2-Springs-2011s

2-Springs-2011s - MAE M168/CEE M135C Introduction to Finite...

Info iconThis preview shows pages 1–14. 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

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight 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: MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 2 Spring Models Review: Problem-solving strategy with FEM 1. Define a model • Mathematical idealization of the real physical problem • Choose what details to include/omit: Static vs. dynamic? Beam or 3- D solid? Loads/boundary conditions? Connections/contact? Elastic vs. elastoplastic? Composite vs. homogeneous? . reliminary Analysis 2. Preliminary Analysis • Simplified “hand-calculation” version of the model 3. FEA solution 4. Check answers • Compare to prelim. analysis/experiment, think and evaluate 5. Revise/refine Only step 3 is done by the software! Rest is up to you! Review: Basic FEA procedure 1. Discretize continuous body into elements 2. Approximate local behavior of elements in terms of discrete DOFs 3. Patch together, or assemble elements to form a global system of algebraic equations and solve for discrete DOFs. Spring Models h Why are spring models useful? Simple idealization of a structure. Example: 1-D structure P Al Steel k (1) k (2) D 1 D 2 P Spring model: Basic FEA procedure 1. Discretize continuous body into elements 2. Approximate local behavior of elements in terms of discrete DOFs 3. Patch together, or assemble elements to form a global system of algebraic equations and solve for discrete DOFs. P Al Steel Discretize Body Q i = Global Nodal applied loads D i = Global Nodal displacements Q 2 k (1) k (2) D 1 D 2 Q 1 Q o D o node 1 node 3 node 2 element 1 element 2 Basic FEA procedure 1. Discretize continuous body into elements 2. Approximate local behavior of elements in terms of discrete DOFs 3. Patch together, or assemble elements to form a global system of algebraic equations and solve for discrete DOFs. Local Element Behavior i j ( ) e k ( ) e i f ( ) e j f ( ) e d ( ) e d Local equilibrium: ( ) ( ) e e i j f f + = i j ( ) ( ) e e j i f f f ⇒ = - = Hooke’s law: k l f Δ = Compatibility of displacements: ( ) ( ) e e j i l d d Δ =- ( ) ( ) ( ) ( ) e e e j i j i k d d f f ∴- = = - ( ) 2 equations Local Element Behavior Or ( ) ( ) 1 e e f ( ) ( ) ( ) ( ) e e e j i j i k d d f f ∴- = = - ( ) 2 equations ( ) ( ) ( ) 1 1 1 1 i i e e e j j d f k d f - = - (e) k (e) d (e) f (e) : element (local) stifness matrix k (e) : element (local) displacement vector d (e) : element (local) force vector f Basic FEA procedure 1. Discretize continuous body into elements 2. Approximate local behavior of elements in terms of discrete DOFs 3. Patch together, or assemble elements to form a global system of algebraic equations and solve for discrete DOFs. Assembly (1) (1) (1) (1) (1) 1 1 1 1 i i j j d f k d f - = - 1 e = (2) (2) (2) (2) (2) 1 1 1 1 i i j j d f k d f - = - 2 e = Global Nodes (1) (1) (1) 1 1 1 i o f D k - =...
View Full Document

This note was uploaded on 08/09/2011 for the course MAE 168 taught by Professor Klug during the Spring '11 term at UCLA.

Page1 / 39

2-Springs-2011s - MAE M168/CEE M135C Introduction to Finite...

This preview shows document pages 1 - 14. Sign up to view the full document.

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