Finite element analysis Introduction for engineering

Finite Element Analysis
Introduction
Computer-Aided Design, Analysis and
Prototyping

FEA Introduction
 Numerical method used for solving problems
that cannot be solved analytically (e.g., due to
complicated geometry, different materials)
 Well suited to computers
 Originally applied to problems in solid
mechanics
 Other application areas include heat transfer,
fluid flow, electromagnetism

Finite Element Method Phases
 Preprocessing
 Geometry
 Modeling analysis type
 Mesh
 Material properties
 Boundary conditions
 Solution
 Solve linear or nonlinear algebraic equations
simultaneously to obtain nodal results
(displacements, temperatures)
 Postprocessing
 Obtain other results (stresses, heat fluxes)

FEA Discretization Process - Meshing
 Continuous elastic structure
(geometric continuum) divided into
small (but finite), well-defined
substructures, called elements
 Elements are connected together
at nodes; nodes have degrees of
freedom
 Discretization process known as
meshing

Spring Analogy
 Elements modeled as linear springs
, ,
, similar to
F l
E
A l
EA
F l F kx
l
   

  
 
  
 
 

Matrix Formulation
 Local elastic behavior of each element
defined in matrix form in terms of loading,
displacement, and stiffness
 Stiffness determined by geometry and material
properties (AE/l)

Global Matrix Formulation
 Elements assembled through common nodes
into a global matrix
 Global boundary conditions (loads and
supports) applied to nodes (in practice,
applied to underlying geometry)
1 1 2 2 1
2 2 2 2
F K K K U
F K K U
 
     

     

     

Solution
 Matrix operations used to determine unknown
dof’s (e.g., nodal displacements)
 Run time proportional to #nodes/elements
 Error messages
 “Bad” elements
 Insufficient disk space, RAM
 Insufficiently constrained

Postprocessing
 Displacements used to derive strains and
stresses

FEA Prerequisites
 First Principles (Newton’s Laws)
 Body under external loading
 Area Moments of Inertia
 Stress and Strain
 Principal stresses
 Stress states: bending, shear, torsion, pressure,
contact, thermal expansion
 Stress concentration factors
 Material Properties
 Failure Modes
 Dynamic Analysis
See Chapter 2 of Building Better Products with FEA, Vince Adams and
Abraham Askenazi, Onward Press, 1999

A Simple FEA Model





































2
1
2
2
2
2
1
2
1
2
2
1
2
2
2
2
1
2
1
1
2
1
2
2
2
1
2
1
1
1
)
(
)
(
)
(
0
)
(
0
)
(
U
U
K
K
K
K
K
F
F
U
K
U
K
F
U
K
U
K
K
F
K
U
U
F
K
U
U
K
U
F
Kx
F
Stiffness matrix

A Simple FEA Model - 2
 DOF’s - 1
 Determines the # of equations needed to
define the model
 Boundary Conditions
 Allows model to be solved
 U0 = 0 (fixed support)
 F1, F2 (external forces)
 Mesh
 2 1D elements
 2 nodes per element

A Simple Model - 3
 Assumptions
 Linear spring (-> 1 DOF)
 Convergence
 Process of using smaller and smaller
elements to reduce error

Finite Element Analysis
Introduction

Finite element analysis Introduction for engineering

More Related Content

Similar to Finite element analysis Introduction for engineering (20)

Recently uploaded (20)

Finite element analysis Introduction for engineering

Editor's Notes