MECH3780 FEA MID SEM

What are the main steps in a FEA workflow

1. Pre processing - geometry simplification, assigning materials, selecting element type, defining boundary conditions, generating mesh.

2. Solution step - apply boundary conditions constraints and loads.

3 post processing - visualisation and interpretation of solution and results

What are the different types of 1D elements?

1. Bar/truss.

2. Heat transfer.

3. Pipe flow.

4. Electric circuits

5. Beam elements.

Describe the characteristics of 1D bar/truss elements.

- Pinned at ends

- No moment

- Cannot sustain shear force

- Ignores transverse displacement

Describe the characteristics of 1D heat transfer elements

- Homogenous

- Temperature stored at nodes

- No internal heat generation

Describe the characteristics of one D pipe flow elements

- Fully developed laminar flow

- Constant cross-section

- Pressure stored at nodes

Describe the characteristics of 1D electrical circuit elements

Describe the characteristics of 1D beam elements

- Long slender members

- Subject transverse loading

- produces significant bending effects

What is the difference between a Euler-Bernoulli beam and a Timoshenko beam?

Euler-Bernoulli

- Thin slender beams (L/H > 10)

- Defamation dominated by flexural bending

- Cross-section remains perpendicular to centroid axis during bending

Timoshenko

- Short thick beams

- significant transverse shear

- Used in vibration analysis

What is the total potential energy formula?

Internal strain (U) + P.E of external forces (Ohms symbol)

What is plane stress?

-Solid whose thickness one direction (eg. Z) is very small compared the dimensions of the other two directions (x and y).

- External forces applied only in the XY plane

- Stress in the z directions are all zero

What is plain strain?

- thickness in the z direction is very large compared to x and y directions

-External forces applied evenly along the Z axis

- Movement in the Z axis is constrained

What are the types of 2-D FEA elements?

1. Constant strain triangles (CST)

2. Bilinear rectangular elements (Q4)

3. Membranes

4. Linear strange triangles (LST)

5. Axisymmetric triangular elements

6. Higher-order quadrilateral elements

What is an CST?

A 2-D element with three nodes, used to discretise irregular bodies.

- six DOF per element

- Stiffer compared to Q4 elements (slower convergence)

What is a Q4 Element?

A bilinear rectangular element which is more accurate than CST and simpler interpretation

- 8DOF per element

- Mesh refinement needed to discretise irregular bodies

What is a membrane ?

A 2-D surface element used for plane stress applications

Used for very thin structures with only in plane loading eg. balloons or structural components that don't support bending loads

- in plane loading only, no out of plane loads

- No resistance to bending moments

- Two DOF / node

What is an LST?

- six nodes

- 12 DOF per element

- Stresses applied at centroid

- More accurate and predicting stress and displacements than CST

- Better results than CST for equal number of nodes and 4x less elements

What are axisymmetric triangular elements?

Derived from 3-D problems formulated in cylindrical coordinates and can be represented as a 2D element. If rotated 360° reforms the 3-D element.

- Develop hoop stress

- triangular torus such that each element is symmetric with respect to geometry and loading about an axis

What are higher order quadrilateral elements?

A two day element that better approximates curve boundaries and are defined isoparametrically

What are the types of 3-D FEA elements?

1. Tetrahedral elements.

2. Quadratic tetrahedral elements.

3. Linear hexahedral elements.

4. Quadratic hexahedral elements.

5. Plate elements.

6. Shell elements.

What is a tetrahedral element?

- Four nodes

- 12 DOF per element

- Yields constant strain variation

- Can lead to shear stiffening

What are quadratic tetrahedral elements?

Second order elements that better capture curvature and changes in stress and strain

- Increased memory and processing time

- Additional nodes leading to a more accurate representation of complex geometries

- Avoids shear locking

- reduces hourglassing

What are linear hexahedral isoparametric elements?

- A linear brick

- Difficult mesh generation

Robust and accurate

What are quadratic hexahedral isoparametric elements?

- Less susceptible to shear locking over linear hex

- Can overestimate stress state due nodal averaging

- Robust accurate

What are plate elements?

2-D analogues of a 1D beam element which support transverse loads and buckling.

- used to analyse bending deformation

*** flat elements that resist bending about two axis and have a twisting moment

- t<<< L/W by ~10x

- displacement <<< t

- No transverse shear

- neg t -> zz strain = 0

- neg normal stress -> zz stress =0

What are shell elements?

