Bidimensional isostatic meshes in finite elements

Abstract

Current research is engaged in atomatic techniques to improve, in some sense, an already existing mesh by adding new degrees of freedom (new nodes or increasing the order of the polynomial in some elements). The objetive of this study is to find a technique to obtain a good mesh, near the optimum, starting with an initial mesh and keeping the total number of degrees of freedom. The method kwnow as steepest gradient method applied to the functional Total Potential Energy (1) allow us to obtain a new mesh better than the initial, but this technique is strongly time consuming. From a large number of analysed cases, it was observed the geometry of the optimum mesh has the node position along the isostatic lines building regular elements. The main conclusion is from an ainitial mesh it is possible analyze the problem and to obtain the isostatic lines, with this result the nodes can be regulary placed along the isostatic lines and a new analysis using the so constructed mesh produces improving results. The mesh obtained in this way is called Isometric Isostatic Mesh. In order to check the goodnes of the results, it was defined a new functional called Average Quadratic Error.