This snippet demonstrates the polt format that I often used in Wolfram Mathematica.

Previously, the vector space $\mathbb{V}$ and three vector product operations were considered in Simple tensor algebra I and Simple tensor algebra II. But we do not talk much about the tensor. Here, the tensor will be introduced.

The vector space $ \mathbb{V}$ is introduced in Simple tensor algrbra I, several rules are provided in it. To reduce the abstract, we represent the vectors $ \boldsymbol{x}, \boldsymbol{y}$ with the scalar coefficients $ ({x_1},{x_2},{x_3})$ and $ ({y_1},{y_2},{y_3})$ in $ \mathbb{E}^3$, respectively. The composition of two vectors $ \boldsymbol{x}, \boldsymbol{y} \in\mathbb{E}^3$ is expanded by,

The vector space $ \mathbb{V} $ with the operation (+) over a field of real number $ \mathbb{R} $ is an abelian group with a scalar multiplication. So, suppose $  \boldsymbol{x} $, $ \boldsymbol{y} $ and $ \boldsymbol{z} \in \mathbb{V}$, they satisfy the following conditions:

This marks my second attempt at compiling VTK on a Mac. A month ago, I invested considerable time figuring out how to compile it using CMake and eventually succeeded. However, it’s surprisingly easy to forget the steps involved. To prevent that from happening again, I’m documenting the entire compilation process here.

This snippet posts an Excel to calculate the matrix with Euler angles. To describe the rotation of a crystal frame, commonly, we use three angles: $ \alpha$, $ \beta$, and $ \gamma$. They are also known as Bunge angles.

Convex hull is the smallest envelope that contains the points set. It is used to construct the grain in grain-based model. There are several methods to generate the convex hull data, but it may need some efforts if you want to put it into ABAQUS model. Here, I post a simple method which is suitable for programming.

This is a homework of computational nanomechanics. The basic requirement is to use the Lagrangian function to describe the motion of particles. In homework, it requires 5 particles. As an enhancement, I rewrote the code with Qt and use GNU Scientific Library(GSL) to finish the task.

Shear wall is a common structural member adopted to resist lateral forces. It is generally used to resist the wind or seismic loads. This post analyzes a typical shear wall structure under seismic loading condition. This post will not focus on the model creation since such structure can be easily created by APDL loops. I just want to put more details on applying seismic loading to the structure.