1 introduction lecture notes dr. rakhmad arief siregar universiti malaysia perlis 0124430010 applied...
TRANSCRIPT
1
Introduction
Lecture NotesDr. Rakhmad Arief SiregarUniversiti Malaysia Perlis
0124430010
Applied Numerical Method for Engineers and Scientists
2
Text bookApplied Numerical Methods with MATLAB
McGraw-Hill, 2005 Steven C. Chapra
Hardcover Paperback RM55
3
Exercise book
Each student should have one exercise book
This book is needed in to exercise answering questions
It will be checked in any time without notice
4
Computer software
Spreadsheet software (Calc or Excel) MATLAB LS-DYNA
5
Learning Approach
Lecture : 28 hours (33%) Practical : 42 hours (50%) Tutorials : 14 hours (17%)
6
Evaluation contribution
Final Examination: 50% Course Works: 50%
7
Course work (50%)
Lab 25% (4 MATLAB report + 1 FEM report) Mid test 15% 4 Assignments / 2 tests 10%
8
HEA requirement
Round-off and truncation errors Roots of equations Systems of simultaneous linear
algebraic equations Curve fitting Numerical integration Ordinary differential equations Basic concept of Finite Element Method Stiffness Matrices, Spring and Bar
Elements Interpolation function for general
element formulation Application in Engineering
9
Plan of Lecture
Week 1 Chapter 1 (Mathematical Modeling and Engineering Problem Solving)
Week 2 Chapter 3 (Approximations and round-off errors)
Chapter 4 (Truncation errors and the Taylor Series)
Week 3 Chapter 5-6 (Bracketing Methods & Open Methods)
Week 4 Chapter 9-11 (Gauss Elimination and Gauss Seidel)
Week 5 Mid semester break (Mid test will be done before or after mid semester
break) Week 6 Chapter 17 (Least-squares regression)
Week 7 Chapter 18 (Interpolation)
Week 8 Chapter 21 (Newton-Cotes Integration Formulas)
10
Plan of Lecture
Week 9 Chapter 22 (Integration of Equations)
Week 10 Chapter 25 & 26 (Runge-Kutta Methods & Stiffness method)
Week 11 Chapter 29 (Elliptic Equation)
Week 12 Chapter 30 (Finite difference: parabolic equation)
Week 13-14 Chapter 13 (Finite Element Method) Final Semester Examination Note: Some topics that are not stated in HEA may be
eliminated to due time constrains
11
Course Objective
No. Hasil
Pembelajaran, CO
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PO
9
PO
1
0
PO
1
1 Delivery Mode
Assess-ment
1. Students can understand basic concepts of heat transfer i.e fundamental theory of numerical analysis for engineering
3 2 1 3 2 1 3 1 0 2 0
Lecture, Tutorial, Lab
QuizExam,Report
2. Student capable of utilizing proper technique of solving engineering problem using numerical analysis
2 3 2 2 2 0 2 2 0 2 0
Lecture, Tutorial, Lab
AssignmentQuizExam,Report
3. Student able to analyze and identify application of mechanical engineering using FEM
3 3 2 3 2 0 2 2 0 2 0
Lecture, Tutorial, Lab
AssignmentQuizExam,Report
12
Course Objective
1. Students can understand basic concepts of heat transfer i.e fundamental theory of numerical analysis for engineering
2. Student capable of utilizing proper technique of solving engineering problem using numerical analysis
3. Student able to analyze and identify application of mechanical engineering using FEM
13
Introduction
Importance of Numerical Methods in Engineering Most engineering analysis problems involve
The development of a mathematical model to represent all the important characteristics of the physical system;
The derivation of the governing equations of the the model by applying a physical laws, such as equilibrium equation, Newton’s laws of motion, conservation of mass and conservation of energy
Solution of the governing equations Interpretation of the solution
14
Computer Programming Languages
Some high-level languages: FORTRAN, BASIC, C, C++, PASCAL, etc
Programming structure: For typical high-level language uses the
following types of statements to process the data:
Assignment Input/Output Control of decision Specification Subprogram
15
Errors
Error and relative error Propagation error Truncation error Round-off Error Computational Error
16
Summary of part of topics
Roots equations
Linear of algebraic equation
17
Summary of part of topics
Curve Fitting
18
Summary of part of topics
Integration
19
Summary of part of topics
Integration
20
Summary of part of topics
Finite Element Method
Advance topic (will not be covered)
21
Summary of part of topics
Finite Element Method
Bar element only for Numerical Analysis topic
22
END