Fixed grid finite element analysis for 3D structural problems (2005)
Fixed Grid (FG) methodology was first introduced by García and Steven as an engine for numerical estimation of two-dimensional elasticity problems -- The advantages of using FG are simplicity and speed at a permissible level of accuracy -- Two dimensional FG has been proved effective in approximating the strain and stress field with low requirements of time and computational resources -- Moreover, FG has been used as the analytical kernel for different structural optimisation methods as Evolutionary Structural Optimisation, Genetic Algorithms (GA), and Evolutionary Strategies -- FG consists of dividing the bounding box of the topology of an object into a set of equally sized cubic elements -- Elements are assessed to be inside (I), outside (O) or neither inside nor outside (NIO) of the object -- Different material properties assigned to the inside and outside medium transform the problem into a multi-material elasticity problem -- As a result of the subdivision NIO elements have non-continuous properties -- They can be approximated in different ways which range from simple setting of NIO elements as O to complex noncontinuous domain integration -- If homogeneously averaged material properties are used to approximate the NIO element, the element stiffness matrix can be computed as a factor of a standard stiffness matrix thus reducing the computational cost of creating the global stiffness matrix. An additional advantage of FG is found when accomplishing re-analysis, since there is no need to recompute the whole stiffness matrix when the geometry changes -- This article presents CAD to FG conversion and the stiffness matrix computation based on non-continuous elements -- In addition inclusion/exclusion of O elements in the global stiffness matrix is studied -- Preliminary results shown that non-continuous NIO elements improve the accuracy of the results with considerable savings in time -- Numerical examples are presented to illustrate the possibilities of the method