imperfect interfaces

The present paper studies the dynamic effective property of piezoelectric composites embedded with cylindrical piezoelectric fibers under anti-plane harmonic electro-elastic waves. By using the dynamic generalized self-consistent method (DGSM) of electro-elastic coupling wave, the problem of randomly distributed cylindrical fibers in a piezoelectric medium can be analyzed in terms of a representative volume element with a coated fiber embedded in an equivalent effective medium. The interfaces between the fibers and the matrix are assumed to be imperfect which are here modeled as spring- or membrane-type interfaces. Through wave function expansion method and an iterative method, the effective piezoelectrically stiffened shear modulus and the effective wave number are obtained. Examples are conducted to verify the present solutions and to illustrate the dependence of the effective piezoelectrically stiffened shear modulus on the wave number (frequency) as well as the interface properties. The special size effect related to interfacial imperfection is also discussed.     

激波聚焦诱导点火和爆轰的数值研究

以二维轴对称多组分Euler方程为基础,采用非正交结构化网格和改进的波传播算法,模拟了激波在抛物形反射壁面聚焦反射诱导点火和爆轰的过程,描述了其流场形态。讨论了预混气组成、入射激波强度及反射壁面形状对点火和爆轰的影响。结果表明,激波在抛物形反射壁面顶点处聚焦反射可形成局部高温高压区域,该区域在一定条件下可点燃预混气甚至形成爆轰,其中低稀释剂浓度的预混气、较大的入射激波Mach数和较深的反射壁面有利于可燃预混气形成爆轰。     

Numerical investigation of toroidal shock wave focusing in a cylindrical chamber

In this paper, focusing of a toroidal shock wave propagating from an annular shock tube into a cylindrical chamber was investigated numerically with the dispersion controlled dissipation (DCD) scheme. The first case for an incident Mach number of 1.5 was conducted and compared with experiments for validation. Then, several cases were calculated for higher incident Mach numbers varying from 2.0 to 5.0, and complicated flow structures were observed. The numerical study was mainly focused on two aspects: focusing process and flow structures. The process, including diffraction, focusing, and reflection, is displayed to reveal the focusing mechanism, and the flow structures at different incident. Mach numbers are used to demonstrate shock reflection styles and focusing characteristics. PACS 47.40.Ki; 47.40.Nm; 52.35.Tc     

Dynamic anti-plane shear of a cracked piezoelectric ceramic

The dynamic theory of antiplane piezoelectricity is applied to solve the problem of a line crack subjected to horizontally polarized shear waves in an arbitrary direction. The problem is formulated by means of integral transforms and reduced to the solution of a Fredholm integral equation of the second kind. The path-independent integral G is extended here to include piezoelectric effects, and is evaluated at the crack tip to obtain the dynamic energy release rate. Numerical calculations are carried out for the dynamic stress intensity factor and energy release rate. The material is piezoelectric ceramic.     

Dynamic analysis of an axially moving plate subjected to thermal loading

Dynamic analysis of axially moving thermally loaded two-dimensional system is presented in this paper. Using the Hamilton's principle, the differential equation of the transverse motion of the moving plate is derived. Using the extended Galerkin method the approximate solution is determined in this work. To verify the present approach, the calculation results of buckling thermal load for stationary plate are compared with the results published in literature. Dynamic analysis of axially moving aluminum plate subjected to thermal loading is presented. Besides the thermal critical loading the effects of transport speed and axial tension on dynamic behavior of axially moving aluminum plate are presented.     

用环形激波聚焦实现爆轰波直接起爆的数值模拟

利用基元反应模型和有限体积法对环形激波在可燃气体中聚焦实现爆轰波直接起爆进行了数值模拟。研究结果表明,标准状态下的氢气-空气混合气体在马赫数为3.1以上的环形激波聚焦产生的高温高压区作用下会诱发可燃气体的直接起爆形成爆轰波,爆轰波与激波和接触间断相互作用产生了复杂的波系结构;爆轰波爆点位置在对称轴上并不是固定的点,而是随着初始激波马赫数的变化而发生移动;可燃气体初始温度和压力对起爆临界马赫数都有影响,但是初始温度的影响大得多。     

承压热冲击下反应堆压力容器的塑性失效分析

承压热冲击(PTS)使反应堆压力容器(RPV)的完整性面临极大的挑战,尤其是在喷嘴周围的环带区.考虑到瞬态温度处于零韧性参考温度之上,引入非线性材料性能来模拟一个真实RPV的混合温度场和应力场.应用扩展有限元法对喷嘴区中的裂纹扩展过程进行模拟,并得到了承压热冲击下的临界裂纹尺寸.结果显示,PTS初期的热应力效应显著,后期热-机械耦合作用产生的峰值应力很可能会引起结构失效.应用直接和间接耦合法得到的数值结果吻合,且后者的计算效率较高.在塑性极限承载状况下,裂纹尖端在靠近内壁的位置容易产生扩展.离内壁较远的裂纹尖端由于受热冲击影响较小,发生裂纹扩展的可能性相对较低.随着基体墙厚度的减小,容许的裂纹尺寸急剧缩小,接近临界承载状态时稳态裂纹扩展的程度明显降低.     

