Elements for varying moduli, thermo-mechanical and initial strain/stress problems

Abstract

So far in this book, we have examined the difficulties experienced by the displacement approach to the finite element formulation of problems in which some strain fields are constrained. It was noticed that in order to obtain accurate solutions at reasonable levels of discretization, it was necessary to be able to modify these strain fields and use these in the subsequent computation of the stiffness matrix and also in stress recovery. The criterion governing the relationship between the various terms in the modified strain field interpolation was described as consistency — i.e. the strain field interpolations must maintain a consistent balance of its contributing terms so that the constraints that emerge after discretization are physically meaningful. This was the rule that guided the design of the elements in all our earlier chapters.