The purpose of this section of the site is to describe a simulation of a roof
support structure, but I feel that I first should introduce the method that is
used to conduct such an analysis, the finite element method.
The finite element method is a numerical technique that allows scientists and engineers to simulate the response and behavior of structures to various conditions. The finite element method came into light with the advent of the electronic computer. As computational power evolved, so did this numerical technique. The fundamental idea behind this method is to break a structure that you want to analyze up into many small pieces or elements of a well characterized geometry like a hexahedron (6 rectangular sided shape) or tetrahedron (4 triangular sided shape) for which the behavior can be relatively easily described in mathematical terms to the computer. If we could mathematically predict the behavior of one of these fundamental elements to arbitrary forces applied to its corners, then we could solve problems for complex geometries merely by breaking the geometry up into these characterizable shapes, then coupling each individual element's mathematical description together with its neighboring elements based on their connectivity to one and other. Early on it was demonstrated that you didn't have to subdivide your geometry indefinitely to get the "right answer". In other words, the elements did not have to be infinitely small in order to realistically predict the behavior of the structure; they were finite in size. Therefore, the term finite elements is used. In fact, many problems can be accurately solved using only a handful of finite elements.
Some typical applications of this method would be to simulate the response of a bridge to an earthquake, how a microwave oven heats food, how a vehicle crumples during a collision, how a firearm performs during firing, or something as simple as how far the tip of a diving board deflects when a person is standing at the end of it.
The finite element method has been combined with other numerical techniques to enable new technologies. For example, if we want to design the lightest possible bicycle frame that will still properly perform (won't break and will be rigid enough), we could start out with an initial design, apply the expected forces to it, find out how stiff it is and how close to failure it is, then slightly modify a thickness, length or radius here and there, then find out if it gets lighter and still satisfies its design criteria. If it does, keep changing the thickness, length or radius in the same manner as before until we reach the limit. If we can automate the process, and make it intelligently modify parameters that seem to help, then we can run a series of simulations improving the design each time and end up with a much lighter and therefore much faster bicycle that will not break. This is called design optimization, and it is revolutionizing the design of just about everything. Recent advances in computer performance have made this possible; previously, each simulation would take so long that it wasn't possible to conduct the number of simulations required to optimize a design.
As computers get faster and cheaper, engineers have been able to increase the complexity of their models which unties their hands and allows them to investigate increasingly complex phenomena and ultimately design better products.
Anyway, this is what I do for a living, and I’ve put together a few
pages that describe the application of the finite element method to a roof
truss structure in my dad’s warehouse.
