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)
The buckling load of a compressed beam is function:
a) of the cross-section bending stiffness
b) of the cross-section torsional stiffness
c) of the cross-section axial stiffness
d) of the cross-sections shear stiffness
a)
The internal forces in a statically determined structure depend on the material elastic properties (T/F)
False
The Timoshenko beam model does not account for transverse shear deformation (T/F)
False
The position of the shear center of a thin-walled beam depends on the loading conditions (T/F)
False.
Consider a cantilever beam modeled according to Euler-Bernoulli and loaded with a uniformly distributed load. The exact solution is:
Polynomial(quartic)
A plain-strain constitutive law has:
Null axial strain.
A two-cell section modelled according to the semi-monocoque scheme can be solved by using:
Shear flow equations, equivalence to internal moment and compatibility equation/
According to the Kirchhoff plate model, deformed setions remain normal to the reference surface (T/F)
True
The exact solution of the elasticity problem satisfies both natural and essential boundary conditions (T/F)
True
A truss is fixed at both ends and is loaded with a uniformly distributed axial load. The axial displacement is:
Quadratic.
The natural BC’s associated with the Timoshenko beam model involve:
Shear and bending equilibrium.
The transverse shear deformability for a thin walled beam is generally larger than:
Than a corresponding compact section (same dimensions and bending stiffness)
The assumption of plane stress imply 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
According to the semi-monocoque scheme the shear stresses are constant along the thickness of the panel (T/F)
True
Any structure with one dimension much larger than the other two can likely be modeled as a beam (T/F)
True
According to the Timoshenko beam model, the transverse shear stresses are linear on the cross section (T/F)
False
The position of the shear center of a closed-cell section can be evaluated using the shear flow equations and the equivalence to internal moment
False
A system of slender beams can be modeled by beams finite elements
a) never
b) if the structure can sustain the loads through an internal axial load path
c) whenever the shear deformability is negligible
d) always
d)
An Euler-Bernoulli cantilever beam with uniform stiffness is clamped at one
extremity and loaded with a concentrated force at the tip. The solution
obtained using a displacement-based method based on polynomial functions
with two unknown coefficients is
a) exact
b) an approximation of the exact solution with errors below 10 \%
c) an approximation of the exact solution with errors depending on the
problem data
a)
When the shear force is applied at the shear center
a) the shear flows are null
b) the torsion is null
c) the torsion can be different from zero only if the torsional moment,
computed with respect to the shear center, is not null
c)
The axial stress of a bent beam is function of its material elastic modulus (T/F)
False
When using a displacement-based method the Natural (Newmann) boundary conditions may not be satisfied exactly (T/F)
True
The cross-sections of a beam subject to a torsional moment do always rotate around the area center (T/F)
False
The PCVW allows to
a) find the compatible solution among the equilibrated ones
b) find the equilibrated solution among the compatible ones
c) find the compatible and equilibrated solutions among all the possible
independent stress and displacement fields
d) none of the above
a)
Shear deformability needs to be accounted for
a) never
b) always
c) it depends on the beam at hand
c)
When a torsional moment is applied to a thin-walled beam, without any other
load
a) the shear flows are null
b) the torsion is null
c) the torsion is different from zero, but only if the cross-section is free to
warp
d) the torsion is different from zero
e) the torsion is different from zero only if the transverse shear deformability
is not negligible
d)
The assumption of plane strain implies that a component of stress is null (T/F)
False
The essential BC’s are satisfied in a weak sense by the PVW (T/F)
F
According to the semi-monocoque model, the axial stress σ_zz, in the panels, can be computed from the axial derivative of the shear stress (T/F)
F
The shear stress transmitted by a glued connection is
a) higher at the extremities
b) lower at the extremities
c) constant
d) described by a sin function
e) described by a cos function
f) described by a quadratic polynomial function
g) none of the above
a)
The bearing stress is related to
a) glued connections
b) riveted connections
c) the average shear stress in a semi-monocoque cross-section subject to
constant torsional moment
d)– the through-the-thickness shear stress in a Timoshenko shell model
e) the through-the-thickness shear stress in a Mindlin shell model
f) none of the above
b)
The transverse shear deformability for a thin-walled beam
a) is null
b) is generally larger with respect to a corresponding (same dimensions and
bending stiffness) compact section
c) is generally smaller with respect to a corresponding (same dimensions
