Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control

The paper concerns an analysis of an equilibrium problem for 2D elastic body with two semirigid inclusions. It is assumed that inclusions have a joint point, and we investigate a junction problem for these inclusions. The existence of solutions is proved, and different equivalent formulations of the problem are proposed. We investigate a convergence to infinity of a rigidity parameter of the semirigid inclusion. It is proved that in the limit, we obtain an equilibrium problem for the elastic body with a rigid inclusion and a semirigid one. A parameter identification problem is investigated. In particular, the existence of a solution to a suitable optimal control problem is proved.     

MODELING COMPLIANT NONPENETRATION CONSTRAINT FOR VP MOTION SIMULATION

A unilateral non-penetration constraint dynamical simulation model with friction is constructed based on compliant model for mechanical system VP (virtual prototyping) simulation. This model combines computer graphics with multi-body system dynamics. It avoids handling multiplicity of solution, such as cases of no solution, multi-solution brought about by friction during traditional construction of non-penetration constraint based on rigid model. At the same time, the realism of VE (virtual environment) is improved in process of simulation. Furthermore, the valid condition of rolling and sliding unilateral contact is constituted based on singular perturbation and linear complementary theory. Finally, the compliant method is verified by an interaction between a multi-legged robot and VE.     

工程接触问题的罚优化方法与罚因子的选取

工程中接触问题普遍存在,经典的数学工具解决接触问题可以得到精确解,但适用范围有限,本文采用一种数值计算法罚函数法,从优化的角度求解接触问题,通过将接触边界的互不嵌入条件引入系统总势能,弹性接触的约束变化问题转化了优化问题,并进一步推导了罚优化法的有限元迭代控制方程,给出了求解过程,并讨论了罚因子的选择,通过算例验证了有方法的有效性。