Theory Quiz

Understanding the Physics of Structural Mechanics ITC

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1 / 45

What is the most appropriate analysis type to use when simulating two cars crashing in to each other?

Time- history dynamics analysis

Modal analysis

Harmonic analysis

Static analysis

2 / 45

A nonlinear analysis was performed of an engineered structure in operation, and nonlinear materials were defined. The resulting force-deflection curve showed the response to be linear. Which of the following statements is the most reasonable conclusion that can be made of the analysis?

The analysis was incorrect since a nonlinear analysis will always result in a nonlinear response.

If the design (i.e., geometry) were modified significantly, a linear analysis should be run on the new design.

If the applied loads were doubled, the displacements would also be doubled since the response will always be linear.

The analysis could have also been set up with linear materials and still obtained accurate results.

3 / 45

Consider a situation where there are two geometrically identical brackets, each made with a different grade of plastic that have different elastic moduli (stiffness). Both brackets are constrained and loaded in the same manner. Select two statements which are true, assuming linear response.

The location of maximum strain will be the same on both brackets.

The magnitude of maximum strain will be the same for both brackets.

The location of maximum deformation will be the same on both brackets.

The location of maximum deformation of either bracket will depend on their elastic modulus (stiffness) value.

4 / 45

Which of these applications require performing dynamic analyses? Select two best options.

Stress analysis of wind turbine column due to weight and rotation of turbine

Stress analysis of turbine shaft due to rotation of turbine blade

Buckling of wind turbine blade due to wind loads

Stress analysis of turbine blade due to varying ambient temperature

5 / 45

A tensile stress state in a pre-stressed modal analysis will tend to _____. Select the best option to complete the sentence.

suppress rigid-body motion

decrease the natural frequency

increase the natural frequency

keep the natural frequency the same

6 / 45

What is the primary reason for fluid sloshing in a tanker truck during transportation?

Vibrations due to IC engine operation

Inertia of motion of the fluid

Fluids do not slosh inside a tanker

Vibrations due to road roughness

7 / 45

Which of the following is a characterization of small strain theory?

$P=-\frac{1}{3}\sigma {_{ii}}$

$\varepsilon = \int \frac{dl}{l}$

$\sigma = E\varepsilon$

$\frac{\Delta L}{L}$

8 / 45

In which of these applications is it safe to ignore inertial effects?

Drop test analysis of mobile phone

Crashworthiness analysis

Thermal stress analysis due to thermal shock

Modal analysis of heavy machinery

9 / 45

Consider two masses connected by a single spring, and the masses are only allowed movement in a single direction (1D). How many natural frequencies are there in this system?

1

3

2

4

10 / 45

Which statement is true about a stress tensor? Choose two best options.

A stress tessor is symmetric along the diagonal.

Stress tensor is not absolute. Under different coordinate systems, its values will be different. However, they all represent the same stress state.

Stress tensor under different coordinate systems represents different stress states.

Under different coordinate systems, the components of a stress tensor remain the same values.

11 / 45

Volumetric expansion occurs when all shear strain components are zero and all normal strain components are equal to each other (i.e., $e_{xy}=e_{xz}=e_{yz}=0$ but $e_{xx}=e_{yy}=e_{zz}$). Select the correct statement.

Equivalent strain is zero when there is only volumetric expansion.

Equivalent strain cannot be determinned without additional information regarding the deformation.

Equivalent strain will be equal to the normal strain.

Equivalent strain will be equal to twice the normal strain.

12 / 45

Which of the following descriptions are correct for von Mises stress visualized in principal stress space? Choose three best options.

In principal stress space, von Mises stress values are all the same on a cylindrical surface representing the von Mises stress.

In principal stress space, the further the position on the cylindrical surface representing von Mises stress is from the origin, the larger the von Mises value is.

In principal stress space, von Mises stress is plotted as a cylindrical surface of infinite length.

In principal stress space, the larger the radius of the cylindrical surface is, the larger the von Mises stress value it represents.

13 / 45

Which of the following derived quantities is always a positive value?

Shear Strain

Normal Strain

Equivalent Strain

Principal Strain

14 / 45

As deformation increases, the difference between true and engineering strain _____.

Decreases

Increases

Remains the same

Increases linearly

15 / 45

Which of these equations represents an undamped system?

