Theory Quiz

Methods of Solving Problems in Structural Mechanics - Theory Quiz

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1 / 45

In a dynamic analysis using the mode superposition method, the displacement can be expressed as _____. Select the best option.

a linear combination of mode shapes

a non-linear combination of mode shapes

a non-linear combination of mode shapes with coefficients determined by experiment

a linear combination of mode shapes with coefficients determined by experiment

2 / 45

Bending of a fishing rod shows non-linear behavior because _____. Select the best option.

It is designed to behave only non-linearly

Force deflection curve is following Hooke's law

Increasing slope of force deflection curve

Once fish is caught it will move randomly

3 / 45

When the excitation frequency is equal to the natural frequency and the damping is zero, the modal coordinate value is _____.

unknown

equal to the lowest displacement

infinite

zero

4 / 45

An engineer redesigns a part with material removed from the part in the new design. Which of the following statements holds? Select the three best options.

In same analysis multiple design iterations can be performed.

New design can be analyzed using simulation.

There will be no change in the analysis result with redesign.

New design can further be improved using the simulation.

5 / 45

Which expression represents the harmonic equation of motion in modal form?

$\left [ u \right ]=\left [ u_{max}e^{i\phi } \right ]e^{i\Omega t}$

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

$\left ( \Omega ^{2}+i2\omega _{j}\Omega \zeta _{j}+\omega_{j}^{2} \right )y_{jc}=f_{jc}$

$\left [ F \right ]=\left [ F_{max}e^{i\Psi } \right ]e^{i\Omega t}$

6 / 45

A structure that experiences _____ for a given load can still support that load without catastrophic failure. Select the best option to complete the sentence.

material failure

local buckling

dynamic failure

global buckling

7 / 45

Which of these are correct statements about time intgeration methods? Select the two best options.

The implicit method can always reach stable results while the explicit method depends on the time step size to have stable results.

The implicit method allows for larger time-step size while the explicit method requires very small time-step size.

The solving speed of the implicit method is faster than the explicit method for one time-step.

For nonlinear problems, both implicit and explicit methods require an iterative solver to find results within one time-step.

8 / 45

To solve a nonlinear dynamic problem, which of the following statements are correct about implicit and explicit time integration methods? Select the two best options.

The explicit method cannot be used to solve a nonlinear dynamic problem.

The explicit method can be used to solve a nonlinear dynamic problem because a linear solution of each small time-step can form a nonlinear response as a whole over the full time period of the solution.

Only the implicit method can be used to solve a nonlinear dynamic problems.

Both the implicit and the explicit methods can be used to solve nonlinear dynamic problem.

9 / 45

Which of the following is a method used for solving non-linear response of structure? Select the best option.

Newton Raphson method

Cholesky decomposition

Simpson's rule

Jacobi method

10 / 45

In a harmonic steady state response with more than one excitation, which variable dictates the relative timing of the excitations.

Imposed circular frequency

Time Increment

Phase angle

Damping

11 / 45

A structure is deemed unstable when _____. Select the best option to complete the sentence.

it undergoes very large deformation for a small load increment

it experiences plastic strain

its stiffness becomes nonlinear

it undergoes large deformation

12 / 45

Which of these statements is NOT true about buckling? Select the option that is false.

Buckling is a structural instability.

Material failure is not a cause of buckling.

Buckling doesn't always lead to catastrophic failure.

Buckling occurs only under compressive loads.

13 / 45

Exciting a physical system at the natural frequency can occur, _____. Select the two best options.

but there will always be some amount of damping to prevent predicting a non-physical infinite response

but there might be damping that can further increase the displacement response

and the response will always be excessive, independent of the amount of damping

and the phase angle of the response will be 90 degrees from the input

14 / 45

A large electric motor that drives a system of pulleys in a factory environment experiences excessive vibration while it is slowly being brought up to operating speed. A Harmonic Analysis of the application shows an amplitude vs frequency plot that proves that the motor is passing thru two natural frequencies during this start up. Assuming the operating speeds cannot be altered, choose the two best options for improving the design.

Add vibration isolators to the motor mount assembly as their added mass should alter the natural frequencies of the system.

Add vibration isolators to the motor mount assembly to dampen out the response as the motor passes thru the natural frequencies.

Remove vibration isolators from under the motor mount assembly.

Explore alternative materials and design geometries to change the stiffness and mass and thereby alter the natural frequencies so they fall outside the operating range of the application.

15 / 45

From the force-displacement curve of an unstable structure in a static analysis, how can one identify the point of instability? Select the best option.

