材料力学总结

材料力学总结

材料力学名词解释及填空

名词解释

1、Stress(应力)

the force per unit area , or intensity of the force distributed over a given section, is called stress. σ=F/A

2、normal stress(正应力)

The internal force is therefore normal to the plane of the section and the corresponding stress is described as the normal stress.

3、Shearing stress(剪应力)

The internal force is the shear on the plane of the section and the corresponding stress is described as the shearing stress.

4、Linear Strain(应变)

The normal strainεin a member can be defined as the deformation of the meter of the per unit length.

5、The main objective of the study the mechanics of materials（材料力学的任务）is to provide the future engineer with the means of analyzing and designing various machines and loading-bearing structures.

6、Saint-venant’s principle（圣维南原理）For two sets of statically equivalent forces, except in the immediate vicinity of the points of application of the loads, the stress distribution may be assumed independent of the actual mode of application of the loads (this statement is not only to axial load, but to practically any type of load)

7、Work-energy principle(功能原理)

The Work-energy Principle: In the process of the deformation of a elastomer, the strain energy which is stored in elastomer is equal to the work of the external force in number. This is the Work-energy Principle and it can be represented as Vε=W.

8、effective length （有效长度）is defined as real length multiplied by factor of length

9、principle plane(主平面)

is the plane in which the shearing stress equals zero, and normal stresses achieve maximum or minimum.

Principle stress(主应力)

The normal stress which is exerted on the principle plane is called the principle stress.

10、Radius of radius of gyration【revolution】（惯性半径）of an area can be calculated by the following formula i=I/A

Where i =the moment of inertia of an area

A=the area of an cross section

11、isotropic materials （各向同性材料）are the materials whose elastic constants are independent of direction.

12、homogeneous materials （均匀性材料）are the materials whose elastic properties are the same everywhere.

13、The strain energy density(应变能密度)

The strain energy in the unit volume can be defined as the strain energy density.

14、Hooke’s law （胡克定律）may be expressed more fully by saying that

1】when the stress increases,the measured strain increases in the same ratio

2】when the stress diminishes, the measured strain diminishes in the same ratio

3】when the stress is removed, no strain can be measured

For a small deformation,the stress is directly proportional to the strain.

15、Hooke’s law for shearing stress(剪切胡克定律)

The relation τ=Gγis known as Hooke’s law for shearing stress. Strain and constant Gis called the modulus of rigidity or shear modulus of material.

16、Generalized Hooke’s law（广义胡可定律）

17、Poisson ratio (泊松比)is defined as the ratio of lateral contraction (strain) to longitudinal extension (strain) of a bar under terminal tension.

18、factor of safety （安全因数）ultimate load over allowable load

19、stress-concentration factor k（应力集中因数K）=maximum stress over average stress

20、statically indeterminate problem（静不定问题）is the problem in which the reactions and internal forces can not be determined by static

only , analysis of deformation is needed.

21、neutral surface（中性层）is defined as the surface between the top and bottom of a beam in which longitudinal line do not change.

22、Neutral axis （中性轴）

①The neutral surface intersects a transverse section along a straight line called the neutral axis of the section.

②The intersection of the neutral surface with a transverse section is called the neutral axis of the section.

23、principle of superposition（叠加原理）

for all linear systems (a beam can be modeled as a linear system ),

24、the quantity the term λ=μl /i (柔度) is known as the slenderness ratio of the column. Where μl= effective length

i= the radius of gyration

25、The theory of strength(强度理论)

The assumption concerning the damage or the losing effect of the material is called the theory of strength.

26、buckling (失稳)

A stage when the column suddenly becomes sharply curved instead of remaining straight as the load is applied is called buckling.

27、The critical force (临界压力)

The value of the compressive force which is right on the boundary between the stable balance and the unstable balance is called the critical force.

28、The critical stress (临界应力)

The corresponding stress of the critical force is described as the critical force.

29、Euler’s Formula (欧拉公式)

Euler’s Formula can be expressed as

Fcr=π2EI／le2

in which: Fcr denotes the critical load

E denotes the modulus

I denotes the minimum moment of inertia of area

le denotes the equivalent length

30、Assumption for a bar (拉压的平面假设) The hypothesis assumes that the section keeps being a plane after deformation.

31、Assumption for torsion (扭转平面假设) When a circular shaft is subjected to a torsion, every cross section remains plane and undamaged.

32、Assumption for bending (弯曲平面假设) Under bending, the cross section of the beam remains plane and has a constant curvature. And the new cross section still perpendicular to axis.

32、极惯性矩

The polar moment of inertia of an area is defined as the polar moment of inertia of an area with respect to a point as the integral Ip=∫ρ2dA

33、惯性矩

The moment of inertia of an area is defined as the second moment of the area with respect to an axis as the integral I=∫y2dA.

34、静矩

The static moment of an area is defined as the first moment of an area with respect to an axis as the integral Sz=∫ydA.

填空题

1 三个材料假设

Homogeneousity assumption 、Continuity assumption 、Isotropy assumption

2 三个关系

Geometric relation 、Physical relation、Equilibrium relation

3 限制梁挠度的三个条件

Boundary condition 、Constraint condition、Continuity condition

4 三种约束方式

1）固定端fixed end

2）固定铰支座fixed support of pin joint

3）可动铰支座roller support of pin joint

5 三种梁

1）简支梁simply supported beam

2）外伸梁overhang beam

3）悬臂梁cantilever beam

6 For perfect column, the factor of length for conditions both pinned; both fixed; one fixed the other free; one fixed the other pinned are 1、0.5、2、0.

7 respectively.

7 The four classic strength theories include maximum tensile stress theory、maximum elongated normal strain theory、maximum shearing stress theory and maximum distortional strain energy theory.

8 The tensile diagram of low carbon steel consist of four stages: elastic stage 、yielding stage、hardening stage and necking stage.