The finite element method
Overall, the role of boundary conditions, as they exist in the form of mathematical equations, is to further constrain the problem, which better approximates the actual value using the FEM. However, setting the optimum boundary conditions is very tricky even for the most experienced engineer, as an over or under constrained model is useless in the pursuit of precision. Thus, the finite element method is an iterative process, meaning that continuous approximation of the problem is required to increase the accuracy of the model and set ‘ correct ’ boundary conditions. And through countless rounds of computational analysis and resetting with small changes, the optimum approximated solution can finally be obtained. 20 Alas, my investigation into the finite element method is far from complete. Although this numerical method can never calculate a fixed answer for a problem, its accuracy and applicability in almost all areas of engineering is fundamental for many different theoretical models that are adapted to specific fields such as computational fluid dynamics. Finally, through an overall understanding of the FEM, the iterative approximation method of complex real-world models can reduce the time and cost of physical testing and, therefore, is an invaluable resource in the field of engineering.
https://www.simscale.com/docs/simwiki/numerics-background/what-are-boundary-conditions/. Consulted: 12/8/2024. 20 Murad (n. 3).
102
Made with FlippingBook flipbook maker