# Archives

### Mesh refinement in Topology Optimization

Mesh refinement or discretization is a fundamental step in finite element analysis. In finite element analysis, the refinement of mesh is done only in those areas that are of interest (eg: the region of high stress in the stress analysis) so that to obtain good accuracy with minimum computational efforts. However, in the context of […]

### Size, Shape and Topology Optimization

Structural optimization is determining the best possible material distribution within a physical volume domain to transmit the applied load safely. To achieve this, the constraints imposed by the manufacturer and eventual use must also be considered. These may include increasing stiffness (increasing strain energy or minimizing compliance), minimizing stress levels, minimizing displacement, altering the fundamental […]

### Variational Calculus: Deriving the strong and weak form

There are many ways in which we can obtain the weak form and the strong form. We focus on the Variational Principles to derive them because FEniCS works on the variational form

### Built-in meshes in FEniCS

In FEniCS, we can either work with the inbuilt meshes or we can also import the mesh file generated in another pre-processing tool as a xdmf format. In order to create inbuilt meshes, firstly, dolfin module is imported as: Matplotlib library is used to display the mesh plots. The different types of inbuilt meshes in […]

### Boundary conditions in FEniCS

Boundary conditions (B.C.) are constraints necessary for the solution of a boundary value problem. A boundary value problem is a differential equation (or system of differential equations) to be solved in a domain on whose boundary a set of conditions is known. Boundary value problems are extremely important as they model a vast amount of […]

### A primer on shell structures

Through this post, I attempt to provide a starter pack for shell structures. This includes trying to understand their structural behaviour, a very brief overview of shell-kinematics and the basic methodology for shell analysis through FEM. The theory and implementation follows the widely popular Kirchhoff-Love theory described for thin shells (thickness/length < 20)

### Data Structure of FEM in FEniCS

Storing the element connectivity, element nodes, nodal degrees of freedom etc.. are of significant importance in any numerical package which implements finite element analysis. And this constitutes the data structure of FEM. In this post, I will try to explain how FEniCS does this.