Análisis de placas sometidas a deformaciones impuestas, empleando una formulación de elementos finitos mixtos

Analysis of plates subjected to imposed deformationsusing a mixed finite element formulation

Planar plates are structural elements commonly used in engineering practice. However, their behaviour, analysis and design is not as clearly understood as for linear structural elements. Traditional structural analysis procedures normally consider deformations through equivalent mechanical actions. Conceptually, however, deformations can be included directly as geometrical actions which providea a better understanding of the strctural behaviour as well as practical advantages. Actions, as diverse from a thermal, creep and shrinkage and even prestressing can be easily considered as similar geometrical actions. Due to the bi-dimensional geometry of plates, in these structures exist an internal redundancy, which clearly is not the case for beams. Therefore, not all the systems of imposed deformations are compatible and they must satisfy some continuity conditions in order to avoid internal stresses. Even using general structures analysis techniques, such as the finite element method, the plate of analysis presents important difficulties. Here the problems arise, primarily, by the formulation of the finite elements using potential energy. The Reissner functional is an interesting alternative procedure to formulate the finite elements which allows a theoretically exact, precise and efficient analysis. Using this functional the bending moments are primary unknowns and they may be aproximated by polynomials of the same order as for the vertical displacement.