摩擦约束弹塑性基本问题和Hilbert力学函数空间

Elemental Problems in Elastoplasticity with Friction and Mechanical Hilbert Space

给出了摩擦约束线弹性、有限变形弹性、塑性全量理论和塑性流动理论等 4个基本问题的概括描述 为使所考虑的问题具有代数运算的合理性和可行性 ,给出了合理的拓扑结构和代数结构 据此 ,可以建立等价于所述 4个基本问题的摩擦约束广义变分不等原理 ,进而可进行有限元近似 。

It first summarizes four elemental problems involving linear elasticity,finite deformation elasticity,plastic deformation theory and incremental theory,and then proposes reasonable topological and algebraic structure in order to guarantee the feasibility and rightness of algebraic operation.According to this,the generalized variational inequality theory with frictional constraint equivalent to four elemental problems is established.It helps to carry through finite element approach,then generate the foundation of analysis in theory or in compute for practical problems in plastic forming with frictional constraint.