中国大学mooc慕课Theory of Elasticity(Southeast University) 答案

1. Introduction to elasticity Quiz for Chapter 1

1、 In the history of elasticity theory, who first investigated the contact mechanics between deformable elastic bodies?

A:Hertz
B:Navier
C:Cauchy
D:Saint-Venant
答案: Hertz

2、 How many elastic constants do the most anisotropic elastic solids have?

A:1
B:2
C:15
D:21
E:36
答案: 21

3、 The fundamental assumptions of elasticity theory include:

A:Continuity
B:Homogeneity
C:Isotropy
D:Small Deformation
E:Elasticity
答案: Continuity;
Homogeneity;
Isotropy;
Small Deformation;
Elasticity

4、 Has elasticity theory found its applications in which of the following engineering areas?

A:Civil engineering
B:Mechanical engineering
C:Aeronautical and aerospace engineering
D:Materials science and engineering
答案: Civil engineering;
Mechanical engineering;
Aeronautical and aerospace engineering;
Materials science and engineering

5、 In the history of elasticity theory, Poisson first derived the deflection equation of thin plates.

A:正确
B:错误
答案: 正确

6、 Elasticity theory imposes no limits on the geometric shape of elastic solids.

A:正确
B:错误
答案: 正确

7、 How many elastic constants do the equations of equilibrium proposed by Navier have? 
答案: 1

8、 Elasticity analysis is primarily concerned with the determination of displacement, strain and (   ) distributions in elastic solids.
答案: (以下答案任选其一都对)stress;
stresses

2. Mathematical preliminaries Quiz for Chapter 2

1、 In cylindrical coordinates, the radial and angular unit vectors are dependent on which of the following coordinate variable?

A:Radial coordinate (r)
B:Angular coordinate (θ)
C:Vertical coordinate (z)
D:None
答案: Angular coordinate (θ)

2、 In indicial notation, no index can appear more than ( ) times in a single algebraic term.

A:1
B:2
C:3
D:no limit
答案: 2

3、 In spherical coordinates, unit vectors are functions of which of the following coordinate variables?

A:Spherical radial (R)
B:Spherical longitudinal coordinate (φ)
C:Spherical latitudinal coordinate (θ)
D:All
答案: Spherical longitudinal coordinate (φ);
Spherical latitudinal coordinate (θ)

4、 Which of the following are isotropic tensors, so that their components do not change under coordinate transformations?

A:Any scalar
B:Any vector
C:Kronecker delta
D:Levi-Civita symbol
答案: Any scalar;
Kronecker delta;
Levi-Civita symbol

5、 Force can be represented by a scalar.

A:正确
B:错误
答案: 错误

6、 The operation of Laplacian differential operator on a tensor does not change its order.

A:正确
B:错误
答案: 正确

7、 How much is the determinant of the transformation matrix between different coordinate systems?
答案: (以下答案任选其一都对)1;
-1

8、 The left divergence of a second order tensor can be obtained by the contraction operation between the first and the (   ) index of its right gradient.
答案: (以下答案任选其一都对)third;
3rd;
3

3. Displacement and strain Quiz for Chapter 3

1、 How many invariants does the strain tensor have?‍

A:Zero
B:One
C:Two
D:Three
答案: Three

2、 The principal values of the total strain tensor and the deviatoric strain tensor differ by the amount of (    ).

A:Mean
stress
B:1/3 of the mean stress
C:Zero
D:Three times of the mean stress
答案: Mean
stress

3、 How many independent compatibility equations does a two-dimensional elastic problem have?

A:Zero
B:One
C:Three
D:Six
答案: One

4、 Which of the following factors contribute to the displacements of a material point? ‍

A:Rigid-body translations
B:Rigid-body rotations
C:Strain deformations
D:None
答案: Rigid-body translations;
Rigid-body rotations;
Strain deformations

5、 The total strain tensor and the deviatoric strain tensor have the same principal directions.

A:正确
B:错误
答案: 正确

6、 The mean strain tensor is an isotropic tensor so that its components remain invariant under coordinate transformation.

A:正确
B:错误
答案: 正确

7、 By definition, strain tensor is given by the (  ) part of right displacement gradient and its transpose.
答案: (以下答案任选其一都对)symmetric;
symmetrical

8、 By definition, rotation tensor is given by the (  ) part of right displacement gradient and its transpose.
答案: (以下答案任选其一都对)antisymmetric;
anti-symmetric;
antisymmetrical;
anti-symmetrical

4. Stress and equilibrium Quiz for Chapter 4

1、 The first subscript of a stress component stands for its acting surface whereas the second one represents its (    ). ‍

A:Direction

B:Magnitude

C:Acting surface

D:None

答案: Direction

2、 How much is the ratio between the octahedral shear stress and the equivalent stress of the maximum distortion energy yield criterion?

A:The square root of 2/9
B:2/9
C:1
D:1/3
答案: The square root of 2/9

3、 The right and left divergence of the Cauchy stress tensor are (   ).

A:equal
B:negative to each other
C:transpose to each other
D:anti-symmetric to each other
答案: equal;
transpose to each other

4、 Which of the following can be the units of stresses?

A:Pascal
B:Newton per unit area
C:Mega-Pascal
D:Giga-Pascal
答案: Pascal;
Newton per unit area;
Mega-Pascal;
Giga-Pascal

5、 Cauchy stress tensor is symmetric.

A:正确
B:错误
答案: 正确

6、 The total stress and the deviatoric stress have different principal directions.

