Optimising Layups in Civil Structures
In Civil Structures, we are generally familiar with classical isotropic materials such as steel and concrete which dominate the market for most infrastructure projects. These materials are well-understood for their use cases and have been standarised through codes. They’re also homogenous and isotropic in nature which makes them predictable in their behaviour. What about an orthotropic material like Fibre Reinforced Polymers (FRP)? Despite their application in civil structures being uncommon, there is an opportunity to widely adopt this material and fully leverage its advantages. In this Blog post I will be looking at how we can fully optimise layups and their mechanical properties for structural engineering purposes.
Unlike concrete, FRP is an orthotropic material where its stiffness varies depending on the orientation. To simply put it, it’s stiffer in the fibre direction than it’s in the transverse direction. Due to this variance, more elastic parameters would need to be considered than a standard isotropic material. For instance, there are nine elastic parameters for a typical orthotropic material. However, in our case considering a unidirectional FRP, the situation is simpler. We can assume that the fibre direction is dominant, and that the effects in the thickness and width directions effectively cancel each other out. This leaves us with only five parameters to consider; two Young’s modulus, two Poisson’s ratios and one shear modulus. This is important because we would need to determine these parameters to understand the behaviour of the material.
When designing FRP, we use laminated layups stacked together in various angels to create an element. Typically, a designer has a lot of freedom on how this layup is composed. For example, if a designer opts to use a unidirectional layup, this will result in having the highest stiffness in one direction but weak in others. On the other hand, if a designer chooses a balanced laminate with an equal number of plies oriented at 0°, +45°, -45°, and 90°, it is referred to as a quasi-isotropic laminate. This is because it has the capability to bear equal loads in all directions. A figure of this is shown below.
Unidirectional layup versus and quasi-isotropic laminate.
In our example we will use the classical laminate theory (CLT) to predict how layered materials behave under different conditions i.e. how the laminate will bend, twist, or stretch when forces are applied to it. The key elastic parameters that can be determined using this theory is the elastic modulus (both longitudinal and transverse), shear modulus, and Poisson's ratio. We will use a tool developed my Delft University of Technology to calculate these parameters.
