Fixed Grid Finite Element Analysis for 3 D Linear Elastic Structures

Fixed Grid (FG) methodology was first introduced by Garc ı́ and Steven [ 7] 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 [ 9], Genetic Algorithms (GA), and Evolutionary Strategies [ 4]. 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 media transform the problem into a multi-material elasticity problem. As a result of the subdivisionNIO elements have non-continuous properties. They can be approximated in different ways which range from simple setting of NIO elements asO to complex non-continuous domain integration. If homogeneously averaged material properties are used to approximate the NIO lement, 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.