强奇异积分方程小波Petrov-Galerkin快速算法

通过构造具有高阶消失矩、小支集和半双正交性质的分片多尺度小波基底,给出第2类强奇异积分方程的小波Petrov-Galerk in快速算法,并证明该算法收敛阶达到最佳,条件数有界,计算复杂性几乎最佳。

一类多节对偶积分方程组正则化为超(强)奇异积分方程组求解法

基于Mellin变换法,首先方程组进行Mellin变换,然后,通过引入新的未知函数的Mellin变换代换原来未知函数的Mellin变换,使对偶积分方程组退耦正则化为超(强)奇异积分方程组．将未知函数分解并表示成未知函数和已知幂函数的乘积,幂指数(a_i,v_i)需使超(强)奇异积分方程组中的超(强)奇异积分,在端点(a_i,b_i)有界或可积奇异,求解超(强)奇异积分方程组可以使用有限部分积分式．将未知函数展成任意完备函数系(?)_n*(u)的级数,将超(强)奇异积分方程组,化成线性代数方程组,通过求解级数中的各项系数,由此给出对偶积分方程组的一般性解．并严格证明了对偶积分方程组和由它化成的超(强)奇异积分方程组的等价性,解的存在性和解的表示形式不唯一性．本文给出的理论解和解法,可供求解数学,物理,力学中的混合边值问题应用．

Two coplanar cracks in a functionally graded piezoelectric material strip under mechanical and transient thermal loadings

In this paper,the fracture problem of a functionally graded piezoelectric material strip(FGPM strip) containing two coplanar cracks perpendicular to its boundaries is considered.The problem is solved for an FGPM strip that is suddenly heated from the bottom surface under static mechanical loading.The top surface is maintained at the initial temperature.The crack faces are supposed to be completely insulated.Material properties are assumed to be exponentially dependent on the distance from the bottom surface.By using the Laplace and Fourier transforms,the thermoelectromechanical fracture problem is reduced to a set of singular integral equations,which are solved numerically.The stress intensity factors for the cases of the two embedded cracks,two edge cracks,and an embedded crack and an edge crack are computed and presented as a function of the normalized time,the nonhomogeneous and geometric parameters.