富精磨递点宽患戒携宠慷霓亮
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
答案: Hertz
2、 How many elastic constants do the most anisotropic elastic solids have
答案: 21
3、 The fundamental assumptions of elasticity theory include:
答案: Continuity;
Homogeneity;
Isotropy;
Small Deformation;
Elasticity
4、 Has elasticity theory found its applications in which of the following engineering areas
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.
答案: 正确
6、 Elasticity theory imposes no limits on the geometric shape of elastic solids.
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
答案: Angular coordinate (θ)
2、 In indicial notation, no index can appear more than ( ) times in a single algebraic term.
答案: 2
3、 In spherical coordinates, unit vectors are functions of which of the following coordinate variables
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
答案: Any scalar;
Kronecker delta;
Levi-Civita symbol
5、 Force can be represented by a scalar.
答案: 错误
6、 The operation of Laplacian differential operator on a tensor does not change its order.
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
答案: Three
2、 The principal values of the total strain tensor and the deviatoric strain tensor differ by the amount of ( ).
答案: Mean
stress
3、 How many independent compatibility equations does a two-dimensional elastic problem have
答案: One
4、 Which of the following factors contribute to the displacements of a material point
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.
答案: 正确
6、 The mean strain tensor is an isotropic tensor so that its components remain invariant under coordinate transformation.
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.
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 ( ).
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
答案: The square root of 2/9
3、 The right and left divergence of the Cauchy stress tensor are ( ).
答案: equal;
transpose to each other
4、 Which of the following can be the units of stresses
答案: Pascal;
Newton per unit area;
Mega-Pascal;
Giga-Pascal
5、 Cauchy stress tensor is symmetric.
答案: 正确
6、 The total stress and the deviatoric stress have different principal directions.
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.
答案: 正确
5. Constitutive relations Quiz for Chapter 5
1、 For isotropic elastic materials, there are in total ( ) independent elastic constants.
答案: 2
2、 For isotropic elastic materials, Young’s modulus is ( ) shear modulus.
答案: greater than
3、 The fourth order stiffness tensor is symmetric about its:
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.
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.
答案: 正确
6、 Rubber’s coefficient of thermal expansion is far greater than those of metals.
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.
答案: 5
10、 For the most anisotropic elastic materials, there are in total ( ) independent elastic constants.
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.
答案: three
2、 In stress formulation, stress components are first solved from compatibility conditions and ( )
答案: equilibrium equations.
3、 Solutions strategies of elastic problems include:
答案: Direct method;
Inverse method;
Semi-inverse method
4、 The boundary conditions of elastic problems include:
答案: Traction conditions;
Displacement conditions;
Mixed conditions
5、 In the displacement formulation of elasticity theory, strain compatibility is of a concern.
答案: 错误
6、 Along a general non-coordinate surface, externally applied surface tractions cannot reduce to individual stress components.
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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