Elastic Deformation Flashcards
Definition of a force.
Influence in a body that causes it to accelerate.
What are the conditions for a body to be at equilibrium?
The vector sum of the forces acting on it must be zero.
The body must have a constant momentum.
The sum of the components of the forces must also be zero in any given direction.
What is the extra condition of static equilibrium?
There must be no torque caused by the lines of actions of the forces.
Definition of a torque/moment.
The product of a force and its perpendicular distance to the point of turning.
What does a free body diagram show?
The isolated body and all the forces acting upon it.
What to look out for on free body diagrams?
The lines of actions of each force, if it’s not through the CoM then a torque could be caused.
Conditions for equilibrium.
Vector sum of forces is zero
Vector sum of moments at any point is zero.
Sketch shear force and bending moment diagram for 3 point bend applied force P.
Check
Sketch shear force and bending moment diagram for 4 point bend for two applied forces P.
Check
For stress, what are the letters of the double suffix.
First letter is direction of applied force
Second letter in the direction of the normal to the surface.
Derive the equations for normal and shear stresses for a rotated set of axes within a square of material.
Check derivation
Derive the Mohr’s circle stress equations.
Check derivation.
What are the axes in Mohr’s circle?
Normal on horizontal
Shear on vertical
How are rotations by an angle θ in real space represented on Mohr’s circle?
Real θ equates to 2θ on the circle.
What is the principle shear stress on Mohr’s circle?
The maximum value of normal stress.
What do the letters on a displacement gradient tensor show, double suffix?
The first is the direction of displacement
The second is the direction of the original length.
Define engineering strains.
Check
Define tensor strains.
Check
When are engineering strains used?
For relationships with elastic constants such as YM and SM.
When are tensor shear strains used?
Useful when considering transformations of reference axes.
Mohr’s circle
What directions are positive and negative on Mohr’s circle?
If a clockwise rotation is caused it is positive, if an anticlockwise rotation is caused then negative.
Equations for Poisson’s ratio
Check
State the equations that form the basis of Hooke’s law
Check Leonard-Jones and VdW
Hooke’s Law equations incorperating Poisson’s ratio for isotropic materials.
Check
State both shear modulus equations
Check
Derive the link between shear modulus and YM
Check derivation
Equations for spring and dashpot.
Check
Derive Maxwell model of viscoelasticity
Check derivation
Derive the Voigt or Kelvin model of viscelasticity
Check derivation
Derive the standard linear model for viscoelasticity (Zener model)
Check derivation
Derive the stresses in a thin spherical pressure vessel.
Check
Derive the stresses in a thin cylindrical pressure vessel
Check
Equations for torsion of a thin walled cylinder
Check
Derive the equation for torsion of a solid rod.
Check
Derive the equations for stress and strain in a beam under bending
Check
Equation for total bending moment in bent beam.
Check
Derive the equation relating normal stress to moment of inertia and YM
Check
