粘弹性接触问题的数学规划解法

主要研究粘弹性物体间的接触问题，同时考虑了刚体位移、摩擦及几何非线性等因素。导出了该问题数学规划解法的标准形式，并通过实例展示了粘弹性物体接触状态随时间的变化规律。

A Less Crude Approach to an Engineering Viscoelastic Contact Problem

When the first author was doing Ph. D. research, he actively participated in an engineering project dealing with a viscoelastic contact problem. We now present our research findings on a mathematical programming approach to such a contact problem. Our mathematical programming approach has gradually evolved and is somewhat different from other programming approaches. Of the 24 equations we used or derived,eqs.(4),(7),(11),(12),(13),(21),(23) and (24) are particularly important. These eight equations are now described in five groups: (1) Eq.(4) is the constitutive equation of viscoelastic material. (2) Eqs.(7) and (13) are discretized finite element formulations. (3) With eqs.(11) and (23), the viscoelastic contact problem can be transformed into one of mathematical programming. (4) With eqs. (12) and (24),the mathematical programming problem is further transformed into a standard linear complementarity one. (5) Eq.(21) is the generalized friction law. We took as numerical example an engineering viscoelastic contact problem idealized as shown in Fig.2. In Fig.2,body A is viscoelastic and B is elastic. Body A is under a concentrated load P =196 N. Fig.3 was obtained by our approach. The three curves in Fig.3 show the settlements at points at various distances from load P for t =0, t =0.5 s and t =1 s respectively. These results of our numerical example appear to indicate that our mathematical programming approach is effective.