### Theoretical base

The explicit code is based on the simple formula of F=M*A where F represents a force, M is the mass of a body and A is the resulting acceleration of that body.

All the code does is to calculate the acceleration for the body, use a small step in time to translate this acceleration into a little displacement of the body. This displacement is then used to calculate a responding force since the body is elastic and can be stretched (thus creating a reaction force). This force is then used to calculate an acceleration and then the process is repeated again from the beginning.

As long as the timestep is sufficiently small, the results are accurate.

## Literature of Interest

There are a large number of books available on Finite Element Theory. Most of them describe Finite Element from a static point of view and is therefore of limited interest to the potential Impact programmer.

On the other hand, the theory of element formulation is often usable to a large extent and having that in mind, here are a few proposals:

- Concepts And Applications Of Finite Element Analysis, Third edition - Robert D. Cook, David S. Malkus, Michael E. Plesha, ISBN 0-471-84788-7
- The Finite Element Method - Linear Static and Dynamic Finite Element Analysis - Thomas J. R. Hughes, ISBN 0-484-41181-8
- Nonlinear Finite Elements for Continua and Structures - Ted Belytschko, Wing Kam Liu, Brian Moran. ISBN 0-471-98773-5

The first book is recommended to beginners and engineers in general since it deals with most issues from a linear algebra perspective. This makes the code writing quite close to the Impact format. It is also a very good book and the one I have had best feedback from.

Ted Belytschko's book is the "bible" in this field. The man behind explicit codes have finally written a compendium on the theory and some principle algorithms are also shown. However, for an engineers perspective, this book is quite deep in its places and is more suitable as a reference than as a learning book for beginners.

There are also some papers written which are of interest:

- Explicit Algorithms For The Nonlinear Dynamics Of Shells - Ted Belytchko, Jerry I. Lin, Chen-Shyh Tsay, Computer methods in applied mechanics and engineering 42 (1984), page 225-251
- An Explicit Formulation For An Efficient Triangular Plate-Bending Element - Jean-Louis Batoz, International journal for numerical methods in engineering, Vol. 18, page 1077-1089 (1982)

These papers form the basis of coming shell element extension to Impact.