A:正确
B:错误
答案: 错误

7、 The principal values of the total and the deviatoric stresses differ by the amount of (   ).
答案: (以下答案任选其一都对)mean stress;
average stress

8、 The equilibrium equations defined for a material point inside an elastic body can be derived from the conservations of linear and (   ) momenta.
答案: (以下答案任选其一都对)angular;
angle

5. Constitutive relations Quiz for Chapter 5

1、 For isotropic elastic materials, there are in total (   ) independent elastic constants.

A:2
B:13
C:5
D:9
答案: 2

2、 For isotropic elastic materials, Young’s modulus is (   ) shear modulus.

A:greater than
B:less than
C:equal to
D:not relevant to
答案: greater than

3、 The fourth order stiffness tensor is symmetric about its:‍

A:First two subscripts
B:Last two subscripts
C:First and second pair of subscripts
D:All subscripts
答案: First two subscripts;
Last two subscripts;
First and second pair of subscripts

4、 For conventional elastic materials, which of the following arguments are correct for Poisson’s ratio.

A:It is greater than zero.
B:It is less than 0.5.
C:It is defined as the negative of the ratio between axial and transverse strain under a uniaxial stress state.
D:It is a dimensionless quantity.
答案: It is greater than zero.;
It is less than 0.5.;
It is defined as the negative of the ratio between axial and transverse strain under a uniaxial stress state.;
It is a dimensionless quantity. 

5、 Young’s modulus, shear modulus and Poisson’s ratio are not independent since we can find an equality relating them together.

A:正确
B:错误
答案: 正确

6、 Rubber’s coefficient of thermal expansion is far greater than those of metals.

A:正确
B:错误
答案: 正确

7、 Transversely isotropic materials have (   ) independent elastic constants.
答案: (以下答案任选其一都对)5;
five

8、 For the most anisotropic elastic materials, there are in total (   ) independent elastic constants.
答案: (以下答案任选其一都对)21;
twenty one

6. Formulations and solution strategy Quiz for Chapter 6

1、 For three-dimensional displacement formulation of elasticity theory, we aim to solve the three displacement components from (  ) Navier’s equations of equilibrium.

A:three
B:six
C:one
D:nine
答案: three

2、 In stress formulation, stress components are first solved from compatibility conditions and (   )

A:equilibrium equations.
B:strain-displacement relations.
C:Hooke’s law.
D:no other conditions are needed.
答案: equilibrium equations.

3、 Solutions strategies of elastic problems include:

A:Direct method
B:Inverse method
C:Semi-inverse method
D:Guessing
答案: Direct method;
Inverse method;
Semi-inverse method

4、 The boundary conditions of elastic problems include:

A:Traction conditions
B:Displacement conditions
C:Mixed conditions
D:Symmetry conditions
答案: Traction conditions;
Displacement conditions;
Mixed conditions

5、 In the displacement formulation of elasticity theory, strain compatibility is of a concern.

A:正确
B:错误
答案: 错误

6、 Along a general non-coordinate surface, externally applied surface tractions cannot reduce to individual stress components.

A:正确
B:错误
答案: 正确

7、 The goal of elasticity theory is to determine the distribution of displacements, strains and (   ).
答案: (以下答案任选其一都对)stresses;
stress

8、 The compatibility conditions of stresses may be expressed by either six second-order partial differential equations or (   ) fourth-order partial differential equations.
答案: (以下答案任选其一都对)three;
3

7. Formulations of plane elasticity Quiz for Chapter 7

1、 In plane strain formulation, what’s the ratio between the out-of-plane stress and the sum of two in-plane stress components?

A:Poisson’s ratio
B:Negative of Poisson’s ratio
C:0
D:Not related
答案: Poisson’s ratio

2、 For harmonic body force potentials, the stress formulation of plane elasticity theory may be transformed into a single biharmonic equation about which of the following quantity?

A:Airy stress function
B:Stress
C:Strain
D:Displacement
答案: Airy stress function

3、 About plane strain and plane stress formulations, which of the following statements are correct descriptions?

A:One formulation can be converted to another by the simultaneous replacements of Young’s modulus and Poisson’s ratio.
B:With the help of Kolosov’s constant, they be expressed with the identical form.
C:The governing equations of two formulations differ only by elastic constants.
D:The method of Airy stress function is valid for both formulations.
答案: One formulation can be converted to another by the simultaneous replacements of Young’s modulus and Poisson’s ratio.;
With the help of Kolosov’s constant, they be expressed with the identical form.;
The governing equations of two formulations differ only by elastic constants.;
The method of Airy stress function is valid for both formulations.

4、 For a simply-connected plane domain subjected to harmonic body force potentials and only traction boundary conditions, which of the following statements are correct?

A:The Airy stress functions of plane strain and plain stress formulations satisfy the same governing equation.
B:The stresses for plane strain and plane stress formulations are identical.
C:The stresses for plane strain and plane stress formulations are independent on elastic constants.
D:The displacements for plane strain and plane stress formulations are identical.
答案: The Airy stress functions of plane strain and plain stress formulations satisfy the same governing equation.;
The stresses for plane strain and plane stress formulations are identical.;
The stresses for plane strain and plane stress formulations are independent on elastic constants.

5、 In plane strain problems, the out-of-plane stress component must be zero.

A:正确
B:错误
答案: 错误

6、 In plane stress problems, the out-of-plane strain component must be zero.

A:正确
B:错误
答案: 错误

7、 Long cylinders subjected to body forces and tractions that both are independent on the axial direction and do not have the axial component may be formulated in terms of the plane (   ) elasticity theory.
答案: (以下答案任选其一都对)strain;
strains

8、 Thin plates subjected to tractions acting only in their middle planes may be formulated in terms of the plane (   ) elasticity theory.
答案: (以下答案任选其一都对)stress;
stresses