Numerical methods in finite element analysis, K.‐J. Bathe and E. L. Wilson, Prentice‐Hall Inc., Englewood Cliffs, N.J., 1976

The types of analytical problem facing the present-day geomechanics engineer, apart from limit equilibrium calculation, tend to fall into three categories, namely equilibrium, eigenvalue and propagation problems. The sets of equations which have to be solved are usually generated by finite difference or finite element approximations to differential equations. Since it is of the greatest importance that the equations are economically and accurately solved, these two texts on this theme are timely. Both caver much of the same ground, but from somewhat different standpoints. The first two chapters of both books introduce the reader to the concepts of linear algebra and matrix notation. Thereafter Jennings writes in general terms, whereas Bathe/Wilson orientate their presentation specifically towards finite element approximations. Their Chapters 3 to 6 cover formulation of the FEM, isoparametric elements, variational formulations and implementation of the FEM by means of an in-care static analysis program STAP. A feature of Jennings’s book is the presentation of parallel subroutine algorithms in ALGOL and FORTRAN for matrix handling and equilibrium equation solution, for example by Gaussian elimination and by Choleski’s method for variable bandwidth equations, in Chapters 3 to 6. In Chapters 8 and 9 of Bathe/Wilson, solution of propagation (initial value) problems is discussed, with a good discussion of algorithm performance. The final chapters of both books, 7 to 9 of Jennings and 10 to 12 of Bathe/Wilson deal with eigenvalue problems which are less familiar ground for geomechanics specialists, although assuming greater importance daily in connection with earthquake and offshore engineering for example. Here the scope for inefficiency in algorithm choice is much wider than in linear equation solution and the reader’s attention is rightly directed to Sturm sequence and subspace/simultaneous iteration processes. Bathe/Wilson include program coding for such a method. Both of these texts should be of value to geomechanics engineers, particularly in the areas of storage efficiency, linear equation solution accuracy and eigenvalue algorithm choice.