The Variational Principles In Plasticity And Their Applications

Three main aspects of plastic mechanics are discussed in the paper, which are upper bound theorem and lower bound theorem, the variational principles and generalized variational principles in increment strain theory, and the variational principles and generalized variational principles in total strain theory respectively. In chapter 3, theorem of upper and lower bound are deducted using the principle of virtual power, and we give a further discussion about the situation in which the velocity on the boundary of velocity does not equate to zero, what is more, the expressions of the upper and lower bounds of total forces on the velocity boundary are obtained by the method of enlarging and reducing in this paper. Then in the next chapter, the variational principles and generalized variational principles in increment strain theory are deducted in chapter 4 using the variational integral which is more meaningful in physics, instead of using the classical method of introducing into Lagrange multipliers. At last, in chapter 5, the variational principles and generalized principles in total strain theory are obtained by the method which is similar with that in chapter 4. However, what is different from the other methods of deducting the variational principles and generalized principles in total strain theory is that we deduct them using the differential relationship between stress and function of density of strain energy on the basis of some other fundamental equations and so the charm of variational principles is shown to us from another view by this way. Of course some examples are given in order to throw us more lights on the understanding of these theorems and principles we obtain or deduct in the paper.