UOK-FEM-Lecture1

Transcript UOK-FEM-Lecture1

University of Kurdistan

Finite Element Method

Lecture1: An Introduction to Finite Element Method Lecturer: Kaveh Mollazade, Ph.D.

Department of Biosystems Engineering, Faculty of Agriculture, University of Kurdistan, Sanandaj, IRAN.

Definition o What is the Finite Element Method (FEM)?

In mathematics

, the finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for differential equations. It uses variational methods (the calculus of variations) to minimize an error function and produce a stable solution. Analogous to the idea that connecting many tiny straight lines can approximate a larger circle, FEM encompasses all the methods for connecting many simple element equations over many small subdomains, named finite elements, to approximate a more complex equation over a larger domain.

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

How does FEM work?

o Example: Integrating using numerical methods for the function Exact solution: The integration represents the area under the curve Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

How does FEM work?

Numerical solution: Note: As the number of sections increases, the error decreases.

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Definition o What is the Finite Element Method (FEM)?

In Engineering

, FEM is a computerized method for predicting how a real world object will react to forces, heat, vibrations etc., in terms of whether it will break, wear out or work the way it was designed. It is called analysis but in the product design cycle it is used to predict what is going to happen when the product is used .

Visualization of how a car deforms in an asymmetrical crash using finite element method Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

How does FEM work?

The finite element method works by breaking a real objects into a large number of elements such as little cubes. The behavior of each little element which is regular in shape, is readily predicted by a set of mathematical equations. The computer then adds up all the individual behaviors to predict the behavior of the actual object.

Mesh modeling of an aircraft for finite element analysis Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

History of FEM • 1941 – Hrenikoff proposed framework method • 1943 – Courant used principle of stationary potential energy and piecewise function approximation • 1953 – Stiffness equations were written and solved using digital computers.

• 1960 – Clough made up the name “finite element method” • 1970s – FEA carried on “mainframe” computers • 1980s – FEM code run on PCs • 2000s – Parallel implementation of FEM (large-scale analysis, virtual design) Courant Clough Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications of FEM in engineering 

Structural & Stress Analysis

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Thermal Analysis

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Dynamic Analysis

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Acoustic Analysis

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Electro-Magnetic Analysis

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Manufacturing Processes

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Fluid Dynamics

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Aerospace Engineering (AE) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Civil Engineering (CE) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Electrical Engineering (EE) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biomedical Engineering (BME) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) o Mouazen, A. M. and Nemenyi, M. 1999. Tillage tool design by the finite element method: Part 1. Finite element modeling of soil plastic behaviour. Journal of Agricultural Engineering Research, 72: 37-51.

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) o Petru, M., Novak, O., Herak, D., and Simanjuntak. 2012. Finite element method model of the mathematical behaviour of

Jatropha Curcas

L. seed under compression loading. Biosystmes Engineering, 111: 412-421.

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) o Dintwa, E., Van Zeebroeck, M., Ramon, H., and Tijskens, E. 2008. Finite element analysis of the dynamic collision of apple fruit. Postharvest Biology and Technology, 49: 260-276.

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) o Celik, H. K., Topakci, M., Canakci, M., Rennie, A. E. W., and Akinci, I. 2010. Modal analysis of agricultural machineries using finite element method: A case study for a V-belt pulley of a fodder crushing machine. Journal of Food, Agriculture, and Environment, 8(3&4): 439-446.

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) o Janjai, S., Lamlert, N., Intawee, P., Mahayothee, B., and Haewsungcharern, M. 2008. Finite element simulation of drying of mango. Biosystems Engineering, 99: 523-531.

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Applications: Biosystems Engineering (BE) Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

Finite Element Method – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade

UOK-FEM-Lecture1

Transcript UOK-FEM-Lecture1

Finite Element Method

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