中国大学mooc慕课Theory of Elasticity（东南大学） 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;
Stress;
Stresses;
STRESS;
STRESSES

9、 How many elastic constants do the equations of equilibrium proposed by Navier have? (integer only)
答案: 1

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;
Third;
THIRD

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

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

9、 Rotation tensor is given by the anti-symmetric part of the right displacement gradient and its transpose.

A:正确
B:错误
答案: 正确

10、 By definition, strain tensor is given by the (  ) part of the right displacement gradient and its transpose.
答案: (以下答案任选其一都对)symmetric;
Symmetric;
symmetrical;
Symmetrical;
SYMMETRIC;
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;
Angular;
Angle;
ANGLE;
ANGULAR

9、 The principal values of the total and the deviatoric stresses differ by the amount of mean stress.

A:正确
B:错误
答案: 正确

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

9、 Transversely isotropic materials have (   ) independent elastic constants.

A:5
B:2
C:3
D:9
答案: 5

10、 For the most anisotropic elastic materials, there are in total (   ) independent elastic constants.

A:21
B:9
C:13
D:5
答案: 21

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