陪脯锋溉搞斤枯协钩鞠饥访瓤
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
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