Plane stress and plane strain

wo-dimensional elastic problems were the first successful examples of the application of the finite element method.''2 Indeed, we have already used this situation to illustrate the basis of the finite element formulation in Chapter 2 where the general relationships were derived. These basic relationships are given in Eqs (2.1)-(2.5)
and (2.23) and (2.24), which for quick reference are summarized in Appendix C.
In this chapter the particular relationships for the plane stress and plane strain problem will be derived in more detail, and illustrated by suitable practical examples,a procedure that will be followed throughout the remainder of the book.
Only the simplest, triangular, element will be discussed in detail but the basic approach is general. More elaborate elements to be discussed in Chapters 8 and 9
could be introduced to the same problem in an identical manner.
The reader not familiar with the applicable basic definitions of elasticity is referred to elementary texts on the subject, in particular to the text by Timoshenko and
G ~ o d i e r , ~ whose notation will be widely used here




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