Question

A. ikE oa0dtk Suppose ceR Let neN iS non-zerO.Use the definitio of the snear ma Sik(c) to Find the out pot of4he pduct T ushfy your answer Shear matix Def C) Int RCee T wnere ik) Oif iAs

Answer 1

Answer:)

By definition,
e
is a row vector with only the ith component (column) non-zero i.e
e 0,0,.1(at ih position) .00]

Furthermore, if we multiply this with the stress matrix , we will get a row vector which corresponds to the ith row in the stress matrix. That is :

Sik(c) C

C+1 C eSik(c) [0 .th 01(at position)0 0 c1 C C nxn th = i"row in the Shear Matrix

Eg, say we want to find this for i = 1:

c1 C T ef SIk (c) [1 0 0 c+1 C C nxn 1strow in the Shear Matrix c1 c

Further, upon multiplying this row vector by the column vector $e_k$, whose components are all zero except for the kth component (row), i.e:

0 0 ek th 1in k position) 0

Then, when we multiply the previous result with this, we will get a single number, corresponding to the component in the kth column and the ith row in the stress matrix.

Eg, let's take the example of i = 1, k = 2:

0 1 ei S2(e) e [e+1 c..

Thus, we see that:

= c+1 if i = k

eSik (c)ek

= c if i not equal to k

eSik (c)ek