Page 173 - Visions of the Future Chemistry and Life Science

Figure 9.1. One important factor in the design of a car is protecting its occupants during collisions, known as crashworthiness. One
aim is to minimise the deceleration forces that act upon the occupants, which is achieved by making the car body absorb impact
energy by deforming in a particular way. But large deformations will result in physical intrusions into the passenger compartment,
which are also undesirable. The trick is to balance these two opposing factors, rigidity and deformability, in an efficient way. The
most cost-effective way of doing this is to use use finite-element modelling on a computer. The intact car is first divided into a
large number of small elements (discretisation). The relatively simple equations that describe the physical interactions between
adjacent elements are then formulated, taking into account the material properties of the elements. This set of equations is then
solved whilst an appropriate stimulus is applied. In this example, the stimulus is an obstacle at the front of the vehicle (simulation).
The resulting deformations and deceleration forces are then investigated in detail, in order to predict how best to modify the design
in order to improve its performance (reconstruction).
The beauty of finite-element modelling is that it is very flexible. The system of interest may be continuous, as in a fluid, or it
may comprise separate, discrete components, such as the pieces of metal in this example. The basic principle of finite-element
modelling, to simulate the operation of a system by deriving equations only on a local scale, mimics the physical reality by which
interactions within most systems are the result of a large number of localised interactions between adjacent elements. These
interactions are often bi-directional, in that the behaviour of each element is also affected by the system of which it forms a part.
The finite-element method is particularly powerful because with the appropriate choice of elements it is easy to accurately model
complex interactions in very large systems because the physical behaviour of each element has a simple mathematical description.