A Non-homogeneous Finite Elastic Deformation Theory And Application

In this paper, based on the couple stress theory, and MPUA (Moment per Unit Area) theory, a finite elastic deformation theory considered micro-rotating was established according to the strain gradient theory.Firstly, the paper briefly introduces the strain gradient theory and the size effects of the development of the current situation at home and abroad as well as the significance of this issue. At the micro scale, strain gradient theory raised makes the theoretical study of plastic deformation stage of the size effects reach a very high level. But it has still the size effects in the elastic deformation stage. At present, not a very good theory to explain making the study of elastic theory have a new field.Secondly, pointed out the flaw of the MPUA theory, the MPUA theory has not only solved the problem of stubby beams, but also explained why the stress theory is only applied slender stem. But the MPUA theory makes no any explain why torsion and bending beams have couple stress. The MPUA theory itself should be contradictions when it determines the problem of stubby beams. On this basis, we analyzed fundamental reasons of the effect of micro-rotating and selfcontradiction of the equilibrium equation of the classically elastic theory. So this paper advances a theoretical viewpoint of the stress and couple stress coexisting in the infinitesimal element, a finite elastic deformation theory considered micro-rotating was established according to the strain gradient theory, and discusses the balanced differential equation, the boundary condition as well as this construction relations under the new theory viewpoint.Finally, the theory with a new perspective to be to continue to discuss the problem of torsion and bending beams, continue to discuss the couple stress in the torsion , the bending beams introduction, deducing out the new theory viewpoint of torsion , bending formula, the course analyse the size effects problem in microcosmic dimension, when the pawn materia constant and dimensioning of object are suitable well-balanced, it exists very strong size effects problem in the elastic deformation stage, this size effects is also aroused by the couple stress,but tht size effects in the elastic deformation stage is smaller than in the plastic deformation stage.