REVIEWED BY T. BELYTSCHKO 1 The finite element method has been the topic of approximately 30 books and monographs that have been published over the last 15 years. Nevertheless, many instructors still have difficulties in finding a text for advanced undergraduate or beginning graduate courses which will develop a sound, fundamental understanding of the method. This book presents a significant advance in that direction for those who wish a more rigorous, mathematical development. The book consists of six chapters. The first two are devoted to one-dimensional problems, emphasizing the development of a symmetric variational formulation for second-order, two-point boundary value problems and the smoothness required in the space of approximating functions. In the third chapter, a finite element program for one-dimensional problems is described, including the FORTRAN statements. Chapters 4 and 5 repeat the same material for twodimensional problems, including shape functions for triangles and quadrilaterals and numerical quadrature. Chapter 6 presents an introduction to three-dimensional problems, fourth-order problems, and time-dependent problems. A notable feature of this book is that it develops the weak, or variational form, from the partial differential equations, rather than simply presenting the variational form as given; the latter approach bothers many of the better students who usually wonder where the variational form comes from. The concepts in this book are all developed with rigor, clarity, and conciseness. Once a student has mastered this book, he will certainly have a broader understanding of the mathematics of the finite element method than would be obtained from more conventional treatments. In using this book in my class, I found two types of response. Engineering students with a modest mathematical background found the book a little difficult as an introduction; it requires simultaneously tackling the concepts of the weak form, finite element approximations, and notation and concepts to which they are unaccustomed. On the other hand, mathematically inclined students tend to find this book delightful. In addition to its value as a text, it is also recommended to finite element specialists who wish to familiarize themselves with the more recent developments in the mathematical aspects of the method. Even recently I have

Summary A wellbore cement sheath is expected to provide zonal isolation and borehole integrity during well construction and well life. Mechanical interactions of the cement sheath to existing and operationally induced stresses, along with other elements in proximity to the wellbore, have increasingly large technical, economic, and environmental ramifications. Staged-finite-element procedures during well construction consider sequentially the stress states and displacements at and near the wellbore. The model replicates complicated stress states arising from simultaneous action of far-field stresses, overburden pressure, cement hardening and shrinkage, debonding at the interfaces, and plastic flow of cement sheath and rock formation. At present, temperature, flow, and poroelasticity effects are not included. The technique tracks the time-dependent behavior of cement slurry, curing (with or without shrinkage), and hardened cement during the critical period after slurry placement. Material models for casing, cement, and rock formation and failure criteria for cement, formation, and interface bonds were calibrated using published information and experimental data. Calculations were conducted for various loading and unloading scenarios, geometric configurations, properties of rock formations, and cement-slurry formulations. Results are discussed in terms of field implication;, for example:Interface microchannels may or may not develop, depending upon shrinkage magnitudes; andsimplifying modeling assumptions that are often used, such as 2D stresses and/or deformations, may obscure critical casing, cement, and formation behavior in the wellbore region and in the producing horizon. This paper, part of a series quantifying the interacting physical components and processes at and near the wellbore region, initiates useful comparisons of analytical results and field realities. The series illustrates and compares results and practical implications from simple to increasingly complex, but more realistic, assumptions, such as isotropic/directional-stress states and isotropic/anisotropic casing, cement, and formation-material parameters.

SUMMARYA newly developed numerical Laplace transform inversion technique is described. A derivation of the method, termed the 'multidata method', is presented along with a description of a similar collocation method. Similarities and differences between the two numerical methods are described and discussed. Results of parameter studies of both methods are presented which demonstrate the sensitivity to error displayed by the collocation method and the magnitude of the improvement in accuracy obtainable with the multidata method as compared with the collocation method, especially when errors exist in the function to be inverted.

Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

No abstract