Aerospace Structures Flashcards
Neumann boundary condition prescribe the displacement. (T/F)
FALSE
Dirichlett or essential BC precripe the displacement.
Neumann BC’s or natural BC prescribe the stress.
You cannot prescribe a natural BC on the outer surface of a body if no loads are applied there. (T/F)
FALSE.
Natural BC: σ n = 0.
On the constrained part of the body you can compute the applied forces per unit surface as σ n. (T/F)
TRUE
A plain-strain constitutive law:
Has null axial strain.
The exact solution of the elasticity problem satisfied both natural and essential BC’s. (T/F)
TRUE
The assumption of plane stress implies that the deformation along the thickness is zero. (T/F)
FALSE
The equilibrium equations can be obtained by integrating by parts the PVW (T/F)
TRUE
The PCVW is used to find the equilibrium solution. (T/F)
FALSE
The solution of the elastic problem:
Must guarantee equilibrium and compatibility
The PVW can be applied only for hyperelastic constitutive laws (T/F)
FALSE
An hyperelastic constitutive law is not necessarily linear (T/F)
TRUE
The assumption of infinitesimal displacements implies that the equilibrium conditions are referred to the undeformed configuration. (T/F)
True
The equivalence between the PVW and the Principle of Minimum Potential Energy holds for:
Holds for Hyperelastic material law.
The shear flows acting on the rib are:
The flows equilibrating the applied load.
In finite elements, the hourglass phenomenon can be due:
Can be due to an excessively low number of integration points.
The solution due to De Saint Venant does not account for local effects because local effects are always negligible (T/F)
False
The Hooke’s Law is a constitutive law for linear elastic materials (T/F)
True
Shear deformability effects are generally more relevant for thin-walled beams than for compact beams (T/F)
True
Can the elastic problem be formulated in terms of displacement?
Always.
The shear center of an open thin-walled beam section according to the semi-monocoque scheme can be determined by:
By imposing the equivalence of torsional moment.
A beam model cannot be used for evaluating local effects due to load introduction (T/F)
True.
The semi-monocoque approximation provides the exact shear distribution along the panels thickness. (T/F)
False
Essential BC’s are mroe important than natural ones. (T/F)
False.
The semi-inverse approach for the De-Saint Venant solution for isotropic, homogeneous beams leads to:
Leads to the exact solution of the problem.
The shear center of beam section with one closed cell requires the application of:
Of the compatibility equation theta’ = 0.
The principle of Virtual Work:
a) Is used to impose the equilibrium
b) Is used to impose the equilibrium and compatibility
c) is used to impose the compatibility
a)
The shear force in an Euler-Bernoulli beam:
a) is null because the shear deformation is negligible
b) is different from zero and be computed from the derivative of the bending moment
c) is infinite so that the shear deformation is null
d) cannot be computed
b)
In a thin-walled beam, a rib contributes to:
a) preserve the shape of the section
b) reduce the shear flows in the panels
c) reduce the force carried by the stringers
a)
The finite element method required the boundary conditions to be identically fullfilled (T/F)
False
The trial functions used in the Ritz approximation must be part of a complete set of functions (T/F)
T
A structure is modelled using finite elements. It is unconstrained and subjected to a set of loads in self equilibrum. the solution of the linear static problem:
a) Can be obtained after constraining the structure isostatically
b) Is defined up to a rigid ody motion; thus, not being unique, can never be obtained
c) Is stress free
d) Can be obtained only if the loads are concentrated
a)
Consider a truss fixed at one end and free the other, and loaded with a
uniformly distributed traction. The finite element solution obtained with
quadratic elements:
a) is an approximation of the exact solution
b) is exact for both displacement and axial force
c) is exact for the displacement, but approximated for the axial force
d) is exact for the the axial force, but approximated for the displacement
e) is exact for the the displacement and strain, but approximated for the
axial force
b)
The torsional stiffness of a single-cell thin-walled beam:
a) is zero according to the semi-monocoque approximation
b) requires first the shear center position to be evaluated
c) can be evaluated using the Bredt’s formula
d) can be evaluated using Eulero’s formula
c)
The polyomial order of the finite element shape functions does not affect the rate of convergence of the solution (T/F)
False
The torsional stiffness of an open section profile modelled using the semi-monocoque scheme is null (T/F)
True
Consider a Euler-Bernoulli beam, whose static solution is obtained using the FE method. The approximating functions need to be C^2. (T/F)
False.
In the finite element method, the analysis of a statically indetermined structure:
a) is done with no differences with the case of a statically determined one
b) requires special compatibility requirements to be added to the solving
equations
c) cannot be performed due to the overconstraints
a)
The rotation of a multi-cell thin walled cross section with N cells:
a) can be computed using Bredt’s formula
b) can be computed by solving a system of equations with N-1 compatibility
equations an 1 equilibrium equation
c) can be computed by finding the location of the shear center
b)