Applied to thin structures with in-plane, out of plane and bending loads or layer composites

- loads in all directions

- computationally efficient as they are large elements compared to the thickness

- Factual stress varies with through thickness

- for shells in 3D, membrane and bending effects are usually coupled globally

How do you handle stress singularities?

1. Use results from adjacent elements.

2. Apply a stress concentration factor.

3. Smooth model geometry.

4. Use a sub model.

5. Use a non-linear material model to induce localised yielding and stress redistribution

Model symmetry...

- reflective symmetry reduces computational costs

- Loads must be reduced

*** caution when using vibration and buckling cases as there are not many symmetry modes

What is geometric nonlinearity?

Large deformations can change geometry and loads without material yielding.

- Large strange rotations or displacements are indicators

- Changes in element shape change the elements stiffness

- Element strain causes in plane stress, out of plane stress can be significantly affected

**** This is a characteristic of thin structures with axial stiffness >>>> bending stiffness eg. Cables, thin beams, shells.

What is material nonlinearity?

Do you know elastic stress-strain relationship that arises from post - yield plasticity, hyper elasticity

The yield of the material results in a stress redistribution .

What is contact nonlinearity?

Abrupt changes in stiffness may occur when bodies come in to or out of contact with each other or themselves

What are the types of contact nonlinearity?

1. Bonded/glued - no penetration, separation or sliding.

2. No separation - similar to bonded but frictionless sliding can.

3. Frictionless - no penetration but can slide freely.

4. Rough - similar to frictionless but no sliding.

5. Friction - sliding is proportional to the coefficient of friction.

What is symmetric contact implementation?

When contact surfaces are constrained from penetrating the target surfaces and vice versa

What is a symmetric contact implementation?

When only contact surfaces are constrained from penetrating target surfaces

- If convex surface contacts flat/concave, flat/concave = target

Dash,

- if contact between course and fine mash, course mesh = target

- if two surfaces, stiffer = target

- Largest of two surfaces = target

What is a lump mass matrix?

A diagonal matrix which yields frequencies less than the expected values but is more computationally efficient as it requires less storage

What is a consistent mass matrix?

A non-diagonal matrix that is more accurate for flexural problems but increases computational expense flashcards

What does buckling analysis assume?

- No resistance to buckling post defamation

- Linear elastic material behaviour

- Small deflections

- Linear contact behaviour

What applications uses buckling analysis?

- Thin wall structures

- Tanks and vessels

- Compression members

- Thin, slender columns

What does 1 < BLF mean?

Buckling is not predicted as loads are less than the estimated critical loads

What does 0 < BLF < 1 mean?

Buckling is predicted as loads are more than the estimated critical loads

What does BLF = 1 mean?

Buckling is predicted as loads equal the estimated critical loads

What does BLF = -1 mean?

Buckling is not predicted as it will only occur when load directions are reversed

What does -1 < BLF < 0 mean?

Buckling is not predicted but would occur if loads are reversed

What does BLF < -1 mean?

Buckling is not predicted even withreversed loads

What are the pros and cons of implicit transit dynamics?

Pros

- large times steps

- Global equilibrium verified every time step

Cons

- Slow to compute each time step

- Greater computational requirements

What are the pros and cons of explicit transit dynamics?

Pros

- each time step is calculated quickly (no convergence required)

Cons

- Extremely small time steps

- No criteria for small times steps

What are the types of load boundary conditions?

* Force > applies a force to point, line, area

* Moment › applies moment to point, line, area

* Bearing load > applies bearing load to a curved surface

* Remote force › applies force/moment at a remote point

* Pressure › applies pressure (normal to surface)

* Hydrostatic Pressure › applies graded pressure load

* Bolt pretension › simulates bolt pre-tension

* Line pressure › distributes pressure across a line

* Joint loads › Load to joints for transient analysis (not used in static structural)

* Interface loads › To transfer results from other simulations to a structural simulation

What are the type of constraint boundary conditions?

* Fixed > DOFs are fixed (i.e. = 0)

* Frictionless > In-plane DOFs are free, out of plane is fixed

* Displacement > lets you apply a given displacement

* Remote displacement › applies displacements with respect to an external point

* Compression only › loads are only applied in the compression direction

* Cylindrical support › Applies fixed constraints in the cylindrical coordinate system

* Elastic supports › Lets you apply a compliant (elastic support)