《2022年力学专业外文翻译》由会员分享，可在线阅读，更多相关《2022年力学专业外文翻译（24页珍藏版）》请在金锄头文库上搜索。
1、附 录:外文翻译5.1IntroductionCylindrical shells are used innuclear,fossil and petrochemical industries. They are also used in heat exchangers of the shell and tube type.Generally.These vessels are easy to fabricate and install and economical to maintain. The design procedures in pressure vessel codes for
2、cylindrical shells are mostly based on linear elastic assumption,occasionally allowing for limited inelastic behavior over a localized region.The shell thickness is the major design parameter and is usually controlledby internal pressure and sometimes by external pressure which can produce buckling.
3、Applied loads are also important in controlling thickness and so are the disconti-nuity and thermal stresses.The basic thicknesses of cylindrical shells are Based on simplied stress analysis and allowable stress for the material of construction.There are some variations of the basic equations in var
4、ious design codes.Some of the equations are based on thick-wall Lame equations.In this chapter such equations will be discussed.Also we shall discuss the case of cylindrical shells under external pressure where there is a propensity of buckling or collapse.5.2 Thin-shell equationsA shell is a curved
5、 plate-type structure.We shall limit our discussion to Shells of revolutions.Referring to Figure5.1 this is denoted by anangle ,The meridional radius r1 and the conical radius r2,from the center line.The horizontal radius when the axis is vertical is r. If the shell thickness is t,with z being the c
6、oordinate across the thickness,following the convention of Flugge, We have the following stress resultants: (5.1) (5.2) (5.3)Figure 5.1 Thin shell of revolution. (5.4)These stress resultants are assumed to be due only to an internal pressure, p,acting in the direction of r. For membrane shells where
7、 the Effects of bending can be ignored,all the moments are zero and further development leads toThe following equations result from considering force equilibrium along with the additional requirement of rotational symmetry: (5.6) (5.7)Noting that,we have,by solving Eqs.(5.6)and(5.7), (5.8) (5.9)The
8、above two equations are the results for a general shell of revolution. Two specic cases result:1. For a spherical shellof radius R, r1= r2 =R,which gives (5.10)2. For a cylindrical pressure vessel of radius R,we have r1 =; r2 = R,which gives (5.11) (5.12)This gives the hoop stress (5.13)and the long
9、itudinal stress (5.14)These results will be shown to be identical to the results that follow. Let us consider a long thin cylindrical shell of radius R and thickness t, subject to an internal pressure p.By thin shell we mean the ones having the ratio R/t typically greater than about10.If the ends of
10、 the cylindrical shell are closed,there will be stresses in the hoop as well as the axial (longitudinal) directions.A section of such a shell is shown in Figure5.2. The hoop(circumfer-ential)stress, and the longitudinal stress, are indicated in the gure.The shell is assumed to be long and thin resul
11、ting in andto be uniform through the thickness.Therefore in this case and are also referred to as membrane stress(there are no bending stresses associated with this type of loading).Considering equilibrium across the cut section,we have,Figure 5.2 Thin cylindrical shell.which gives (5.15)Considering
12、 a cross-section of the shell perpendicular to its axis,we haveWhich gives (5.165.3 Thick-shell equationsFor R/t ratios typically less than 10,Eqs.(5.15) and (5.16) tend not to be accurate,and thick-shell equations have to be used. Consider a thick cylindrical shell of inside radius Ri and outside r
13、adius Ro subjected to an internal pressure p as shown in Figure5.3 .The stress function for this case(refer to AppendixI)is given as a Function of radius r as (5.17)Figure 5.3 Thick cylindrical shell.with A and B to be determined by the boundary conditions. If we indicate the radial stress as and th
14、e hoop and longitudinal Stress as indicated previously by and,we have (5.18) (5.19)The constants A and B are determined from the following boundary conditions: at at (5.20)Substituting(5.20)into(5.18)and(5.19),we have (5.21)Denoting the ratio of the outside to inside radii as m,so that m =Ro/Ri, We obtain theradial and hoop stresses (5.22) (5.23) Figure5.4 shows the radial and hoop stress distributions.The longitudinal stress, is determined by considering the Equilibrium of forces across a plane normal to the axis of the shell,which gives
