MIT2_092F09_lec20 - 2.092/2.093 — Finite Element Analysis...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2.092/2.093 — Finite Element Analysis of Solids & Fluids I Fall ‘09 Lecture 20- Wave Propagation Response Prof. K. J. Bathe MIT OpenCourseWare Quiz #2: Closed book, 6 pages of notes, no calculators. Covers all materials including this week’s lectures. L w C = t w (C depends on material properties) For this system, C is the wave speed (given), L w is the critical wavelength to be represented, t w is the total time for this wave to travel past a point, L e is the “effective length” of a finite element, and is equivalent to L n w (given). To solve, we should use Δ t = L C e . Mesh L e should be smaller than the shortest wave length we want to pick up. To establish a mesh, we use low-order elements (4-node elements in 2D, 8-node elements in 3D). We use the central difference method, which requires stability. We need to ensure that Δ t ≤ Δ t cr = ω 2 n . Recall that in nonlinear analysis, the wave speed changes. We know that ω n ≤ max ω n ( m ) m where ω n is the largest frequency of an assembled finite element mesh and max ω n ( m ) is the largest element m frequency of all elements in the mesh. Then we can use 2 Δ t = ( m ) max ω n m and conservatively, we use a slightly smaller value....
View Full Document

This note was uploaded on 02/24/2012 for the course MECHANICAL 2.092 taught by Professor Klaus-jürgenbathe during the Fall '09 term at MIT.

Page1 / 5

MIT2_092F09_lec20 - 2.092/2.093 — Finite Element Analysis...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online