If someone mentions the term Photovoltaic System (PV Systems), the first thing that one would probably think about is a solar panel installed on top of the roof of a house, like the one shown below. Well, even though this equipment is undeniably the most popular worldwide, this article deals with the current and short-term situation of those huge PV Power Plants which are connected to a National Electric Grid and, therefore, participate in a National Electricity Market.
First of all, I would like to start by providing some background and a number of previous concepts that might be needed later. A simple diagram is shown below, which represents a normal grid-tied PV Plant:
I’ve noticed that a lot of people try to avoid using the four wheels of the car when they go over a speed bump. Out of curiosity, I asked some of those drivers and all of them gave me the exact same answer: “Because if you only hit the obstacle with the wheels of one side of the car, you will cause less damage to the vehicle and, besides, it is less uncomfortable for occupants”. Is that true? Let’s find out.
Let´s start from the beginning. The first thing we need to know is that cars have two axles (i.e.front and rear) and each of them has two wheels (i.e. right and left). On the other hand, speed bumpers are road obstacles which are designed to make drivers reduce the speed in certain areas and they are usually as wide as the lane. Why is that? Well, basically bumps are thought to be encountered by the two wheels of each axle simultaneously, creating a scenario known as “vertical symmetric load case”. This situation causes results in a bending moment which is applied to the structure of the car.
However, sometimes we can find some bumps which present a smaller width or even gaps. These are the situations where some drivers decide to vary the direction of the car so that the wheels of one of the sides avoid the contact with the obstacle. Therefore, only one wheel goes over the bump. Hence, the vehicle will suffer an “asymmetric vertical load case”. In other words, the automotive structure will be subjected to a torsional load, which is a worse scenario than the one introduced above since it can cause one of the wheels to lift off. I will show you how a relatively simple approach can be used to prove this statement.
One of the experimental techniques for characterising materials under the effect of high strain rates is the split Hopkinson pressure bar (SHPB) test. This week a brief introduction to the basics of this technique is covered.
If you have an engineering background, it is likely that you have come across one of the most famous testing methods for characterising materials: the tensile/compression test. In that case, a sample is usually subjected to a controlled displacement (usually in mm/min). The result is the force-displacement curve and from those results and the geometry of the sample, the determination of the stress-strain curve for the material is pretty straight forward. Despite the fact that this test can be performed for a different range of speeds, these velocities are normally quite low. In these terms, there are many cases where engineers are interested in the stress-strain curve for dynamic cases, since some materials can exhibit different behaviour depending on the strain rate (e.g. crushing of an automotive component). For that reason, in order to obtain the desired characteristic curve, other methods have to be used, such as the split Hopkinson pressure bar test.
One of the most interesting things about the SHPB test is that there is no official standard to follow. However, there are some common features with regards to the necessary equipment. In these terms, every Hopkinson bar test should have:
Two cylindrical long bars. Their length has to be big enough in order to obtain one-dimensional wave propagation. They are called incident and transmitted bar, respectively.
Fixtures to ensure that the bars are perfectly aligned and that they can freely move after an impact occurs.
Gas gun. This device is the launches a striker bar which impacts the incident bar. Hence, a controlled compressive pulse is achieved.
Two sets of strain gages. Each set should be placed in the middle of both the incident and transmitted bars.
Equipment for data acquisition (e.g. amplifiers, oscilloscopes…).
Figure 1 Schematic of the split Hopkinson pressure bar test 
When using Finite Element Analysis (FEA) for studying composite materials, one of the most used failure criterion is the one which was proposed by Hashin in 1980. This theory is included in all the main FEA packages and, probably, you are more than familiar with this particular model. However, what you might not know is that the failure criteria that you are defining is not exactly the Hashin’s one. If you want to know why, this is your place.
Since the available failure criteria at that point presented some inconsistencies, in 1980 Hashin developed a new criteria which differentiated between failure modes. His theory considered four different ways in which the material could fail:
Failure criteria for composite materials are usually classified in two categories: non-interactive and interactive theories. In literature, you can find that the main non-interactive failure criteria are the Maximum Stress Theory and the Maximum Strain Theory. However, one question arises: is the second one a non-interactive theory in reality? Let’s figure it out.
To begin with, a non-interactive failure criterion is that one which only takes into account the effect of one stress or strain component for each failure condition. In other words, it does not consider any interaction between the different components. For example, the Maximum Stress Theory considers that the material fails when one of the stress components reaches a maximum value. Hence, considering a sample loaded in tension:
Where subindex 1 refers to the fibre direction and 2 corresponds to the transverse direction. When the stress reaches the limit value (measured experimentally under uniaxial stress conditions), the material fails. It is clear how in that failure criterion only one stress component is considered for each condition.
Every time you use Finite Element Analysis you need to assign a material model to all the components. Since there are plenty of them, one question arises: which one should you use for your particular case?
To begin with, there might be more than one material model which can provide an accurate solution to your problem. However, it is likely that one of them will present some advantages when compared to the others, such as computational time or the number of parameters which have to be defined. When you have spent time working with a certain kind of material (e.g. metals) you will have gained some experience that will help you choosing between different options whenever you face a similar Finite Element model. But, what happens when you are new and you don’t know where to start?
One of the dangers of FEA is that it provides results, even if they are wrong. Hence it is the engineer’s responsibility to critically analyse and validate them. In these terms, one of the most common rookie mistakes is “hourglass”. If you want to learn what it is and how to correct it, this is your place.
To begin with, let me introduce two different concepts: underintegrated elements and fully integrated ones. Underintegrated elements are only evaluated at one single integration point, whereas fully integrated ones have more than one. In order to illustrate this idea, Figure 1 is introduced.
Figure 1 (a) Underintegrated element; (b) Fully integrated element
Some of you may have found some difficulties when trying to create a structured mesh for circular/spherical parts. For that reason, this week I’m going to write about a simple procedure that you can follow in order to solve this problem: the “Butterfly Method”.
For achieving more accurate results, it is always recommended to use quad-structured meshes. Most of the FE packages include options for meshing parts in an automatic way, where you only have to define the number (or size) of elements and the type (i.e. quad, tri or even a combination of quad+tri elements). However, when geometries include circular parts or when you are creating an sphere or a cylinder, the automatic option for creating a structured mesh is not available any more. How can we solve that? Let’s find out.
The main idea of this post is to provide an overview of the outline of a Finite Element Analysis for people who are not familiar with this engineering tool.
The starting point for every Finite Element Analysis is a real problem which has to be solved. For that purpose we have to create an idealised structure and, from that idealisation, we should be able to design a discrete model. Hence, using the Finite Element Method, a discrete solutions can be obtained for that model.
Have you ever come across the term “FEA” or “FEM” when talking about structural analysis? If you have and you still don’t understand what it means and how it works, this post is for you. Don’t be afraid, no scary equations are presented here!
Finite Element Analysis (FEA), or Finite Element Method (FEM), can be defined as a methodology for solving field problems using numerical approaches. This kind of problem needs the determination of a spatial distribution and this can be seen, for instance, as the distribution of temperature in the piston of an engine. From a mathematical point of view, a numerical solution of a field problem is defined by differential equations or by integral expressions.