Finite element method for 2d and 3d linear elasto-stastic model Salah Alrabeei Haja Sherief Musthafa Jan 2019 Abstract This report is a final project which is part of the requirements of the course Engineering Computing (PCS911). We study the displacement, stress and strain of objects occupying two and three dimensional domains. We used P1 finite elements ( triangles and tetrahedral) for discretization. The implementation of this project is also included in detail. 1 Motivation and Background Various physical process in science and engineering can be mentioned in details of partial differential equations. Getting solutions from these equations by analytical methods for complex geometrical shapes is relatively futile. The Finite Element Method (FEM) is a numerical method to get approximate solutions to ordinary and partial differential equations, which will model physical problems in engineering and physics. FEM has found applications in fluid mechanics, thermodynamics, mechanical structure analysis and electromagnetic fields in design and performance analysis [2]. Finite element analysis is a method in engineering for the numerical analysis of complicated mechanical structures based on the properties of the material to find the stress and strain distributions, when they are subjected to loads. FEA combined with computer aided design can be used to fasten up and optimize the design and manufacturing of mechanical structures[3]. The main aim of this project is to form a finite element model to estimate an elastic mechanical response of 2D and 3D linear elastic isotropic materials. Here we are using Matlab to execute P1 finite element procedures for numerical solutions of elasticity situations. The basic five steps involved in applying FEM are : 1. Preprocessing : Dividing the problem domain into finite elements (Discretization). 2. Formulation of Elements: Development of equations for the finite elements. 3. Assembly of element equations: Achieving the equations of the whole system from the equations of the individual elements. 4. Finding the numerical solution of the equations. 5. Post processing: Finding the stress and strain, and attaining graphical representation of the solution. 1