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- StudyBlue
- Massachusetts
- University of Massachuetts, Lowell
- Mechanical Engineering
- Mechanical Engineering 22.513
- Sherwood
- Final Exam

Jen C.

A finite element model is comprised of what?

Elements, nodes, mesh, material properties

What does each column of the stiffness matrix represent?

The load vector that would need to be applied in order to get a unit displacement at the corresponding degree of freedom

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What does ([A]T)T equal?

[A]

What does ([A][B])T equal?

[B]T[A]T

What does ([A][B][C])T equal?

[C]T[B]T[A]T

What is an influence coefficient?

Denoted by a12, the static deflection of the system at point 1 due to a unit force applied at point 2 when the unit force at point 2 is the only force acting

What is Maxwell's reciprocal theorem?

a21=a12, since path of load application should not affect resultant potential energy total of an elastic system

With respect to derivation of element, what dictates order of polynomial for displacement field?

Number of degrees of freedom

What is a functional?

An integral expression that implicitly contains differential equations that describe the problem

What is the B matrix?

Relates nodal displacements to strain field

What is a consistent load vector?

Derived using shape function that is consistent with the element formulation

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How do you recognize the shape function matrix?

Relates nodal displacement (d) to displacement field; it is whatever products/ terms that relate the nodal displacement vector to the assumed displacement field

How is tensorial shear strain related to engineering shear strain?

epsilon xy = 1/2 gamma xy

How do you show that the 3-noded triangular element with 6-DOF is a constant strain triangle?

epsilon x, epsilon y, gamma xy are constant because du/dx and dv/dy are constants

In the Raleigh-Ritz method, what are your DOFs?

Generalized coordinates, aka coefficients (a0, a1, a2, etc)

Where are the stress values within an element most accurate?

At the Gauss points

How can you tell between the strong and weak form of the governing partial differential equation?

In the strong form the derivatives are continuous for all orders. The weak form has relaxed continuity requirements

Why use Gauss quadrature for isoparametric elements?

Can't do quad elements algebraically, must be done numerically

What lesson was learned fom the plasma cutting torch electrode?

You must change the boundary condition of the temperature of the tungsten at the electrode when finding how well the water bath cools the system. A flux condition should be chosen

How do you know a finite element solution has converged?

Plot the mesh density vs. solution and see asymptote

When deriving an element, what conditions need to be satisfied?

The equation needs to be complete and admissible (satisfy essential boundary conditions)

How many DOFs are in a brick element?

3 (translation only)

Give an example of when to use skew supports.

Using non-perpendicular supports on a truss or a tank in a trussel

When do you use implicit vs. explicit FE code?

Implicit is used for static to quasistatic situations (few time steps). Explicit is used in high speed impact analysis (many elements and time steps).

How and why would you use explicit code in quasistatic situations?

you need to do mass or time scaling. You would do this because contact algorithms are better in explicit codes

What does rank deficient mean?

That the rank of [K] is less than the number of element DOFs - number of rigid body modes. The rank of a matrix is the maximum number of independent rows or columns.

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