FEA Flashcards
Define finite element Method:
The FEM is a numerical method to solve static or dynamic responses of systems for which the governing equations are expressed in the form of partial differential equations.
What are the main steps of the FEM?
- The continuum is discretized using a mesh of finite elements.
- Interpolation (shape) functions are selctected
- Element properties are determined
- All the element equations are assembled to find the global equation system for the whole region
- The global system equations are solved
- Additional field variable are obtained.
What are the three steps for the solution process in FE software?
- Pre-processing or mesh generation process
a. Node coordinates
b. Element conectivity - Solver
a. For each element prepare stiffness matrix and
equivalent nodal force vectors
b. Assemble all element matrices to global matriocies
c. Solve the final equations to find nodal
displacements - Post-processing
a. Calculate displacements, strain and stress at any
location of the solid or structure.
Why do we use symmetric and anti-symmetric boundary conditions in FEA and when can they be applied?
a. It saves on computer memory, storage area and CPU time/speed. They reduce the size of the analysis domain by at least a factor of 2.
b. The geometry and the restraints must be symmetric about a plane. The loads must either be symmetric or anti-symmetric
What restraints are applied to the displacement and rotational degrees of freedom of nodes lying on the plane of symmetry or anti-symmetry?
Symmetric:
- Displacement vector components perpendicular to the symmetric plane are zero
- Rotational vector components parallel to the plane are zero
Anti-symmetric:
- Displacement vector components in the anti-symmetric plane are zero
- Roational vector components normal to the plane are zero
What is the difference between solid and Shell elements in terms of DOF?
Solid elements don’t have rotational degrees of freedom, only translational
Shell elements have both rotational and translational DOF.
What is the behaviour of linear and quadratic elements in terms of displacement, stress and strain fields?
Linear elements:
- Linear displacement field
- Constant stress and strain field
Quadratic elements:
- Quadratic displacement field
- Linear stress and strain field.
What aspect ratio should be sued for shell elements and what angles should be avoided in FEA?
The aspect ratio (longest to smallest length) should be kept between 2 and 4
Angles closed to 0º and 180º should be avoided
What should the unit of Force, Stress and Energy be if the unit of length are:
a. m
b. mm
a. N & Pa & J
b. kN & GPa & KN-mm
How is the approximated solution of a particular DE (u(x,y,z)) found using FEM?
u(x,y,x) = n, i=1 Σ Ni(x,y,z) * {dx;dy;dz} = [N(x,y,x)] * {d}
Ni = shape functions
d = displacement vector
Are shape functions the same for all DOF?
No it is not necessary to use the same shape function for all DOF. Fro example N1x can be different to N1y. But often we uses N1x=N1y=N1z
What is the simple linear 1D approximation for the displacement field in a bar element?
u(x) = α1 + α2*x
α1 & α2 = random unknown coefficients
For a 1D bar What are the Shape function Ni(x) and Nj(x) equal to in term of x and L
At each end of the bar what are the chape functions equal to and what is this important property called?
Ni(x) = 1 - x/L
Nj(x) = x/L
Ni(x=0) = 1 & Ni(x=L) = 0
Nj(x=0) = 0 & Nj(x=L) = 1
This is called Partition of unit property
Describe an example of compatibility and conformity requirement.
The displacement approximation needs to carry continuously across common element boundaries.
Why is the weak form used in FEM rather than the strong form?
The strong form imposed continuity and differentiability requirements on the potential solutions to the equation. The weak form relaxes these to a certain extent.
