During my previous usage of Mathematica commands to create a low-poly image with triangle patterns, I found an issue where the generated image consistently had white borders. But attempting to precisely control the image size with the crop command is useless, I have to process the image using highlight and binarization techniques. However, the issue of white borders remained unresolved. So, while I plot function graphs in Mathematica and set up grid lines, I found that the edges of the grid would often exceed the intended boundary. This resulted in the grid appearing as if it were laid over the function graph. So, I dedicated some time to search a solution and put my findings here.

Last time, when solving differential equations with Mathematica built-in solver, I found that while the precision of the solutions was great, the speed left much to be desired. To increase the calculation speed of seismic response spectra and enable the simultaneous computation of spectra under various damping ratios, we need a new method. The standard approach is the Newmark method, but this time, I explored a more conventional recursive algorithm. This method is simple and efficient in computation. Also it can provide displacement, velocity, and acceleration spectra all at once.

Previously, I calculated the velocity and displacement time histories of an earthquake wave based on its acceleration. I want to know whether it was possible to directly compute the response spectrum of the earthquake wave. Given that Mathematica comes equipped with a differential equation solver, solving second-order differential equations without having to write code manually is much more convenient. Therefore, this post will utilize Mathematica NDSolveValue to calculate the response spectrum of an earthquake wave.

In my previous time history analyses, I utilized SeismoSignal software, a seismic wave processing software developed by SeismoSoft. It allows for filtering, baseline adjustment, and computation of displacement spectra among other features. Considered its capabilities and ease of use, I want to create a similar tool myself.

Previously, due to some requirements, I need to extract coordinate data from a deformed image and found that Mathematica can indeed do a lot of things. So, I combined information from forums and help documents to see if there was anything interesting to explore. I discovered that Mathematica can perform image matching, and thus I wanted to use Mathematica image matching to locate the position of a small part of an image within a larger image.

Creep is a typical nonlinearity problem due to material. For such problem, it is necessary to understand the material properties and correctly setting the material related attributes. In Ansys, setting up creep behavior involves activating the material’s Creep option and assigning it elastic properties. This post analyzes a bolt in operation, with a length of 200mm and a cross-sectional area of 150mm^2, continuously working at 800°C. The goal is to analyze the internal stress evolution/condition of the bolt, as shown in the model below,