l-組合變形-應(yīng)變狀態(tài)理論322.ppt

1、2 . 應(yīng) 變 狀 態(tài) 分 析,Analysis of strians,(1) 應(yīng)變狀態(tài)矩陣 (strain state matrix ),If the linear strains along any direction and the shearing strains between any two vertical directions at one point are all known , we say the state of strain at this point is determined .,結(jié)構(gòu)一點(diǎn)處應(yīng)變情況的總和稱為一點(diǎn)應(yīng)變狀態(tài).,如果一點(diǎn)處沿任何方向的線應(yīng)變以及任意兩

2、個(gè)相互垂直方向間的切應(yīng)變都已知,則說(shuō)該點(diǎn)的應(yīng)變狀態(tài)是確定的.,Like the state of stress at one point , the state of strain can be determined by a matrix . It is called strain state matrix .,類似一點(diǎn)應(yīng)力狀態(tài)的描述,一點(diǎn)應(yīng)變狀態(tài)可以用一個(gè)矩陣確定,該矩陣稱為應(yīng)變狀態(tài)矩陣.,Strain state matrix,Strain state matrix is a symmetrical matrix too . That is :,應(yīng)變狀態(tài)矩陣,In Mechanics o

3、f Materials all the problems ordinary are plane state of stress , so their state of strain ordinary is three-dimensional state .,材料力學(xué)的問(wèn)題一般是平面應(yīng)力問(wèn)題,其應(yīng)變狀態(tài)通常是三向應(yīng)變狀態(tài).,斜方向上的應(yīng)變 :,拉為正壓為負(fù),直角增大為負(fù)減小為正,斜方向上的應(yīng)變 :,(2) 主應(yīng)變與應(yīng)變主方向,Principal strains and principal strain directions,At one point if there are three dire

4、ctions vertical to each other and the shearing strains between them are all equal to zero , these directions are called pricipal strain directions and the normal strains along these directions are called principal strains .,Principal strain directions,Principal strains,(a) 概念 ( Concepts),For the iso

5、tropic materials , the principal stress directions and principal strain directions are just same .,Directions 1 , 2 , 3 are the principal strain directions too .,對(duì)線彈性各向同性材料來(lái)說(shuō),主應(yīng)力方向和主應(yīng)變方向是一致的.,2.4 應(yīng)變的測(cè)量,應(yīng)變片( strain gage ),分析和討論: 應(yīng)變片可以直接測(cè)量切應(yīng)變嗎？,k 靈敏度系數(shù),Measurements of strain,應(yīng)變片的測(cè)量結(jié)果常用 微應(yīng)變 來(lái)表示，記為 。,直角應(yīng)變花 ( rectangular rosette ),等角應(yīng)變花 ( equ