1. 1. General introduction to finite element method
ME 520 Fundamentals of Finite Element Analysis
1. General introduction to finite element method
Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department
Gebze Technical University

2. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Finite Element Method: FEM
Finite Element Analysis: FEA
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

3. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Course Content
Finite Element Discretization Concepts
Finite Element Formulations
FEM Computer Applications (ANSYS Workbench)
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

4. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Computational Mechanics:
Computational Mechanics branch can be separated according to problem’s physical content.
Computational
Mechanics
Nano and Micromechanics
Continium Mechanics:
Solids and Stuctures,
Fluids,
Multiphysics
Systems
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

5. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Computational Solid and Structural Mechanics
Computational
Solid and Structural
Mechanics
Statics
Dynamics
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

6. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Computational Solid and Structural Mechanics:
Computational
Solid and Structural
Mechanics
Linear
Nonlinear
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

7. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Solution Methods used in Computational Mechanics:
Finite Element Method
Finite Difference Method
Boundary Element Method
Finite Volume Method
Mesh-Free Method
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

8. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Formulations and Solution Methods used in Finite Element Method:
FEM Model Formulation
FEM Model Solution
Displacement
Equilibrium
Mixed
Hybrid
Stiffness
Flexibility
Mixed
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

9. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Summarizing: This Course Covers
Computational structural mechanics
Linear static problems
Spatially discretized by displacement-formulated FEM
Solved by the stiffness method
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

10. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Reasons of Using Finite Element Method:
Design Analysis: Reduces the number of experiments and hand calculations and enables computer
FEM/FEA is the commonly worldwide used analysis and simulation method
Can work with CAD/CAM applications in an integrated manner
...
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

11. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Engineering Applications of Finite Element Method:
Mechanics/Space/Aeronautics/Civil/Automotive
Stuructural Analysis (statics/dynamics, linear/nonlinear)
Heat/Fluid
Electromagnetics
Geomechanics
Biomechanics
...
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

12. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
A Brief History of the FEM:
Courant (Variational methods)
Turner, Clough, Martin and Topp (Stiffness)
Clough (“Finite Element”, plane problems)
1970s Applications on mainframe computers
1980s Microcomputers, pre- and postprocessors
1990s Analysis of large structural systems
2000s Mini Computer and pre- and postprocessor Apllications
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

13. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Available Commercial FEM Software Packages:
ANSYS (General purpose, PC and workstations)
SDRC/I-DEAS (Complete CAD/CAM/CAE package)
NASTRAN
DYTRAN (Nonlinear and dynamic analyses)
ABAQUS (Nonlinear and dynamic analyses)
COSMOS (General purpose FEA)
ALGOR (PC and workstations)
PATRAN (Pre/Post Processor)
HyperMesh (Pre/Post Processor)
Dyna-3D (Crash/impact analysis)
...
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

14. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Finite Element Method: FEM
The finite element method (FEM), or finite element analysis
(FEA), is based on the idea of building a complicated object with
simple blocks, or, dividing a complicated object into small and
manageable pieces (discretization).
Elements 9 9
Finite element model consists
of elements and nodes.
E1: Element number
4,5,9: Node numbers
Nodes E1
1 Element
Finite Element Model
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

15. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
FEM in Structural Analysis
Procedures:
· Divide structure into pieces (elements with nodes)
· Describe the behavior of the physical quantities on each element
· Connect (assemble) the elements at the nodes to form an
approximate system of equations for the whole structure
· Solve the system of equations involving unknown
quantities at the nodes (e.g., displacements)
· Calculate desired quantities (e.g., strains and stresses) at
selected elements
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

16. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Objectives of This FEM Course
· Understand the fundamental ideas of the FEM
· Know the behavior and usage of each type of elements covered in this course
· Be able to prepare a suitable FE model for given problems
· Can interpret and evaluate the quality of the results (know the physics of the problems)
· Be aware of the limitations of the FEM (don’t misuse the FEM - a numerical tool)
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

17. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
Linear Static Analysis
Many of structural engineering problems can be threated as linear static problem with the acceptance of the following assumptions.
Small deformations (loading pattern do not change with deformation)
Materials are elastic
Loads are static (load is applied slowly and uniformly)
Linear static analysis gives an idea about the behavior of the structure and can be accepted as a good approach for many of the analyses. Also for many cases static analysis is the base for nonlinear analysis.
Within this course only static analysis subjects will be covered.
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

18. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

19. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU

20. Mechanical Engineering Department, GTU
1. General introduction to finite element method
Fundemental Concepts
ME Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department, GTU