Dr. Wang Xingbo Email: xbwang.nudt@gmail QQ:168731668 Homepage: wxbstudio.home4u.china

1. Mathematical & Mechanical Method in Mechanical Engineering Dr. Wang Xingbo Email: xbwang.nudt@gmail.com QQ:168731668 Homepage: wxbstudio.home4u.china.com Fall，2005

2. Mathematical & Mechanical Method in Mechanical Engineering Motivation of This Course • Mechanical Engineering is being a subject of science • Development of cross &Multi-subjects,especially Computer science • Future requirements of persons in research work

3. Mathematical & Mechanical Method in Mechanical Engineering Purpose of the course • To show idea of scientific methodology • To introduce fundamental methods • To agitate the creative competence • To dig out one or more elites

4. Mathematical & Mechanical Method in Mechanical Engineering Methodology • Experiential Method • Scientific Method

5. Mathematical & Mechanical Method in Mechanical Engineering Methodology Experiential Method Originates from people’s experience and intuition without any logical or scientific principles

6. Mathematical & Mechanical Method in Mechanical Engineering Experiential Method -Traits • 1. Utility • 2. Simple • 3. Trial

7. Mathematical & Mechanical Method in Mechanical Engineering Experiential Method -Evaluation • A method but not the perfect one • Less cost but high efficient • Without extension

8. Mathematical & Mechanical Method in Mechanical Engineering Scientific Method A process by which scientists, collectively and over-time, endeavor to construct an accurate representation of the world

9. Mathematical & Mechanical Method in Mechanical Engineering Scientific Method-Four Steps • Observation and description • Formulation of a hypothesis • Use of the hypothesis • Performance of experimental tests

10. Mathematical & Mechanical Method in Mechanical Engineering Scientific Method: Hypotheses, Models, Theories and Laws • A hypothesis is a limited statement regarding cause and effect in specific situations • A model is reserved when hypothesis has is valid • A scientific theory or law represents a hypothesis confirmed through repeated experimental tests

11. Mathematical & Mechanical Method in Mechanical Engineering Scientific Method: Solving Problems with Scientific Methods Step1. State the problem Step 2. Research the problem Step 3. Form a hypothesis Step 4 .Test the hypothesis Step 5. Draw conclusions from the data

12. Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models A process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon Four procedures as follows

13. Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models • Building a Mathematical Model   • Verifying and Refining a Model   • Variables and Parameters   • Continuous /Discrete in Time

14. Mathematical & Mechanical Method in Mechanical Engineering Mechanical Models • Newtonian Dynamics • LaGrangian and Hamiltonian Dynamics

15. Mathematical & Mechanical Method in Mechanical Engineering Mechanical Models : Newtonian Dynamics • A body remains at rest or in a uniform state of motion if no external force acts on it. • A body, upon which a force acts, moves in such a way that the time rate of change of the momentum equals the force. • If two bodies act on one another by means of forces, these forces have equal magnitudes and opposite directions.

16. Mathematical & Mechanical Method in Mechanical Engineering Mechanical Models : LaGrangian and Hamiltonian Dynamics • The actual path of a dynamical system in configuration • space extermeizes the action between two defined • locations and times

17. Mathematical & Mechanical Method in Mechanical Engineering Contents in this course Chapter 1: Scientific methods Chapter 2 and 3: Vector and tensor Chapter 4: Differential form  Chapter5: Variational calculus Chapter 6: Lie group Chapter 7: Manifold theory Chapter 8: Classical mechanics  Chapter 9 :Finite deformation

18. Mathematical & Mechanical Method in Mechanical Engineering About Examination Course procedure:20% Homework & Discussion:20% Final Exam:60%

19. Mathematical & Mechanical Method in Mechanical Engineering 11:00am.,Oct.,26,2005 Chapter 1 is over! Take a rest! To be continued……

20. Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models: Building a Mathematical Model • Identify the problem • Begin with a simple model. • Identify important variables and constants. • Develop the equation(s) 

21. Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models: Verifying and Refining a Model • Is the information produced reasonable? • Are the assumptions made? • Are there any factors not considered? • How do the results, if available? 

22. Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models: Variables and Parameters • Output variables • Input variables • Parameters (constants) 

23. Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models: Continuous /Discrete in Time • Is the information produced reasonable? • Are the assumptions made? • Are there any factors not considered? • How do the results, if available? 