Engineers use the Finite Element Method (FEM). This method is essential for every engineer. FEM has become a standard part of structural analysis. FEM is not just used for daily analyses, but also to optimize structural designs. FEM tools let us quickly test different design variants. Our design can be optimized. When I say optimization, what I really mean is mass reductions in our structure. Mass saving in structures today leads to lower transportation and product costs. It is important that structural engineers use FEM. It is a time-saver, allows quick changes to designs, and can be used to produce a lean end product. The FEM will be analyzed mathematically and implemented in java in order to plot profiles of temperature distribution.
Calculate and plot temperature distribution over the domain. We will trace the distribution of temperature for each case. We have selected the right portion because we are only able to do the calculations in one of two directions. We can only calculate the upper section because the heat is only moving in the x axis direction. The heat flow vector is proportional with the temperature gradient minus. Because the heat flux is perpendicular, the following results are logical.
The temperature distribution graphs do not allow us to determine which profile is the most thermally resistant. The thermal resistance is global, but the temperature distribution is local. Calculate the thermal resistivity for the hollow walls in various configurations. By definition, the profile which has the highest thermal resistivity is the best. The profile with the highest thermal resistance is Case C, which has a value of R=2677K/W.
It is important to also consider the profile’s mechanical resistance. The profile which has the greatest airspace, is the best at insulating (air being a better insulator than the profile’s material), but is also the fragile. We must find a balance between insulation and mechanical strength. We can vary the dimensions a b c d to find the optimal profile.
Using the best dimensions, we calculate the highest value of thermal resistance. Examine the effect of density on convergence and time computation. The resistance is a good indicator of convergence. If it doesn’t change if you increase the dichotomy value, then we are at convergence. The error “OutOfMemoryError” prevents us from reaching convergence. Our code is not efficient in memory usage. The graphs are clearly horizontal.
This value represents the thermal resistance. The temperature profile is drawn inside the hollow walls between two points. This figure represents a temperature curve with a constant y=1 in case c. The L profile being symmetrical, the temperature from x=-10 up to x=0 is also symmetrical. We are now interested in a problem involving electrokinetics. The problem studied is an L-shaped L-shaped electric conductor. Calculate its resistance by using code. The equations for electrokinetics and thermals are exactly the same.
Our code can be reused as long as the mathematics remain the same. You can create a connection between:
Temperature & Voltage
Heat fluxes and currents
Thermal resistance and electrical resistance
The finite-element method (FEM), also known as the functional minimization, is a technique that uses computation to solve problems described by partial differentials equations. FEM can be used to design and develop products, in particular when structural analyses are involved. Java’s object-oriented programming model makes it easy to implement FEM analyses. It is generally agreed that Java’s object-oriented programming allows for the development of well-organized finite-element applications with acceptable computation efficiency.
