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本文研究弹性体接触问题,这个问题属于小变形几何非线性问题,它的非线性是由于接触点的接触状态所引起的. 本文提出的二次规划法适用于求解此类非线性问题。首先从理论上研究涉及两个物体的弹性接触问题,把这种问题从数学上归纳为一个标准的二次规划的公式,并导出这类问题解的必要和充分条件。籍助于有限元素法来产生所研究物体的弹性特性数据,并运用二次规划算法来得到具有复杂几何形状问题的数值解.文中介绍了数值例子及其与试验结果的比较,表明该方法是可靠而实用的,且有很高的精度。
In this paper, we study the problem of elastic body contact, which belongs to the problem of small deformation geometric nonlinearity, and its nonlinearity is caused by the contact state of the contact point.The quadratic programming method proposed in this paper is suitable for solving such nonlinear problems. Firstly, the problem of elastic contact involving two objects is theoretically studied. The problem is mathematically summed up as a standard quadratic programming formula, and the necessary and sufficient conditions for solving such problems are derived. The finite element method is used to generate the elastic property data of the studied object and the quadratic programming algorithm is used to get the numerical solution with complex geometry problems.The numerical examples and comparison with the experimental results are presented, Reliable and practical, and with high accuracy.