Solid Mechanics
Notes on Solid Mechanics
Dear god the single hardest class that I've ever taken
Thankfully, the course textbook is readily available online.
This course provides an introduction to the mechanics of solids from a continuum perspective. Topics covered in this course include: vector and tensor analysis, coordinate systems and calculus in curvilinear coordinate systems, kinematics (motion, deformation and strain), stress and momentum balance, energy principles and balance laws, linear isotropic and anisotropic elasticity, thermoelasticity, method of solutions for 2-D and 3-D linear elastic boundary value problems, applications to simple structures.
This is the ceiling on the complexity of information that I have a reasonable grasp on. This course started pretty slow and then accelerated pretty rapidly.
Lecture 1: Scalars
Fields (in this context) are variables which depend on multiple variables, typically position. In PDE's, most students are introduced to temperature fields but fields can be any kind of variable. Temperature or pressure, which are scalars, are simplest but velocity or stress can also depend on location. \tikz \draw (0pt,0pt) -- (20pt,6pt);
Scalar Field.
Vector Field
Index Notation
Algebraic Vector Operations
Addition
Products
Norm
Scalar Dot
Vector Cross
Outer Product
Kronecker Delta
Permutation Symbol
----
Epsilon Delta Identity
Scalar Triple Product
Lecture 2: Vectors
Lecture 3: Tensors
Lecture 4: Eigenvalues
Lecture 5: Tensor Calc
Lecture 6: Curvilinear Coordinates
Lecture 7: Kinematics
Lecture 8: Polar Spherical Coordinates
Lecture 9: Stretch and Right Cauchy Green Deformation
Lecture 10: Motion, Deformation, and Strain
Lecture 11: Strain Measures
Lecture 12: Force and Momentum Balance
Lecture 13: Conservation of Mass
Lecture 14: Proof of Cauchy's Theorem from BLM
Lecture 15: Traction and Stress from Undeformed Configuration
Lecture 16: Elastic Material Behavior
Lecture 17: Material Symmetry
Lecture 18: Elastic Constants
Lecture 19: Strain Energy and Thermo Elasticity
Lecture 20: Linear Thermo-Elastic Boundary Value Problems
Lecture 21: Thermo-Elastic BVP in Cylindrical Coordinates
Lecture 22:
Force
Mechanical interaction (push or pull) between
parts of a body
body and environment
Contact Force
Act on a surface due to contact with environment or other parts of the body
Body Force
Exerted through the interior of a body, due to environment or itself
gravity
electromagnetism
self gravitation
Traction
Stress vector. the second definition is due to newton's second law
Momentum Balance Laws Newton Euler Equations
Balance of Linear Momentum
Velocity
Velocity Gradient
Rate of Deformation
Spin
Rate of Volume Change
Acceleration
Conservation of Mass
Global Version of Newton Euler Equations
Cauchy's Theorem or the Existence of Stress
Proof of Cauchy's Theorem
Physical Interpretation of Cauchy Stress
Principal Stresses
Hydrostatic Stress
Deviatoric Stress
Von Mises Effective Stress
Traction and Stress wrt. Undeformed Configuration
Rarely do we have the outcome, but the initial configuration and what happens to it.
1st Piola-Kirchoff Stress Tensor
Stress Traction Relation
Localization on V0
Other Stress measures
Elastic Material Behavior
Kinematics, Small Strain
Momentum Balance
Knowns and Unkonwns
Constitutive Laws, Thermodynamics, Energy
Balance of Energy
Material Linearity
Voight/Nye Representation
Material Symmetry
Special Cases
Monoclinic
Orthotropic
Transverse Isotropy/Hexagonal Symmetry
Cubic Symmetry
Global/Sample and Material Reference Frames
Isotropy
Elastic Constants
Strain Energy Density
Linear Elastic
Linear Elastic Isotropic
Strain Energy Decomposition
Thermoelasticity
Thermal Strain
Isotropic Thermal Strain
Isotropic Thermoelasticity
Last updated