含竖直裂纹弹性材料与梯度材料粘接的接触问题

摘要

This paper based on functionally graded materials elastic material constitutive equation, we first derive gradient material state equations in different boundary conditions, and then use the Fourier transform technology, we can transform the contact problem into the boundary value problem, establish the mathematical model. Tectonic belt of techniques of integral transform method to mixed boundary value problem for singular integral equation, and the use of Gauss-Chebyshev integral formula of singular integral equation for the computer can realize the discrete algebraic equations, work out computer programming and debugging, we can obtain the results of numerical simulation.%从功能梯度材料的弹性理论出发，首先推导出梯度材料在不同边界条件下的状态方程，进而使用Fourier变换技术将含裂纹弹性材料与梯度材料粘接的接触问题转化为边值问题，建立起该数学模型。构造带技巧性的积分变换方法将混合边值问题化为奇异积分方程，并利用Gauss—Chebyshev积分公式将奇异积分方程离散为计算机可实现的代数方程组，编制计算机程序并上机调试，得出数值模拟结果。