GEOMETRICALLY NONLINEAR FINITE ELEMENT ANALYSIS OF ARBITRARY THIN PLATES

Many plate structures used especially in naval and aerospace applications undergo deflections that are not small in comparison to the thickness of the plate, but they are still small compared to other dimensions of the plate, so analysis must include the effects of the large displacements on the structures. This report developed an elegant finite element formulation for analyzing the geometrically nonlinear static behavior of arbitrary-shaped thin plates. An arbitrary planform of a whole plate was mapped into a square domain where a cubic serendipity shape function represented the arbitrary geometry. An ACM plate-bending element along with the inplane deformations was considered for the displacement function. The nonlinear formulation was done in the total Lagrangian coordinate system using [N]-notation, and the nonlinear governing equations were solved by Newton Raphson iterative method. It was found that the element was capable of accommodating different geometries just like isoparametric element. The efficacy of the element was shown by comparing the deflections and stresses at critical points of the plates of square, skewed, and circular geometries with previously published results.