It is the point at which the force-deflection curve becomes nonlinear.

It is the point at which slope of the force-deflection curve increases.

It is the point at which the slope of the force-deflection curve approaches zero.

It is the point at which slope of the force-deflection curve decreases.

16 / 45

The "d" parameter in the Mooney-Rivlin Strain Energy expression $\Psi =C_{10}(I_{1}-3)+C_{01}(I_{2}-3)+\frac{1}{d}(J-1)^2$ is inversely proportional to _____.

the deviatoric strain energy

Poisson's ratio

the initial shear modulus

the initial bulk modulus

17 / 45

For a fully incompressible hyperelastic material, the strain energy function is usually expressed _____. Select the best option.

exclusively in terms of volumetric energies

exclusively in terms of deviatoric energies

as a tightly coupled expression of both deviatoric and volumetric energies

as an additive split of deviatoric and volumetric energies

18 / 45

The mode superposition method is _____. Select the best option.

an approximate technique

a nonlinear combination technique

an experimental technique

an empirical technique

19 / 45

The tolerance defined by a user for the Newton Raphson method is called _____.

Stiffness Criteria

Convergence Criteria

Internal Force Criteria

Displacement Criteria

20 / 45

What are the benefits to treating some parts as a rigid body in a large assembly? Select the two best options.

Since rigid bodies are extremely stiff, the time-step size used for the simulation is larger.

Using rigid bodies can simplify the model and put most of the computational effort on the parts of interest in the design.

Using rigid bodies, stresses and strains in the body can be computed.

Using rigid bodies can reduce the number of elements because rigid bodies do not require a mesh (the contacting surfaces may need to be meshed but not the entire body).

21 / 45

Which is the best reason for using more terms in a hyperelastic model? Select the best option.

To include compressibility behavior.

To capture highly nonlinear stress strain behavior.

To enhance run time.

To enhance convergence.

22 / 45

Engine vibration mounts serve to _____. Select the best option.

Change the natural frequency of the system

Completely eliminate all vibrations

Isolate the vibration of the engine from the chassis and passengers

Change the path of the cyclic forcing loads.

23 / 45

To maintain numerical stability while using the explicit time integration method, the time-step size should satisfy the CFL condition, which is $\Delta t \leq f \left ( \frac{h}{c} \right )$. Which of the following statements are correct about the CFL condition? Select the two best options.

In the CFL condition, h is the smallest characterize length of all the elements for the simulation.

In the CFL condition, c is the velocity of sound passing through the material.

In the CFL condition, h is the average characterize length of all the elements for the simulation.

In the CFL condition, c is the velocity of the structure.

24 / 45

When considering eigenvalue buckling analysis, why is the point on force-displacement curve at which a structure undergoes buckling called a bifurcation point? Select the best option.

Because the structure can buckle in more than one way (two or more equilibrium solutions)

Because the actual buckling load is half of this calculated load

Because the structure can split in half

Because it is only used for column-like structures that can buckle to the left or to the right

25 / 45

Which of the following statements is relevant to using a full method in a harmonic analysis? Select the best option.

The equations are uncoupled and the solution is computationally efficient.

The equations are coupled and solving them can be computationally expensive.

The full method always requires a large amount of memory.

26 / 45

In reality how many iterations are needed for sum of internal forces to be exactly equal to the applied forces for a nonlinear problem? Select the best option.

1

Infinite

100

10

27 / 45

Local buckling due to weight is noticed along a section of the wall of a large, axisymmetric oil storage tank. You are asked to reproduce the buckling scenario via finite element simulation. Among the options listed, which type of analysis would be best for completing this task?

Nonlinear transient analysis

Linear transient analysis

Prestressed eigenvalue buckling analysis followed by static structural nonlinear analysis

Modal analysis

28 / 45

Stress developed in a hyperelastic material is calculated from _____. Select the best option.

test data

the strain energy function

the elastic modulus

the tangent modulus

29 / 45

While simulating the drop test of a circuit board on to a hard ground using an explicit analysis, if the computing time is very long, which of the following options may help reduce the computational time? Select the three best options.

Use mass-scaling to increase the time-step size.

Remove all unnecessary details from the original geometry.

Treat all the electronic components as rigid bodies.

Treat the hard ground as a rigid body.

30 / 45

Force convergence failure for a Newton Raphson method indicates _____. Select the best option.

