“Computational Civil Engineering - "Intersections" International Journal

“Computational Civil Engineering 2005”, International Symposium 292.4 The Testing of the Two Proposed Hybrid-strain Finite ElementsThe tests of the bi-dimensional hybrid-strain finite element “HYBFLAT”, meant tothe calculation of thick plates, have been made on a great variety of models:rectangular flat plates (“a” in Figure 2), circular and ring-shaped plates (“b” inFigure 2), slabs punctually supported or supported on columns (“c” in Figure 2)and shells (curved plates) (Figure 3). For the three-dimensional hybrid-strainelement “HYBBRICK”, supplementary tests were performed on 3-D elements,such blocks (Figure 4).For the validation of the two hybrid-strain finite elements, the results werecompared to the analytical or approximate known solutions and/or solutionsdelivered by some commercial programs well qualified for structural analysis:“MSC-Nastran”, “MSC-MARC” and “ROBOT Millennium”.2.5 The Analysis of the Proposed Hybrid-Strain Finite ElementsThe analysis of the results obtained for both categories of test-problems, plane aswell as spatial, gave raise to the following conclusions:1. The results obtained with the meshes based on the two proposed finite elements,based on the hybrid-strain finite element approach, are very close or even identicalto those obtained with analytical methods, furnished by the technical literature,when the principles of the optimal discretisation are respected. For exemplificationin Figure 5 is represented the relative error of the solution given by the element“HYBFLAT” for one of the plane test-problem, considering four uniform mesheswith 2, 4, 8 and respectively 16 elements per edge.2. The results supplied by the analysis program based on the two propose finiteelements are comparable with those obtained with the reference commercialprograms for structural analysis: “MSC-Nastran”, “MSC-MARC” and “ROBOTMillennium”.3. The accuracy and the stability of the solutions is situated within the limitsaccepted in the engineering practice, even for the case of some deficient mesheswhich do not respect the classical principles of an optimal discretisation (quadraticform or close, the edges’ ratio ≤ 1.5÷ 2, the absence of sharpened angles andintrusive angles, the gradual variation of the elements’ dimensions, the refining ofthe meshes in the proximity of the singularities etc.).4. The proposed finite elements demonstrate a great robustness, being able to offerrealistic solutions even in the case of a reduced number of nodes in which areimposed the limit conditions.5. For the same degree of refinement of the meshes, the two new hybrid-strainfinite elements offer improved solutions for the stresses and the internal actions asthe structural analysis programs based on a classical displacement approach.