Applying Numerical Methods in Dynamic Problems — Lesson 2

This lesson covers the application of numerical methods for solving equations of motion in dynamic problems. It delves into the direct integration methods, a popular tool in numerical analysis, especially for those using finite element software. The lesson discusses different direct integration methods like Central Defense Method and Numark Method, each with its own advantages and disadvantages. It also explains the concept of convergence in solutions and how it's governed by the time step chosen in numerical integration. The lesson further illustrates these concepts with a problem involving a cantilever pole subjected to an arbitrary force.

Video Highlights

01:03 - Explanation of the direct integration methods.
02:45 - Central difference method and Newmark method, including their formulation, advantages, and disadvantages.
04:31 - Stability and convergence of the direct integration method, emphasizing the importance of the proper selection of delta T.
67:26 - Problem involving a long cantilever pole fixed at the base and subjected to an arbitrary force at the tip, evaluated at three steps: 0, delta T, and 2 delta T.

Key Takeaways

- Direct integration methods are used to solve time domain equations without transforming them into any other form.
- Different direct integration methods include Central Defense Method and Numark Method.
- The convergence of the solution in direct integration methods is generally governed by the time step chosen in the numerical integration.