面外剪切下各向异性三相椭圆夹杂中均匀应力

论证了只要合适选择中间界面层的弹性常数, 各向异性线弹性固体在远场均匀反平面剪切应力作用下三相椭圆夹杂内椭圆上仍存在均匀应力场. 讨论了内外两椭圆除过其中心相同外无其它任何几何限制条件. 所给出的数值算例显示出该结论的正确性. 该方法为纤维增强复合材料的设计提供了一条新途径.     

含椭圆夹杂正交各向异性体的界面应力研究

本文研究了远场作用反平面载荷时含椭圆夹杂正交各向异性体的界面应力分布规律.利用解析函数边值问题理论和共形映射技术,推导了反平面载荷下含椭圆夹杂正交异性体的精确解,获得了夹杂和基体内应力场的闭合解,并通过有限元结果验证了本文解析解的有效性.研究表明:基体材料主方向弹性模量比C55/C44和夹杂形状比γ对界面应力影响显著;基体材料主方向模量比C5JC44对界面应力的影响受夹杂/基体模量比Cf/C44的限制.     

弹性椭圆夹杂纵向剪切问题

获得纵向剪切下弹性椭圆夹杂问题的精确解。将复变函数的分区全纯函数理论,Cauchy型积分和Riemann边值问题相结合,求得各复势函数之间的解析关系,从而得到问题的封闭形式解,并给出了界面应力的解析表达式。本文解答与已有文献结果一致。本文发展的分析方法,为求解复杂多连通域的平面弹性问题提供了一条有效途径。     

各向异性材料界面共线刚性线夹杂的反平面问题

研究两种各向异性材料焊接界面含共线刚性线夹杂的反平面问题,导出了一般问题的公式和几个典型问题的封闭形式解,求出了刚性线尖端的应力分布.从文中解答的特殊情况,直接导出各向同性材料界面与均匀各向异性介质中相应问题的公式与结果,并与有关文献相一致.     

集中力作用下含尖孔无限域的反平面剪切问题

论文采用了一种新的方法求解含孔元发域的反平面剪切问题，以闭合形式导出了在集中力作用下，孔口尖点的应力强度因子表达式。同时，给出了对称翼状尖孔、内摆线状尖孔、震状尖孔及圆孔径向边裂纹的应力强度因子，其结果在理论上和应用中都具有重要的意义。     

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

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ELECTRIC FIELD GRADIENT EFFECTS IN ANTI-PLANE PROBLEMS OF A CIRCULAR CYLINDRICAL HOLE IN PIEZOELECTRIC MATERIALS OF 6 mm SYMMETRY

We study electromechanical fields in the anti-plane deformation of an infinite medium of piezoelectric materials of 6 mm symmetry with a circular cylindrical hole. The theory of electroelastic dielectrics with electric field gradient in the constitutive relations is used. Special attention is paid to the fields near the surface of the hole.     

一种考虑层间位移和横向剪应力连续条件的层合板理论

本文建立了一种新的层合板理论。该理论满足层间位移和横向剪应力连续条件以及上下表面横向剪应力协调条件，其控制方程仅包含五个未知量。数值算例表明该理论具有很高的精度。     

ELASTIC CALCULATION OF STRESSES IN RINGS USING AIRY STRESS FUNCTION

Stress calculation formulae for a ring have been obtained by using Airy stress function of the plane strain field with the decomposition of the solutions for normal stresses of Airy biharmonic equation into two parts when it is loaded under two opposite inside forces along a diameter. One part should fulfill a constraint condition about normal stress distribution along the circumference at an energy valley to do the minimum work. Other part is a stress residue constant. In order to verify these formulae and the computed results, the computed contour lines of equi-maximal shear stresses were plotted and quite compared with that of photo-elasticity test results. This constraint condition about normal stress distribution along circumference is confirmed by using Greens’ theorem. An additional compression exists along the circumference of the loaded ring, explaining the divorcement and displacement of singularity points at inner and outer boundaries.     

A NUMERICAL METHOD OF MODELING ELASTIC WAVE PROPAGATION IN ANISOTROPIC MEDIA

The velocity-stress finite-difference method is adopted to simulate the elastic wave propa-gation in azimuthal anisotropic media.The difference grids are completely staggered in the numerical im-plementation.To reduce the computational work,the absorbin8 boundary conditions for anisotropic mediaare introduced first and the corner points are specially treated.Examples show that more accurate resultscan be obtained from the modeling algorithm,which cost much less computational time than the conven-tional methods.Therefore,the algorithm has broad application prospects in engineering.     

INVESTIGATION OF ANTI-PLANE SHEAR BEHAVIOR OF TWO COLLINEAR CRACKS IN PIEZOELECTRIC MATERIALS BY A NEW METHOD

In this paper, the interaction between two collinear cracks in piezoelectric materials under anti-plane shear loading was investigated for the impermeable crack face conditions. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using Schmidt's method. This process is quite different from that adopted previously. This study makes it possible to understand the two collinear cracks interaction in piezoelectric materials. The authors are grateful for financial support from the Post-Doctoral Science Foundation and the Natural Science Foundation of Heilongjiang Province.     

各向异性介质中弹性波传问题的数值解法

通过运用速度－应力有限差分法研究方位各向异性介质中的弹性波传播问题，在计算实施过程中，使用了交错网格技术，为了减少计算量，首次引入了适用于各向异性体的吸收边界条件，并对角点处的吸收做特殊的处理，算例表明，该算法不仅具有较高的精度；与传统方法相比，计算时间也大为缩短，从而可望在实际中获得良好的应用前景。     

SCATTERING OF ANTI-PLANE SHEAR WAVES IN A FUNCTIONALLY GRADED MATERIAL STRIP WITH AN OFF-CENTER VERTICAL CRACK

The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack.     

SCATTERING OF HARMONIC ANTI-PLANE SHEAR STRESS WAVES BY A CRACK IN FUNCTIONALLY GRADED PIEZOELECTRIC/PIEZOMAGNETIC MATERIALS

In this paper, the dynamic behavior of a permeable crack in functionally graded piezoelectric/piezomagnetic materials is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown is the jump of displacements across the crack surfaces. These equations are solved to obtain the relations between the electric filed, the magnetic flux field and the dynamic stress field near the crack tips using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.