1. Introduction to elasticity

Quiz for Chapter 1

1、单选题:
In the history of elasticity theory, who first investigated the contact mechanics between deformable elastic bodies?​
选项:
A: Hertz
B: Navier
C: Cauchy
D: Saint-Venant
答案: 【 Hertz

2、单选题:
How many elastic constants do the most anisotropic elastic solids have?‌
选项:
A: 1
B: 2
C: 15
D: 21
E: 36
答案: 【 21

3、多选题:
‏The fundamental assumptions of elasticity theory include:‎
选项:
A: Continuity
B: Homogeneity
C: Isotropy
D: Small Deformation
E: Elasticity
答案: 【 Continuity;
Homogeneity;
Isotropy;
Small Deformation;
Elasticity

4、多选题:
Has elasticity theory found its applications in which of the following engineering areas?‏
选项:
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、判断题:
In the history of elasticity theory, Poisson first derived the deflection equation of thin plates.​
选项:
A: 正确
B: 错误
答案: 【 正确

6、判断题:
Elasticity theory imposes no limits on the geometric shape of elastic solids.​
选项:
A: 正确
B: 错误
答案: 【 正确

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

8、填空题:
Elasticity analysis is primarily concerned with the determination of displacement, strain and (   ) distributions in elastic solids.‏
答案: 【 stress##%_YZPRLFH_%##stresses

10. Torsion of prismatic shafts

Quiz for Chapter 10

1、单选题:
Guided by the observations from mechanics of materials, the torsion of non-circular shafts was solve by which of the following method in theory of elasticity?‌
选项:
A: Direct method
B: Inverse method
C: Semi-inverse method
D: Method of separation of variables
答案: 【 Semi-inverse method

2、单选题:
Under the same amount of twisting moments, making a cut on a closed thin-walled tube results in (   ) shear stresses.‌‌
选项:
A: Much higher
B: Much lower
C: Unchanged
D: Zero
答案: 【 Much higher

3、多选题:
By comparing the torsional problem of prismatic shafts with the membrane inflation problem, which of the following arguments are correct?‎
选项:
A: They have the same type of governing equations and boundary conditions.
B: The twisting moment is equivalent to twice of the membrane volume.
C: Prandtl stress function is equivalent to the membrane elevation function.
D: The unit angle of twist is related to the uniform pressure acting on the membrane.
答案: 【 They have the same type of governing equations and boundary conditions.;
The twisting moment is equivalent to twice of the membrane volume.;
Prandtl stress function is equivalent to the membrane elevation function.;
The unit angle of twist is related to the uniform pressure acting on the membrane.

4、多选题:
Based on our lectures, the method of boundary equation works for the torsion problem of non-circular shafts with the following cross-sectional shapes:‎‎
选项:
A: Ellipse
B: Equilateral Triangular
C: Circle with a circular keyway
D: Rectangle
答案: 【 Ellipse;
Equilateral Triangular;
Circle with a circular keyway

5、判断题:
Prandtl stress function is identical to Airy stress function.‎
选项:
A: 正确
B: 错误
答案: 【 错误

6、判断题:
The method of boundary equations is able to solve the torsion problem of prismatic shaft with very thin rectangular cross-sections.‌
选项:
A: 正确
B: 错误
答案: 【 正确

7、填空题:
The torsional deformation of non-circular shafts may be decomposed as the rigid-body rotation of cross-sections and the (   ) displacement.‏
答案: 【 warping##%_YZPRLFH_%##warp

8、填空题:
Prandtl stress function must be (   ) on all lateral surfaces of a prismatic shaft subjected to twisting moments.‎
答案: 【 constant##%_YZPRLFH_%##constants

11. Three-dimensional problems

Quiz for Chapter 11

1、单选题:
Components of the Galerkin displacement potential vector have the dimension of (   ).‏‏
选项:
A: N·m
B: N
C: N/m
D: N/m/m
答案: 【 N·m

2、单选题:
The Lame strain potential has the dimension of (   ).‌‌
选项:
A: N·m
B: N
C: N/m
D: N/m/m
答案: 【 N

3、多选题:
The displacement potentials that you have learned from the lectures include:‎
选项:
A: Lame strain potential function
B: Love strain potential function
C: Galerkin displacement potential vector
D: Papkovich-Neuber displacement potentials
答案: 【 Lame strain potential function;
Love strain potential function;
Galerkin displacement potential vector;
Papkovich-Neuber displacement potentials

4、多选题:
In Hertzian contact problem, the fundamental unknows we aim to solve include:‍
选项:
A: The maximum pressure at the center of the contact circle
B: The radius of the contact circle
C: The relative rigid-body displacement between a pair of contacting points after deformation
D: The distribution pattern of the contact pressure between two deformable contact bodies
答案: 【 The maximum pressure at the center of the contact circle;
The radius of the contact circle;
The relative rigid-body displacement between a pair of contacting points after deformation

5、判断题:
The method of displacement potentials aims to convert the fundamental unknowns of an elastic problem from displacement components to their potential functions. Although the order of the differential equations satisfied by the potential functions is higher, the differential equations are in general much simpler than the Navier’s equations of equilibrium.‍
选项:
A: 正确
B: 错误
答案: 【 正确

6、判断题:
The simple Lame strain potential produces zero volume strain.​
选项:
A: 正确
B: 错误
答案: 【 正确

7、填空题:
The displacement vector can be expressed as the (   ) order derivatives of the Galerkin displacement potential vector.​
答案: 【 second##%_YZPRLFH_%##2nd

8、填空题:
The Love strain potential can be reduced from the (   ) displacement potential vector by keeping only its third component.‍
答案: 【 Galerkin

12. Bending of thin-plates

Quiz for Chapter 12

1、单选题:
Compared with beams, the flexural rigidity of thin plates is (   ).‌
选项:
A: larger
B: the same
C: smaller
D: difficult to compare
答案: 【 larger

2、单选题:
Along a clamped boundary of thin plates, both the deflection and the (   ) function are zero.‎
选项:
A: slope
B: curvature
C: bending moment
D: twisting moment
答案: 【 slope

3、多选题:
The internal forces in a thin plate under bending deformation include:‎
选项:
A: bending moment
B: twisting moment
C: shear force
D: axial force
答案: 【 bending moment;
twisting moment;
shear force

4、多选题:
Along a simply supported boundary of thin plates, which of the following quantities must be zero?‎
选项:
A: deflection
B: bending moment
C: slope
D: twisting moment
答案: 【 deflection;
bending moment

5、判断题:
In the be

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