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**Sample text**

5 describes the basic theory for formulating the stiffness matrices of 'displacement' finite elemeQts. This subject matter occupies several chapters in other books on finite elements (where the reader is referred for a more detailed treatment). 6 completes the chapter with a derivation of the finite element equations for consolidation analysis, a FORTRAN program implementing these equations and some examples of its use . 1 Numerical integration When there is a need to calculate an integral in a computer program, two approaches are possible.

3 The basic steps of this short program are highlighted by the comments in the listing. The identical steps are present in the finite element program for consolidation analysis presented later in this chapter, and in CRISP. To use the program it is necessary to present it with input data describing the problem to be analysed. The input data must be prepared according to the following scheme: Data record Contents A B C D NN NI NOD NOD NS N2 FIX W No. of records NF AK NL I NS NF NL where in record A, NN is the number of nodes, NS is the number of springs, NF is the number of nodes with prescribed displacements, and NL is the number of loaded nodes.

Q 1. 2. The work done in plastic deformation is Mp 'OE P , which gives the flow rule and by integration the yield locus. Elastic strains inside the yield locus correspond to movement on a I<-line. The size of the yield locus is fixed by the isotropic normal consolidation pressure p~ (given a convenient visual interpretation as the yield locus 'sitting on top of' a I<-Iine in (p " V, q) space). From the point of view of the theory of plasticity,!. is the yield function and 2. is the hardening law.