This document discusses computer aided engineering and finite element analysis. It introduces computer aided engineering tools like pre-processors, solvers, and post-processors used in product development. It also discusses one-dimensional, two-dimensional, and three-dimensional elements used in finite element analysis. Finally, it covers shape functions, coordinate systems, and nodal unknowns which are used to relate field variables within an element to the values at its nodal points.

1. Computer Aided Engineering
Unit - I

2. Unit 1 Elemental Properties
Introduction to Computer Aided Engineering (CAE), Use of CAE
in Product development, Discretization methods Finite Element
Method (FEM), Finite Difference Method (FDM) and Finite Volume
Method (FVM), CAE Tools- Pre-processor, Solver and Post-
Processor.
Element Shapes 1D, 2D and 3D elements, Nodal Unknowns and
field variables, Coordinate Systems, Shape Functions- linear,
quadratic and cubic, Convergence Requirements of Shape
Functions, Derivation of Polynomial Shape Functions using
coordinate systems for Bar, Beam, Triangular, and rectangular
elements.

3. Element Shapes - 1D, 2D and 3D elements
Based on the shapes elements can be classified as
(i) One dimensional elements
(ii) Two dimensional elements
(iii) Axi-symmetric elements and
(iv) Three dimensional elements.

5. Axi-symmetric element

6. Lagrange Rectangle Element
Serendipity Rectangle Elements

7. Node

8. Basic unknowns may be displacements for stress
analysis, temperatures for heat flow problems and the
potentials for fluid flow or in the magnetic field
problems.
Nodal Unknowns

9. (i) Global coordinates
(ii) Local coordinates and
(iii) Natural coordinates.
Coordinate System

10. In the finite element analysis aim is to find the field variables
at nodal points by rigorous analysis, assuming at any point
inside the element basic variable is a function of values at
nodal points of the element. This function which relates the
field variable at any point within the element to the field
variables of nodal points is called shape function. This is also
called as interpolation function and approximating function.
Shape Function