GENERALIZED FINITE ELEMENT PROGRAM USING OBJECT ORIENTED METHODOLOGY

Abstract

The Finite Element Method (F.E.M) has potential of solving the entire range of engineering problems as it describes the engineering objects at various levels and converts it into convenient algebraic forms. The F.E.M. is by its nature very modular. Object oriented programming (O.O.P) enables full _advantage to be taken of this modularity. This makes for safer and easier programming. Extending or modifying object oriented programs is very straightforward. Besides this Object Oriented Methodology (O.O.M) enables the programmer to visualize the problem interms of Object, Dynamic and Functional models. In the present work, an object oriented program for a Generalized Finite Element Analysis ((IFEA) has been developed using the C++ language. This program is a general purpose F.E. Program for plane stress, plane strain and axisymmetric for both field and stress analyses problems using Lagrangian and Serendipity elements along with joint/interface elements with linear, quadratic and cubic variations. In this Simplex and Graded elements can be easily included. The concept of Generalized Modulus and Generalized Stresses involves the use of local derivatives of shape functions. The advantage of using local derivatives of shape functions is that they do not vary from element to element. They are to be calculated once for all for one parent element. Besides this, it uses generality of Serendipity shape functions which are derived from Lagrangian shape functions. The inclusion of Simplex and Graded elements is straight forward leading to a Generalized Finite Element Program (GFEP). The further extension to 3D problems is also straight forward. Pre and Post processors offer graphics modules to assist the verification of digital description of the modelled structure and the interpretation of the analyses results. Preprocessor (Meshgen, Preview) has the capability of automatic mesh generation of F.E. meshes using linear, quadratic and cubic quadrilaterals for regular and irregular meshes containing ►nesh grading facility of Lagrangian and Serendipity families with any type of joint and interface elements. Post processor can produce the deformed shape and the contour plots of the desired variables. The generation of FE program can be seen from the examples considered where it is able to solve first for temperature field for a given geometry with field boundary conditions and then apply temperature data for stress analysis with different boundary conditions with the same GFEA (Generalized Finite Element Analysis) package. This is an interactive menu driven package running without graphics on Unix-Irix environment and with graphics on DOS environment.