Finite-Element Method for Computing Fluid and Solid Mechanics Situations

In this paper, we present a variational approach that allows the Stream-Tube Method (STM) to be considered with discretized finite elements, in order to solve solid strain and fluid flow problems. The analysis concerns a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically, using the concepts of streamlines and stream tubes. The variational approach leads to eliminate the pressure in fluid flow problems and avoids developing a mixed displacement-pressure method in the case of incompressible solids. Applications are provided for fluid flow problems and also in the bending problem, in elasticity.