I want to analyze a steel frame with pin connections at both sides or one side at some beams. I found the keyword *Release is very useful and convenient, so I resort to this keyword. I wrote the input file with the same syntax rules, so that it will be more convenient for me to establish more models. However, when I try to run the input file, there are warnings and errors even with the input file generated from a …
Month: January 2019
Euler equation: \[\left\{ \begin{align} & {{x}_{n+1}}={{x}_{n}}+h \\ & {{y}_{n+1}}={{y}_{n}}+{{A}_{n}}h \\ \end{align} \right.\] \[\left\{ \begin{align} & h=\text{step}\text{size} \\ & {{A}_{n}}=f\left( {{x}_{n}},{{y}_{n}} \right) \\ \end{align} \right.\] Error of solution error = exact solution – approximate solution Method 1: smaller step Euler first-order: \(e\sim {{c}_{1}}h\), proportional to step size Method 2: find a better slop \({{A}_{n}}\) Heun’s method = improved Euler method = modified Euler method = RK2 \[\left\{ \begin{align} & {{x}_{n+1}}={{x}_{n}}+h \\ & {{y}_{n+1}}={{y}_{n}}+h\left( \frac{{{A}_{n}}+{{B}_{n}}}{2} \right) \\ \end{align} \right.\] in which, \({{B}_{n}}=f\left( …