Finite elements for structural analysis

The principle of virtual work is used as the basis of the finite element procedure but while the potential energy basis is also given, no mention is made of variational calculus. After a brief discussion on discretization of the solid continuum, the principle of virtual work is stated and used to develop the finite element method for the one-dimensional elastic beam element. This is followed by an introduction to generalized stresses and strains and to axis transformations. The first chapter is completed by brief comments on the potential energy basis for the finite element method and elementary criteria required for convergence.

Subsequent chapters develop the method for the basic structural systems beginning with plane stress and strain. All the details of the matrices are presented for linear strain elements. The calculation of the right-hand side vector is well presented. While the authors comment briefly on their choice of a mesh in an example, they do not give adequate attention
to mesh characteristics, such as element aspect ratios and
discontinuous changes in element size, which can adversely
affect results.

Isoparametric elements for two-dimensional elements are
clearly introduced and the authors explanation of their implementation is enhanced by macroflow charts. Only passing
mention is made of super and subparametric elements. This development is extended to the general three-dimensional solid.

Attention is then given to those systems pertinent to the
structural engineer. This begins with the details of axisymmetric solids which includes a useful discussion of
nonaxisymmetric loads. (Uncharacteristically, the details of
axisymmetric elements which have nodes on the axis of
revolution are omitted.) Subsequent development includes
plate and shell elements.

The authors now turn their attention to two important
aspects of the behavior of the structural system,...