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Mathematical formulation axisymmetric

Track :

Mathematics

Lessons no : 45

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What will you learn in this course?
  • Develop mathematical models for axisymmetric problems in engineering and science using differential equations and boundary conditions
  • Apply symmetry principles to simplify complex axisymmetric mathematical formulations in real-world applications
  • Analyze stress, strain, and fluid flow in axisymmetric systems through mathematical equations and computational methods
  • Formulate and solve axisymmetric heat transfer problems using appropriate mathematical techniques and boundary conditions
  • Utilize mathematical tools to model and analyze axisymmetric electromagnetic and acoustic phenomena
  • Implement numerical methods for solving axisymmetric partial differential equations in engineering problems
  • Interpret mathematical results to optimize design and performance of axisymmetric structures and systems
  • Apply mathematical formulation techniques to model axisymmetric problems in fluid dynamics and structural analysis
  • Use mathematical software to simulate and analyze axisymmetric models for practical engineering solutions
  • Identify key parameters influencing axisymmetric systems and develop mathematical strategies for their control and optimization
  • Translate real-world axisymmetric problems into mathematical language for effective analysis and solution development
  • Evaluate the accuracy and limitations of mathematical models in axisymmetric problem-solving contexts

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Lessons | 45
Advanced Soil Mechanics Intro video
00:03:58

Advanced Soil Mechanics Intro video
Lec 1 Introduction to course content
00:11:12

Lec 1 Introduction to course content
Lec 2 Stress acting at a point Cauchy stress
00:23:17

Lec 2 Stress acting at a point Cauchy stress
Lec 3 Stress acting at a point Stress tensor
00:25:51

Lec 3 Stress acting at a point Stress tensor
Lec 4 Stress acting on a plane
00:09:12

Lec 4 Stress acting on a plane
Lec 5 Stress acting on a plane example
00:05:46

Lec 5 Stress acting on a plane example
Lec 6 Transformation of stress tensor
00:25:00

Lec 6 Transformation of stress tensor
Lec 7 Stress invariants
00:41:58

Lec 7 Stress invariants
Lec 8 Relationship between stress invariants
00:20:50

Lec 8 Relationship between stress invariants
Lec 9 Principle stresses and Eigen vectors
00:05:36

Lec 9 Principle stresses and Eigen vectors
Lec 10 Strain in soils
00:19:51

Lec 10 Strain in soils
Lec 11 Cause effect relationship
00:17:36

Lec 11 Cause effect relationship
Lec 12 Important constitutive relationship
00:48:46

Lec 12 Important constitutive relationship
Lec 13 3D to 2D idealization
00:19:13

Lec 13 3D to 2D idealization
Lec 14 Mathematical formulation plane stress plane strain
00:19:23

Lec 14 Mathematical formulation plane stress plane strain
Lec 15 Mathematical formulation axisymmetric
00:26:10

Lec 15 Mathematical formulation axisymmetric
Lec 16 Summary of Module 1
00:09:44

Lec 16 Summary of Module 1
Lec 17 Basics of shear strength
00:32:00

Lec 17 Basics of shear strength
Lec 18 Stress representation
00:25:58

Lec 18 Stress representation
Lec 19 Shear strength granular soil I
00:28:25

Lec 19 Shear strength granular soil I
Lec 20 Shear strength granular soil II
00:21:21

Lec 20 Shear strength granular soil II
Lec 21 Shear strength cohesive soil
00:35:24

Lec 21 Shear strength cohesive soil
Lec 22 Shear strength cohesive soil Stress strain
00:14:57

Lec 22 Shear strength cohesive soil Stress strain
Lec 23 Pore water pressure and Skemptons equation
00:41:46

Lec 23 Pore water pressure and Skemptons equation
Lec 24 Overall pore water pressure parameter
00:14:05

Lec 24 Overall pore water pressure parameter
Lec 25 Pore water pressure plane strain effect of sampling
00:27:58

Lec 25 Pore water pressure plane strain effect of sampling
Lec 26 Pore water pressure estimation
00:12:31

Lec 26 Pore water pressure estimation
Lec 27 Triaxial test
00:38:45

Lec 27 Triaxial test
Lec 28 Interpretation triaxial test UU UCS
00:37:05

Lec 28 Interpretation triaxial test UU UCS
Lec 29 Interpretation triaxial test CU
00:33:53

Lec 29 Interpretation triaxial test CU
Lec 30 Interpretation triaxial test CD
00:46:40

Lec 30 Interpretation triaxial test CD
Lec 31 Some additional aspects of shear strength
00:35:36

Lec 31 Some additional aspects of shear strength
Lec 32 Summary of Module 2
00:06:38

Lec 32 Summary of Module 2
Lec 33 Stress path and representation
00:33:44

Lec 33 Stress path and representation
Lec 34 Failure line in stress path
00:26:51

Lec 34 Failure line in stress path
Lec 35 Stress path some common cases
00:35:59

Lec 35 Stress path some common cases
Lec 36 Stress path some common cases
00:48:45

Lec 36 Stress path some common cases
Lec 37 Stress path triaxial test drained
00:40:13

Lec 37 Stress path triaxial test drained
Lec 38 Stress path triaxial test undrained
00:33:16

Lec 38 Stress path triaxial test undrained
Lec 39 Stress path additional undrained case
00:40:44

Lec 39 Stress path additional undrained case
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Mathematical formulation axisymmetric course in hindi, in this course delves into mathematical modeling and analysis of axisymmetric problems in various fields of science and engineering.