塑性力学第4讲.pdf

Chapter 4 Strain Analysis 1. Strain tensor (1) The definition of strain-The change ratio of the relative position of any two points in a continuous body between next equilibrium and initial equilibrium. Consider an infinitesimal line in undeformed and defamed body in increment theory ∆t. An infinitesimal line can divide into three stages: translation, rotation, strain to obtain the strain of an infinitesimal line, the step as: A. to delete the train of an infinitesimal line uuur uur uur ∆L r =−r AB OB OA uuur uur uuuur ⎧ =+ r r U ⎪OB OB BB and ⎨uuur uur uuuur r r =+U ⎪⎩OA OA AA uuuur uuur uuur ∆L r =−r A B OB OA uuuur uuur uuur uur uuur uur ∆L −∆L (r =−r ) −(r −r ) A B AB OB OB OA OA 1 ur uuuur uuuur ur ur ∆U = U −U =∆U , T lim r (表示除去後之線變形) BB AA l ∆→l 0 ∆l (一)The definition of line deformation as: ur ur ∆U T lim r l -line direction l ∆→l 0 ∆l B. the definition of line at rectangular coordinate system ur