1、2 . 應 變 狀 態(tài) 分 析,Analysis of strians,(1) 應變狀態(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 .,結構一點處應變情況的總和稱為一點應變狀態(tài).,如果一點處沿任何方向的線應變以及任意兩

2、個相互垂直方向間的切應變都已知,則說該點的應變狀態(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 .,類似一點應力狀態(tài)的描述,一點應變狀態(tài)可以用一個矩陣確定,該矩陣稱為應變狀態(tài)矩陣.,Strain state matrix,Strain state matrix is a symmetrical matrix too . That is :,應變狀態(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 .,材料力學的問題一般是平面應力問題,其應變狀態(tài)通常是三向應變狀態(tài).,斜方向上的應變 :,拉為正壓為負,直角增大為負減小為正,斜方向上的應變 :,(2) 主應變與應變主方向,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 .,對線彈性各向同性材料來說,主應力方向和主應變方向是一致的.,2.4 應變的測量,應變片( strain gage ),分析和討論: 應變片可以直接測量切應變嗎？,k 靈敏度系數(shù),Measurements of strain,應變片的測量結果常用 微應變 來表示，記為 。,直角應變花 ( rectangular rosette ),等角應變花 ( equ