ME 305 INTRODUCTION TO FINITE ELEMENTS
IN MECHANICAL ENGINEERING
Winter 2014
Homework 1 Solution
Problem 1. a
Similarly, for all the nodes,
Node ID
G
F
E
D
C
B
A
Weight-equivalent force (pointing down
Foundations of Finite Element Method
For structural problems:
Principal of minimum potential energy
Equivalent spring network
More generally methods of variational
generally,
calculus
(principal of vi
ME305 INTRODUCTION TO FINITE ELEMENTS
IN MECHANICAL ENGINEERING
March 14 exercise
Stress accuracy and convergence
1. Open Hyperworks and choose the NASTRAN user profile.
2. Import your 4 x 2 quad elem
ME305 W14
March 26
2D Model Cleanup
HW4: Due Friday April 4
1
Move nodes
Use the place node option in the Quality Index panel
Left click and hold mouse on an element node
Drag node and watch elemen
ME305 W14
March 12
2D Elements: Stress Analysis
1
Stress Analysis
1D Elements
Axial stress, Bending stress, Combined stress
,
g
,
2D Elements
Normal stresses
Shear stress
Principal stresses Prin
ME305 W14
March 31
3D (Solid) Elements
HW4: Due Friday 04/04
1
3D Elements
Geometry of the element defined by a volume
Both the simplest and most complex elements
Greater usage over the past 20 years
ME 305 INTRODUCTION TO FINITE ELEMENTS IN
MECHANICAL ENGINEERING
Optimization with Optistruct
A design concept for an automotive control arm required to meet performance specifications will
be created
National
Wind
Watch
TM
Presenting the facts
about industrial wind power
www.wind-watch.org
How big is a wind turbine?
An industrial-scale wind turbine is a lot bigger than one you might see in a schoo
ME 305 INTRODUCTION TO FINITE ELEMENTS
IN MECHANICAL ENGINEERING
Introduction to ME305 FE Software
Part 1
In what follows, unless stated otherwise, click means to click only once(!) with the leftmouse
ME305 W14
March 10
Modeling Symmetry
HW3 handout
HW3 due Friday 03/21
1
Symmetry/Antisymmetry
Geometric planes of symmetry may
Reduce model size = less analysis time
Enable larger models = more accura
ME 305 INTRODUCTION TO FINITE ELEMENTS
IN MECHANICAL ENGINEERING
Introduction to ME305 FE Software
Part 2
In this second part of our FE software introduction, you will create from scratch a simplified
Two Truss Element Problem
Two Truss Element Problem
Two Truss Element Problem
Two Truss Element Problem
Two Truss Element Problem
Two Truss Element Problem
Two Truss Element Problem
Foundations of Finite Element Method
1
2
Principal of minimum potential energy:
p
p
gy
The displacements that satisfy equilibrium are distinguished
by a stationary value of the total potential energy
ME 305 INTRODUCTION TO FINITE ELEMENTS
IN MECHANICAL ENGINEERING
Creating Truss (CROD) Element Model Using Hyperworks
In this exercise, we will use Hyperworks to build a 2 element truss (CROD) finite
ME305 INTRODUCTION TO FINITE ELEMENTS
IN MECHANICAL ENGINEERING
March 12 exercise
Stress accuracy and convergence
We return to the quadrilateral meshes we looked at (for displacement accuracy), but no
% Let outside radius= ro, inside radius=ri
%Let Node A location = ya, Node B location = yb
%
syms ro ri ya yb
%
% Here the area over an element is assumed constant
% Want to make area a function of ro
ME305 W14
March 10
Modeling Symmetry
HW3 handout
HW3 due Friday 03/21
1
Symmetry/Antisymmetry
Geometric planes of symmetry may
Reduce model size = less analysis time
Enable larger models = more accura
ME305 F13
March 14
2D Elements: Stress Analysis
1
ME305 F13
March 14
2D Elements: Stress Analysis
1
Stress Analysis
Nodal stresses
Nodal stresses from each element most inaccurate
of all stress loca
ME305 W14
March 31
3D (Solid) Elements
HW4: Due Friday 04/04
1
3D Elements
Geometry of the element defined by a volume
Both the simplest and most complex elements
Greater usage over the past 20 years
ME305 F13
March 14
2D Elements: Stress Analysis
1
Stress Analysis
Nodal stresses
Nodal stresses from each element most inaccurate
of all stress locations
Centroidal stresses
Compromise between acc
ME305 W14
March 12
2D Elements: Stress Analysis
1
Stress Analysis
1D Elements
Axial stress, Bending stress, Combined stress
,
g
,
2D Elements
Normal stresses
Shear stress
Principal stresses Prin
ME305 INTRODUCTION TO FINITE ELEMENTS
IN MECHANICAL ENGINEERING
Displacement accuracy and convergence for Second-order triangles
CTRIA6 elements
Last week we investigated the use of the standard 3 nod
ME305 INTRODUCTION TO FINITE ELEMENTS
IN MECHANICAL ENGINEERING
Displacement accuracy and convergence for 3 node triangles
To obtain a clear picture of the issues when using triangles for solving elas