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Chapter 10: Q5P (page 520)

Show by the quotient rule (Section 3 ) that Cijkmin (7.5)is a 4th-rank tensor.

Short Answer

Expert verified

The statement has been proven.

Step by step solution

01

Given Information

The tensor Cijkm .

02

Definition of a strain tensor.

Solids are strained under applied forces, resulting in a change in volume and shape is called strain tensor.

03

Verify the statement.

The tensor Cijkm.

Let S is the strain tensor.

Correspondence between point mechanics and mechanics of an elastic body.

r鈫�sF=-鈭�U鈫�PF=ma鈫�PijF=CijklSkl

In the above statementPij=CijklSkl

C is a fourth rank tensor.

Hence, the statement has been proven.

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Most popular questions from this chapter

In the text and problems so far, we have found the e vectors for Question: Using the results of Problem 1, express the vector in Problem 4in spherical coordinates.

E=Fq

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Verify for a few representative cases that (5.6)gives the same results as a Laplace development. First note that if伪,尾,纬=1,2,3 , then (5.6)is just(5.5) . Then try letting伪,尾,纬= an even permutation of 1,2,3, and then try an odd permutation, to see that the signs work out correctly. Finally try a case when 蔚伪尾纬=0(that is when two of the indices are equal) to see that the right hand side of(5.6) is zero because you are evaluating a determinant which has two identical rows.
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