A Study On Finite Deformation Elasto-Plastic Theory And Numerical Methods Of Continuum,Beam And Shell

In resent years, the nonlinear study of geometry and material has been a focus of mechanics field. Based on the analysis of present papers, we offer a new finite deformation elasto-plastic theory and algorithms.Generally speaking, the metal material will keep its volume unchanged in the plastic state. Accordingly, the first invariant I~ of the strain tensor will be zero in the infinitesimal plastic theory. While in the finite deformation theory, the first invariant of the commonly used Green桳agrangian strain, I = 0 is not equivalent to the dilatation equals zero. This will bring large difficulty to the finite deformation plastic theory. But we prove that the first invariant of the logarithmic strain fulfills this requirement exactly in chapter three. Therefore the logarithmic strain measure is adopted and the infinitesimal plastic theory is transplanted to establish the finite deformation plastic theory.Normally, elasto-plastic algorithms consist of two parts: the first part is the elasto-plastic integral algorithm. To this part, We also reform the infinitesimal elasto-plastic consistent algorithm presented and form the finite deformation elasto-plastic consistent algorithm with first-order accuracy.To the second part, Firstly, this paper introduces an important idea of separating displacement freedom and rotational freedom from node freedom in finite element arc-length method in chapter five. Secondly we also introduce the new dimensionless method~ automatically incremental adjustment modulus and the criterion of discriminating limit point. Finally, we propose a practical arc-length algorithm on the base of previous methods.To the characters of beam, plate and shell structures, this paper develops a two-dimensional Timoshenko beam elasto-plastic finite deformation theory based on logarithmic strain by combining the elasto-plastic theory in chapter three and two dimensional accurate beam theory, at the same time, this paper develops a relative freedom elasto-plastic finite deformation theory based on logarithmic strain by combining the elasto-plastic theory in chapter three and the concept of relative freedom.Finally, the elasto-plastic finite deformation theory based on logarithmic strain is proved to be valid and efficient by several numerical examples.