弹塑性课后题参考答案.pdf

第一次测验 p33 1.3 Solution: (d)       111 3 ij ij ii 11 22 33 (e)         3 ij jk ki ik ki ii 11 22 33 p33 1.4 Solution:  andC aresecond ordertensors ij ij B a a B i j ik j k ke C a a C i j ik j e ke Bi j  Ci j ai k aj e (Bke  Cke )   C is second ordertensors ij ij p34 1.12 Solution: (a)the inner product of Cij and Dtm over indices ’i’ and ‘m’ 5 3 2 3 0 2     C D D C 3 6 5 0 2 3 ij ei ei ij    2 5 7 2 3 5     (b) p35 1.17 2 2 ，compute V , V , V V 3 xi 2 y xj 3 xz k i ,i i,i 2 j ,3j Solution: V V V V x  y  z 3  4 xy6 xz i ,i x y z 2 2 2  V  V  V V x  y  z 0  4 x0 4 x i ,i 2 xy y 2 yz 2 2 2  V  V  V V x  y  z 0 0 6 x 6 x j ,3j xz yz z 2 1.18 If  x2 5sin y xyz 3 , compute (a) ,i (b) ,ii Solution    3 3 2 (a)  i  j  k 2x  yz i  5cos y  xz j  3xyz k ,i       x