Too much time taken to solve the problem with sufficient available iterations

Undefine material property

Force imbalance

Unrealistic geometry

31 / 45

Which of the following holds true for a cantilever (such as a diving board) excited by a harmonic external force with its frequency matching the second natural frequency? Select the best option.

Most contribution to the deformation will be from the second natural frequency.

Most contribution to the deformation will be from the fourth natural frequency.

Most contribution to the deformation will be from the third natural frequency.

Most contribution to the deformation will be from the first natural frequency.

32 / 45

Once a ductile metal under a structural load exceeds the elastic limit, it immediately _____. Select the best option.

stops deforming

exceeds to ultimate strength

begins to develop plastic strain

continues to develop only elastic strains

33 / 45

Which of the following statements are correct about the stability of the time integration method in finite element methods? Select the two best options.

If numerical instability is observed for the dynamic simulation, the results of the simulation should be considered not trustworthy.

If the time integration method is unconditionally stable, it does not matter how large the time-step is, the simulation remains numerically stable and accurate.

For a dynamic simulation, numerical instability caused by time integration can be observed as the structure experiences sudden changes of deformation, such as buckling.

For a dynamic simulation, numerical instability caused by time integration can be observed as the amplitude of the oscillation of the structure gradually grows without bound (to infinity).

34 / 45

What is the relationship between displacement, velocity, and acceleration for a dynamic problem? Select the three best options.

Displacement is the time derivative of velocity respect to time.

Velocity is the derivative of displacement with respect to time.

Acceleration is the derivative of velocity with respect to time.

Acceleration is the second order derivative of displacement with respect to time.

35 / 45

Which term describes the area under the stress-strain curve in a unit volume of hyperelastic material? Select the best option.

Strain energy

Integration

Modulus of elasticity

Poisson's ratio

36 / 45

An analyst solves a simple small problem using the full method and the mode superposition method. Which one of the following statements is correct? Select the best option.

The mode superposition method always takes less time compared to any other solution method.

Using the full method for a small problem might take less time than Mode superposition method.

The two solutions will be identical.

37 / 45

Dynamic instabilities occur due to _____. Select the best option to complete the sentence.

uncontrolled increase in the internal energy of the system

uncontrolled loss of energy in the system

uncontrolled increase in the kinetic energy of system

uncontrolled increase in the total energy of the system

38 / 45

In the hyperelastic strain energy equations, as the parameter d (which is inversely proportional to the initial bulk modulus) decreases, the material tends to become _____. Select the best option.

more linear

more incompressible

softer

harder

39 / 45

Most ductile metals under a structural load undergo elastic deformation for strain ranges up to _____. Select the best option.

0.10%

200%

10%

100%

40 / 45

Which of the following is correct for running an Ansys Simulation? Select the best option.

One should never run a large solution on cloud or remotely.

The simulation can only be run on a local laptop/desktop.

The simulation can run locally, remotely or on a cloud.

The simulation can only be run both locally or remotely, but not on cloud.

41 / 45

Structural instabilities may occur due to different reasons, but two common ones are due to a loss of stiffness and due to inertial effects. Dynamic instability describes the latter situation. Which of these cases is NOT a dynamic instability?

Aeroelastic flutter

Brake squeal

Excessive vibration of rotating equipment

Crushing of an empty soda can

42 / 45

Two analysts solve the same dynamic analysis of a large model. One of them changes the solution method to mode superposition (with no other differences in the analysis). The analysts find that there is a significant time difference between them to solve the models. Which of the following statements is correct in regards to his scenario? Select the best option.

The mode superposition method is the faster approach for the large model.

The mode superposition method is always the preferred approach.

The method other than mode superposition is faster and must have completed in a short time.

The method other than mode superposition is always the preferred approach.

43 / 45

The displacement vector for a mode superposition solution with three modes is to be computed. The modal coordinate for each mode 1, 2 and 3 is 1 and for each of these modes, let's assume the value from the mode shape vector for a single node of interest is also 1. What will be the value of the nodal displacement calculated for this node of interest using these three modes?

1

3

6

2

44 / 45

For a response spectrum analysis, the mode superposition method is _____. Select the best option.

a post-processing option

optional

prerequisite

essential as per government requirements

45 / 45

The velocity derived from the complex displacement function is characterized by which expression?

$A(\cos \Omega t + i\sin \Omega t)$

$i\Omega A e^{i \Omega t}$

$-\Omega^2 A e^{i \Omega t}$

$-\Omega^2A(\cos \Omega t + i\sin \Omega t)$

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Methods of Solving Problems

Total Available Time - 90 mins

Total Number of Questions - 45