基于MLPG混合配点法的接触问题形状优化

分别介绍了接触问题和MLPG(Meshless Local Petrov-Galerkin)混合配点法的理论基础,推导了相关公式,给出了两种典型接触状态的定解条件,使用二维线性基函数,采用三次样条曲线权函数,通过移动最小二乘法插值,将MLPG混合配点法运用到接触分析中,使用罚函数法添加本质边界条件,对二维弹性接触问题的接触过程进行模拟,反复迭代得到真实的接触情况,建立了一种新的应力-位移非线性数学求解模型,结合遗传算法对实际工程接触问题进行了求解优化,给出优化结果和目标函数变化曲线,并与相关文献结果比较,验证了该方法的有效性.

Shape optimization for contact problem based on MLPG mixed collocation method

The theory of contact problem and meshless local Petrov-Galerkin(MLPG) mixed collocation method was introduced, the correlative formula was conducted, and the definite condition of two typical contact state was presented. The MLPG mixed collocation method was used in contact analysis through two-dimension linear basis function, cubic spline weight function and moving least square shape function. The essential boundary condition was imposed by penalty function method, the contact process of two-dimension elastic contact problem was simulated, real contact state was received by iteration, and a new stress-displacement non-linear mathematics solution model was proposed, engineering contact problem was solved and optimized with genetic algorithm, the optimization result and the change curve of objective function was presented. Numerical examples show that the proposed method is effective.