and bending stiffness) compact section
d) is equal to that of a corresponding (same dimensions and bending stiffness)
compact section
e) can be neglected
f) none of the above
b)
The assumption of plane strain imlies that a component of strain is null (T/F)
T
The Newmann BC’s are satisfied in a weak sense by the PVW (T/F)
T
According to the semi-monocoque model, the shear stress in the panels can be computed from the axiam derivative of the axial stress σ_zz (T/F)
F
The shear flux in a thin panel is equal to
(a) the shear stress divided by the panel thickness
(b) the shear stress multiplied by the panel thickness
(c) the shear stress
(d) the derivative of the axial stress in the panel
(e) none of the above
b)
The critical buckling compression force for the Euler instability of a beam is
function of:
(a) only the beam length and the constraints
(b) only the beam bending stiffness and the constraints
(c) only the beam torsional stiffness and the constraints
(d) only the beam axial stiffness and the constraints
(e) the beam length, the axial stiffness and the constraints
(f) the beam length, the bending stiffness and the constraints
(g) the beam length, the bending stiffness, the cross-section area and the
constraints
(h) the beam length, the torsional stiffness and the constraints
(i) none of the above
f)
The axial stiffness for a thin-walled beam:
(a) is null
(b) is generally larger with respect to a corresponding (same material and
cross-section area of the material) compact section
(c) is generally smaller with respect to a corresponding (same material and
cross-section area of the material) compact section
(d) is equal to that of a corresponding (same material and cross-section area
of the material) compact section
(e) can be neglected
(f) none of the above
d)
The axial stress σzz is always null for a beam in plane strain (T/F)
False
The reaction forces of overconstrained structures cannot be computed by resorting to the displacement method: (T/F)
False
The stress σzz of an isotropic material is only function of the corresponding deformation εzz (T/F)
False
The shear stress in a thin panel is equal to:
(a) the shear flux divided by the panel thickness
(b) the shear flux multiplied by the panel thickness
(c) the shear flux
(d) the derivative of the axial stress in the panel
(e) none of the above
a)
The shear deformability of a thin-walled beam is:
(a) always negligible
(b) always more significant than the bending stiffness
(c) equal to the axial stiffness
(d) equal to the bending stiffness
(e) equal to the torsional stiffness
(f) often not negligible
(g) none of the above
f)
The axial stiffness for a thin-walled beam:
(a) is null
(b) is generally larger with respect to a corresponding (same material and
cross-section area of the material) compact section
(c) is generally smaller with respect to a corresponding (same material and
cross-section area of the material) compact section
(d) is equal to that of a corresponding (same material and cross-section area
of the material) compact section
(e) can be neglected
(f) none of the above
d)
The PCVW is used to find the equilibrium solution (T/F)
False
De Saint Venant Solution should not be used for evaluation of stresses near abrupt changes of geometry (T/F)
True
The Shear Flow Equations is derivded from an equilibrium condition. Therefore the shear flow equation does not account for compatibility requirements (T/F)
True
The solution of the elastic problem must guarantee:
Equilibrium and compatibility
The semi-monocoque approximation provides an approximate solution for:
For shear stresses.
The linear static response of simply supported beam with bending stiffness EJ and loaded with a uniform load can be analyzed by imposing:
Symmetry Conditions.
beam is loaded with a shear force; the torsional moment is equal to the value
of the force multiplied by the distance between the force line of action and
the barycenter (T/F)
False
the bending moment of over-constrained beam structures cannot be computed
by resorting to the PVW (T/F)
False
the axial stress of a beam transmitting a given bending momentMx is function
of the beam material elastic modulus E (T/F)
False
“Differential bending” is related to:
a) the different bending behavior of beams around the principal axis x and
y
b) torsional stiffness
c) interaction between axial and bending stiffness of a beam
d) the derivative of the axial stress in the panel of a thin-walled cross-section
e) none of the above
b)
The PCVW:
a) cannot be applied to staticaly determined systems
b) can be applied to statically determined systems, but only in order to
compute the reaction forces and moments
c) can be applied to statically determined systems only in order to compute
the displacemnt and/or the rotation of a given point
d) is equivalent to the PVW for statically determined systems
e) none of the above
c)
Hermitian shape functions:
a) are used to approximate the torsional moment using the Ritz method
b) are required in order to build Euler-Bernoulli beam FEs
c) are special C2 shape functions required to build high-performance beam
FEs
d) need to be avoided because they reduce the order of convergence
e) are useless
f) none of the above
b)
