# Benchmark Problems

## Introduction

In engineering every problem has a theoretical solution. Many, however, are unknown and for this reason numerical simulation techniques such as the finite element method are employed. There is, though, a set of problems that have known theoretical solutions. General text books on Strength of Materials or more specialist books like Timoshenko's Theory of Plates & Shells, offer the engineer a range of such problems. These are extremely useful when it comes to Software Verification and form part of the class of problems known as Benchmark Problems. There are other problems which, whilst having no known theoretical solution, have been studied in sufficient detail and usually by a number of researchers, that the numerical solution has gained sufficient provenance as to also be considered as a Benchmark Problem.

### Stress in Thin, Parallel-Sided Rotating Discs

The theoretical solution for the linear elastic stress at the centre of a thin, solid rotating disc with parallel sides is provided.