This course covers fundamentals of continuum mechanics. Continuum mechanics deals with the mechanics governing the deformation of both solid and fluid objects in nature. Topics of this course starts from mathematical preliminaries for analysis of continuum body such as configuration, vector and tensor analysis. Then, lectures cover fundamentals of strain, stress, constitutive equations, conservation of mass, momentum and energy to derive the governing equations of general continuous bodies. Next, lectures focuse on the analysis of the governing equation for both solid and fluid objects.
At the end of this course, students will be able to:
1) explain the fundamental concept of continuum mechanics applied to both solid and fluid objects in nature.
2) have an understanding of the concepts of finite deformation of bodies, stress, strain, and constitutive equations.
Continuum body, Solid mechanics, Fluid mechanics,Tensor analysis
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Towards the end of class, students are given exercise problems related to what is taught on that day to solve.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction of continuum mechanics | Exercises to understand the mathematical preliminaries for analysis of continuum bodies |
Class 2 | Strain | Exercises to understand the definitions of strain |
Class 3 | Stress | Exercises to understand the definitions of stress |
Class 4 | Constitutive equations | Exercises to understand the definitions of constitutive equations |
Class 5 | Mass conservation, continuum equations, Newton's laws of motion | Exercises to understand laws of mass conservation, continuum equations, Newton's laws of motion |
Class 6 | The principal of virtual work, law of the conservation of energy | Exercises to understand the principals of virtual work and law of the conservation of energy |
Class 7 | Analysis of various stress field in solids | Exercises to analyze various stress field in solids |
Class 8 | Elastic wave propagation (1D,2D) | Exercises to analyze 1D and 2D elastic wave propagation in solids |
Class 9 | Mathematical modeling of physical phenomena in the field and vector analysis | Understanding of Mathematical modeling of physical phenomena in the field and vector analysis |
Class 10 | Equation of continuity and equation of conservation of momentum | Understanding of Equation of continuity and equation of conservation of momentum |
Class 11 | Constitutive equations, basic equations of fluid dynamics | Learn about constitutive equations and basic equations of fluid dynamics strain rates, perfect fluids, Newtonian fluids |
Class 12 | Navier-Stokes equations | Exercise to understand Navier-Stokes equations |
Class 13 | Analysis of simple flow | Learn about simple flows Poiseuille flow, Couette flow, Potential flow, and so on |
Class 14 | Final exam or explanation of the assignment | Final exam or explanation of the assignment |
Text book specified by the instructor.
Course materials are provided during class.
Students will be assessed on their understanding of continuum mechanics, solid mechanics and fluid mechanics. Students course scores are based on exams(80%) and exercise problems.
No prerequisites.