$\left [ M \right ]\left \{ a \right \} + \left [ K \right ]\left \{ u \right \} = \left \{ F\left ( t \right ) \right \}$

$\left [ M \right ]\left \{ a \right \} + \left [ C \right ]\left \{ v \right \} + \left [ K \right ]\left \{ u \right \}= \left \{ F\left ( t \right ) \right \}$

$\left [ M \right ]\left \{ a \right \} + \left [ C \right ]\left \{ v \right \} + \left [ K \right ]\left \{ u \right \}= \left \{ 0 \right \}$

$\left [ M \right ]\left \{ a \right \} + \left [ C \right ]\left \{ u \right \} = \left \{ F\left ( t \right ) \right \}$

16 / 45

Which of the below statements are correct about local equilibrium? Choose three best options.

Local equilibrium should be satisfied everywhere in a body.

Only normal stress components are taken into account in local equilibrium calculations.

Body forces are included in the calculation of local equilibrium.

Local equilibrium describes the internal force balance on an infinitesimal volume.

17 / 45

Consider a one-dimensional bar with one end fixed at $u\left ( 0 \right )$ while the other end has been extended for a displacement of $u_{0}$. The length of the bar = $L$. Which of the following options best describes the boundary conditions of the problem?

$u\left ( 0 \right ) = u_{0}, u\left ( L \right ) = u_{0}$

$u\left ( 0 \right ) = 0, u\left ( L \right ) = 0$

$u\left ( 0 \right ) = 0, u\left ( L \right ) = u_{0}$

$u\left ( 0 \right ) = L, u\left ( L \right ) = 0$

18 / 45

Consider a simulation of a steel beam of an office building where the maximum load capacity needs to be determined. What is the appropriate analysis type? Choose the best option.

Time- history dynamics analysis

Static analysis

Modal analysis

Harmonic analysis

19 / 45

Which term in the governing equations accounts for the energy dissipated from damping? The equations of motion are given by this equation:

$\left [ M \right ]\left \{ \ddot{u} \right \} + \left [ C \right ]\left \{ \dot{u} \right \} + \left [ K \right ]\left \{ u \right \} = F\left \{ t \right \}$

$\left [ C\right ]\left \{ \dot{u} \right \}$

$\left [ K\right ]\left \{ {u} \right \}$

$F\left \{ t \right \}$

$\left [ M \right ]\left \{ \ddot{u} \right \}$

20 / 45

In simulation of a two-gear system, if the objective is to find out stress on gear tooth and reaction forces on the axes, what kind of geometry details can be safely removed from CAD geometry before proceeding to simulation? Choose two best options.

Small holes on the faces of gears

Smallest gears with most geometry details

Imprinted labels on the faces of gears

Geometry details on the gear tooth

21 / 45

When we place a dead weight on top of a viscoelastic material sample, what phenomenon do we expect to see?

Strain hardening

Stress stiffening

Creep

Stress relaxation

22 / 45

Large strain formulation will always result in _____. Select the best option to complete the statement.

increased deformation compared to small strain formulation

a nonlinear stiffness calculation that involves higher order terms

decreased deformation compared to small strain formulation

the need for a nonlinear material model

23 / 45

A dog bone tensile test of polyethylene illustrates which two types of nonlinearites?

Nonlinear Material

Nonlinear Contact

Large Deformation

Spin Softening

24 / 45

Response of a structure to cyclic loads is studied using _____. Select the best option to complete the sentence.

Time domain analysis

Cyclic symmetry

Linear periodicity

Frequency domain analysis

25 / 45

Which material option best characterizes aluminum prior to yielding?

Nonlinear Elasticity

Metal Plasticity

Hyperelasticity

Linear Elasticity

26 / 45

Which of the following statements is correct for dynamic analyses? Choose the best option.

Inertia effects are considered in time-history dynamic analysis.

Modal and harmonic analyses cannot be considered as forms of dynamic analyses as they do not solve time-history response.

Dynamic analysis needs sufficient boundary conditions to prevent rigid body motion.

Only when high velocity movement is involved in the simulation, dynamic analysis should be considered as the analysis type for the simulation.

27 / 45

When a material point is in equilibrium, how many unique terms are in its 3 x 3 strain tensor?

