Nonlinear finite elements/Quiz 0

Please answer the following questions. Answers such as "don't know", "knew once but have forgotten", and "never seen that before" are acceptable.

• Mark the topics on the following list that you have studied in the past (in class or on your own):

 

	Linear algebra (Matrices, Vector algebra).
	Vector calculus.
	Tensor algebra and calculus.
	Partial Differential Equations.
	Variational calculus.
	Numerical analysis.
	Finite element analysis.
	Elasticity.
	Plasticity.
	Viscoelasticity.
	Continuum Mechanics.
	Heat Transfer.
	Fluid Dynamics.
	Electromagnetism.

• What do the three terms in the following equation mean?

$\mathbf {K} \mathbf {d} =\mathbf {f}$

What is the physical meaning of the equation (think Newton's laws)?

• What physical process does the following equation model?

${\boldsymbol {\nabla }}\bullet {\boldsymbol {\sigma }}=0$

What do the symbols mean?

• What physical process is modeled by the following equation?

${\frac {\partial T}{\partial t}}-{\frac {1}{C_{v}~\rho }}{\boldsymbol {\nabla }}\bullet ({\boldsymbol {\kappa }}\bullet {\boldsymbol {\nabla }}T)=Q$

What do the symbols mean?

• Have you ever encountered:

 

	Lagrange multipliers.
	Euler-Lagrange equations.
	Weak and strong forms.
	Newton's method for finding roots.

Nonlinear finite elements