环形激波聚焦流场特性的数值研究

针对环形激波聚焦过程产生的高温、高压特性,采用间断有限元方法模拟了环形激波在同轴圆柱形激波管内的聚焦流场特性。计算结果表明,采用间断有限元方法能够有效地捕捉激波聚焦过程形成的二次激波、涡环、三波交点和球面双马赫反射等主要流动特征。此外,通过改变环形管道内外半径对聚焦流场进行模拟发现,环形管道外径对中心轴线上聚焦峰值压力的大小和位置影响较小,环形管道内径对中心轴线上聚焦峰值压力的大小和位置影响较大。计算结果可以为工程应用提供一定的理论指导。     

爆炸冲击波作用下围岩与被覆结构的动力相互作用

爆炸作用下围岩与被覆结构的动力相互作用对于合理确定防护结构荷载、科学设计被覆结构具有重要意义。运用ANSYS/LS-DYNA非线性显式动力有限元程序和流-固耦合算法,对垂直爆炸作用下不同爆距、不同跨度的地下结构与围岩的动力相互作用进行了数值模拟,应用波动理论进行了动力相互作用力分析,讨论了相互作用动载计算公式在岩石结构中的适用性,得到了围岩与被覆结构的最大相互作用力变化规律。研究结果表明:在距拱顶1~25 m垂直爆炸作用下,14~25 m跨地下结构都发生了拱顶局部破坏,整个拱的混凝土均会产生震动裂缝;当爆距为4 m时,围岩与结构的动力耦合作用最大,可以作为确定最大荷载的依据。     

Comments on ‘‘Dynamic crack propagation in piezoelectric materials—Part I. Electrode solution’’ by Shaofan Li, Peter A. Mataga [J. Mech. Phys. Solids 44 (1996) 1799-1830]

In this comment, it is pointed out that the paper [Li and Mataga, 1996. J. Mech. Phys. Solids 44, 1799-1830], which presents original and valid solution strategy for an important problem of dynamic crack propagation in piezoelectric materials, contains ultimate quantitatively and qualitatively incorrect expressions, conclusions and plots due calculation errors. The correct calculations and corresponding correct conclusions and plots are presented.     

冲击波作用下乳化炸药压力减敏的表征方法

引入一个新的物理量压力减敏程度,来更合理地表征乳化炸药发生压力减敏的难易程度,为研究其作用机理提供量化的分析工具。分别利用乳化炸药发生压力减敏前后的爆炸冲击波峰压及其对数、冲击波能量和总能量计算压力减敏程度,比较并分析计算结果的优劣。结果表明,几个参数计算的结果都能达到相近的效果,用冲击波峰压计算起来简单方便,冲击波能量计算效果较好。用冲击波参数计算的压力减敏程度能够反映乳化炸药压力减敏的本质,建议采用冲击波峰压计算压力减敏程度,在数值差别不明显时采用冲击波能量来计算。     

Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization

Converting ambient vibration energy into electrical energy by using piezoelectric energy harvester has attracted a lot of interest in the past few years.In this paper,a topology optimization based method is applied to simultaneously determine the optimal layout of the piezoelectric energy harvesting devices and the optimal position of the mass loading.The objective function is to maximize the energy harvesting performance over a range of vibration frequencies.Pseudo excitation method (PEM) is adopted to analyze structural stationary random responses,and sensitivity analysis is then performed by using the adjoint method.Numerical examples are presented to demonstrate the validity of the proposed approach.     

地下爆炸冲击波引起的基底滑移隔震建筑的动力响应

对埋置在土体中的圆形衬砌内发生意外爆炸引起的附近地表的滑移隔震建筑 (考虑了土 结构相互作用 )的动力响应进行了研究。在土 结构相互作用分析中 ,分别采用有限元、无穷元和集中质点体系建立了衬砌周围的有限土区、四周的无限土区以及基底滑移隔震建筑的计算模型 ;在基底滑移隔震分析中 ,提出了用连续摩擦力模型取代传统的库仑摩擦力模型 ,避免跟踪啮合滑移的过渡边界并可减小计算误差。通过数值模拟 6层基底滑移隔震建筑在遭受地下爆炸冲击波作用且考虑土 结构相互作用所产生的动力响应 ,分析了基底滑移隔震效果以及不同隔震参数对隔震效果的影响 ,为相关的理论研究和工程实践提供了依据。     

Dynamic thermal shock in a layered cylinder with initial interface pressure

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Dynamic stress of a circular cavity buried in a semi-infinite functionally graded piezoelectric material subjected to shear waves

The paper presents a theoretical method to investigate the multiple scattering of shear waves and dynamic stress around a circular cavity in a semi-infinite functionally graded piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary condition of the semi-infinite structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the buried depth of the cavity, the incident wave number and the nonhomogeneous parameter of materials on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of intermediate frequency and the effect increases with increasing wave number. When the nonhomogeneous parameter of materials is less than zero, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of the dynamic stress around the cavity. When the nonhomogeneous parameter of materials is greater than zero, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.