6

3

9

12

28 / 45

Imagine a body of mass m is resting on a platform of mass $M$. Assuming that there is no friction between them, if we set the platform into motion from rest to a constant velocity, $V$, over a time $T$, what will be the net acceleration of the body?

$\frac{m}{M} \cdot \frac{V}{T}$

$\frac{m}{m+M} \cdot \frac{V}{T}$

$\frac{V}{T}$

0

29 / 45

Which statement best defines strain?

It quantifies the change in length of a unit material.

It can only be calculated if material elastic modulus is known.

It only applies to rigid bodies.

It quantifies the change in stress of a unit material.

30 / 45

In many cases, the 3 by 3 stress tensor is converted to a 6 by 1 vector format, why is this? Choose two best options.

Because vector format is more a convenient notation than tensor notation.

Because stress tensor is symmetric, therefore only three off-diagonal stress are needed to record the stress.

Because stress tensor is used for 3D problems and stress vector is used for 2D problems.

Because shear stress component $\sigma_{yx}$, $\sigma_{zy}$ and $\sigma_{zx}$ are negligible for most problems.

31 / 45

Select the three best options that are needed to prepare an engineering problem for simulation.

Isolate a single part from an assembly to analyze

Decide what kind of material model should be used and obtain proper material parameters

Select appropriate loads and boundary conditions to represent the real-life situation

Determine the necessary geometric details to include in the model

32 / 45

Mode Participation factor and effective mass measure _____. Select the best option to complete the sentence.

It just measures the highest value

the amount of mass moving in each direction for each mode

the stiffness change in each direction

It just specifies the direction of excitation of mass and nothing more

33 / 45

What are the main components needed to form the governing equation of a solid mechanical problem? Choose three correct options.

Newton's methods

Material models

Load and boundary conditions

Geometry of deformation/Kinematics

34 / 45

Structural dynamics is the study of _____. Select the best option to complete the sentence.

the response of a structure in motion

the response of a structure to periodic loads

the response of a structure to very fast loads

the response of a structure to very slow loads

35 / 45

Simulation of the interference fit of an elastomeric O-ring in an installed condition involves which two types on nonlinearities?

Large Deformation

Hyperelasticity

Brittle Cracking

Isotropic Hardening

36 / 45

Let us assume that there are two materials - "Material A" and "Material B". The stiffness and the density for Material A are both three times that of Material B. The ratio of natural frequencies for a structure made of Material A compared the same structure constructed with Material B will be _____. Complete the sentence with the best option.

9

1

1.732

3

37 / 45

Why does large deformation introduce nonlinearity in the model?

Large deformation makes material behavior nonlinear

Large deformation results in rigid body motion

Large deformation alone does not introduce nonlinearity in the model

Large deformation results in change in shape which can change the direction of loading

38 / 45

From the uniaxial tensile test, which of the following is a strain that may represent failure for a component?

Strain at Ultimate Strength

It depends on the type of material tested and its engineering application

Strain at Yield

Strain at Fracture

39 / 45

The bending of a javelin thrown in air is an example of _____. Select the best option to complete the sentence.

a damped static situation

forced vibration

a damped forced vibration

free-free vibration

40 / 45

How many independent components of shear stresses are in a stress tensor?

9

6

3

1

41 / 45

Hertzian contact refers to frictionless contact between two bodies. A Hertzian contact between a rigid sphere and a flat elastic surface is considered to be nonlinear due to _____. Select the best TWO options.

the fact that one part is elastic

the plastic deformation in the sphere

the large deformation of the flat surface

the change in contact area due to deformation of the flat surface

42 / 45

Which of these is NOT a dynamic analysis?

Harmonic analysis

Static stress analysis

Modal analysis

Transient stress analysis

43 / 45

If the mass and stiffness matrices have dimensions of $n$ by $n$, then what will be the number of eigen frequencies?

1

$2n$

$n$

$n^2$

44 / 45

Spin softening always involves _____. Select the best option to complete the sentence.

time-dependent properties

nonlinear materials

transient analysis

rotation

45 / 45

Which of the following makes a large strain calculation nonlinear?

Multiple load steps

Newton Raphson solution method

The presence of higher-order terms in the expression

The change in the magnitude and direction of loading.

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Physics of Structural Mechanics

Total time - 60 mins.

Total number of Questions - 45