MT-1620 Fall 2002 Thus X Key concept: The letters used for indices have no inherent meaning in and of themselves Thus:xi= y is the same as: X,=fs ys or x =fi yi Now apply these concepts for stress/strain analysis 1. Coordinate System Generally deal with right-handed rectangular Cartesian: y Paul A Lagace @2001 Unit 3-p. 6
MIT - 16.20 Fall, 2002 Thus: xi = ….. ⇒ x1 = ….. x2 = ….. x3 = ….. Key Concept: The letters used for indices have no inherent meaning in and of themselves Thus: xi = fij yj is the same as: xr = frs ys or xj = f y ji i Now apply these concepts for stress/strain analysis: 1. Coordinate System Generally deal with right-handed rectangular Cartesian: ym Paul A. Lagace © 2001 Unit 3 - p. 6
MT-1620 al.2002 Figure 3.4 Right-handed rectangular Cartesian coordinate system 3 Z 25 Compare notations y1,X Tensor Engineering X Z Note: Normally this is so, but always check definitions in any article, book, report, etc. Key issue is self-consistency, not consistency with a worldwide standard (an official one does not exIs Paul A Lagace @2001 Unit 3-p. 7
MIT - 16.20 Fall, 2002 Figure 3.4 Right-handed rectangular Cartesian coordinate system y3 , z y2, y Compare notations y1 , x y z 3 y y 2 y x 1 Tensor Engineering Note: Normally this is so, but always check definitions in any article, book, report, etc. Key issue is self-consistency, not consistency with a worldwide standard (an official one does not exist!) Paul A. Lagace © 2001 Unit 3 - p. 7