论文标题
具有层间摩擦的多层弹性系统的变化不平等：解决方案的存在和独特性和数值溶液的收敛性
Variational inequalities of multilayer elastic systems with interlayer friction: existence and uniqueness of solution and convergence of numerical solution
论文作者
论文摘要
基于路面力学的数学形态模型，构建了具有层间摩擦条件的多层弹性系统。考虑到复杂的边界条件，得出了部分微分方程的相应变分不平等，因此可以在变异框架下分析问题。首先，证明了变化不平等解决方案的存在和独特性；然后分析基于有限元方法的数值解决方案的近似误差，当有限元空间满足某些近似条件时，证明了数值解决方案的收敛性；最后，在微不足道的有限元空间中，得出数值解的收敛顺序。以上结论为解决变异不平等的框架下的多层弹性系统的位移应变问题提供了基本的理论支持。
Based on the mathematical-physical model of pavement mechanics, a multilayer elastic system with interlayer friction conditions is constructed. Given the complex boundary conditions, the corresponding variational inequalities of the partial differential equations are derived, so that the problem can be analyzed under the variational framework. First, the existence and uniqueness of the solution of the variational inequality is proved; then the approximation error of the numerical solution based on the finite element method is analyzed, and when the finite element space satisfies certain approximation conditions, the convergence of the numerical solution is proved; finally, in the trivial finite element space, the convergence order of the numerical solution is derived. The above conclusions provide basic theoretical support for solving the displacement-strain problem of multilayer elastic systems under the framework of variational inequalities.
