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1.
On the problem of crack system with an elliptic hole 总被引:1,自引:0,他引:1
The problem of cracks with an elliptic hole in an infinite plane is investigated. By introducing the fictitious loads on the
hole edge and using the Muskhelishvili method, the problem is reduced to solving a system of mixed-type integral equations
in which some are Fredholm equations but others Cauchy-type singular ones. A numerical method is suggested and can be used
for the treatment of other similar equations. The numerical results for some typical examples are given, showing that the
method is really effective. 相似文献
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压电体椭圆孔边的力学分析 总被引:5,自引:0,他引:5
基于复变函数的方法,以PZT-4材料为例,分别采用精确电边界条件和非导通电边界条件进行了远场均匀载荷作用下的横观各向同性压电体椭圆孔的力学分析并与相关结果进行对比。结果表明当椭圆孔退化为圆孔时,无论在远场作用力载荷或电载荷,两种电边界条件下的结果均能完全吻合。随着椭圆孔的愈加尖锐化,非导通电边界条件逐渐不能适用。 相似文献
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We obtain a representation of a solution of the Cauchy problem for a linear inhomogeneous differential equation with constant
coefficients and pure delay. We use special matrix functions called a delayed matrix sine and a delayed matrix cosine. They
have the form of matrix polynomials of degree dependent on the value of delay.
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Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 261–270, April–June, 2008. 相似文献
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We propose an algorithm for the construction of an asymptotic solution of the Cauchy problem for a singularly perturbed linear
system of differential equations with degenerate matrix of coefficients of derivatives in the case where the limit pencil
of matrices is singular.
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Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 271–288, April–June, 2008. 相似文献
7.
江福汝 《应用数学和力学(英文版)》1981,2(1):25-50
In this paper we deal with the Dirichlet problem for quasilinear elliptic equation with a small parameter at highest derivatives.
In case the characteristics of the degenerated equation are curvilinear and the domain, where the problem is defined, is a
bounded convex domain, we offer a method to construct the uniformly valid asymptotic solution of this problem, and prove that
the solution of this problem really exists, and being uniquely determined as the small parameter is sufficiently small. 相似文献
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In the paper, we consider a nonlinear elliptic system coming from the predator-prey model with diffusion. Predator growth-rate is treated as bifurcation parameter. The range of parameter is found for which there exists nontrivial solution via the theory of bifurcation from infinity, local bifurcation and global bifurcation. 相似文献
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In this paper, a generalized Darbo’s fixed-point theorem associated with Hausdorff measure of noncompactness is established. Then we apply this new variant fixed-point theorem to study some fractional differential equations in Banach spaces via the technique of measure of noncompactness. Many novel existence and uniqueness results for solutions are obtained under the more general conditions. 相似文献
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We establish new efficient conditions sufficient for the unique solvability of the Cauchy problem for two-dimensional systems
of linear functional differential equations with monotone operators.
Published in Neliniini Kolyvannya, Vol. 10, No. 4, pp. 560–573, October–December, 2007. 相似文献
14.
The Cauchy problem for the equation of the Burgers hierarchy is considered. The Green function for the associated linear problem is constructed. Using the Cole–Hopf transformation the solution of the Cauchy problem for the equation of the Burgers hierarchy is given. Several particular cases are considered and discussed. 相似文献
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《Comptes Rendus Mecanique》2017,345(2):153-157
Starting from the 3D Signorini problem for a family of elastic elliptic shells, we justify that the obstacle problem of an elastic elliptic membrane is the right approximation posed in a 2D domain, when the thickness tends to zero. Specifically, we provide convergence results in the scaled and de-scaled formulations. 相似文献
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The Cauchy problem for quasi-linear symmetric hyperbolic systems 总被引:2,自引:0,他引:2
Tosio Kato 《Archive for Rational Mechanics and Analysis》1975,58(3):181-205
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《International Journal of Solids and Structures》1999,36(17):2527-2540
Based on the complex potential approach, the two-dimensional problems in a piezoelectric material containing an elliptic hole subjected to uniform remote loads are studied. The explicit, closed-form solutions satisfying the exact electric boundary condition on the hole surface are given both inside and outside the hole. When the elliptic hole degenerates into a crack, the field intensity factors are obtained. It is shown that the stress intensity factors are the same as that of isotropic material, while the electric displacement intensity factor depends on both the material properties and the mechanical loads, but not on the electric loads. In other words, the uniform electric loads have no influence on the field singularities. It is also shown that the impermeable crack assumption used previously to simply the electric condition is not valid to crack problems in piezoelectric materials. 相似文献