1298378164

fluid dynamie probłems. Recent acNances In formu-latłng and soh/ing probłems In invlsc(d compressłble ftow and viscous incompressible flow are described. New concepts indude the penalty functlon and upwlnd weighing functlons.

Chapter 10 on heat transfer probłems has been ex-panded from the previous edłtłon. Toplcs łnclude conductlon łn FE formulation. element equatlons, linear and honlłnear steady-state and transłent prob-iems. conductlon contalning surface radłatłon (steady-state and transłent radłatłon), convectIorvdłffusIon equatlons for both one and two dłmensions. free and forced convect!on. and solution techniques.

The last chapter contałns a sample Computer codę, Information on preparatłon of input data and output data. and a FORTRAN listing. A simple heat conduc-tion problem and heat transfer In built up sections are provlded The concludlng sections include a short discussion of automatłe mesh generatlon, numerical Integratlon formulas, and a new section on solvłng linear and nonllnear matrix equations.

The appendlces Include sections on matrices. varia-tional calculus, basie equatlons from linear elastlcity theory. fluid mechanics. and basie equations of heat transfer.

The authors present an up-to-date versłon of FE. The reviewer feels that sections on component modę method, consistent mass in structural dynamlcs should have been included. The penalty functlon method should be expanded and mesh layout for stress concentration of clrcular holes In plates and shełls should also be included.

H. Saunders 1 Arcadian Drive Scotia, New York 12302

THEORY OF ELASTIC SHELLS

M. Dikmen

Pitman Publlshłng, Inc.. Marshfield, MA 1982. 364 pages, $65.95

As stated by the author. thls book "covers a rangę of toplcs that have not been brought together in a single

normograph on shell theory ... I have chosen to conc en tratę on foundatłons, methods and essential facts." Thls book requlres a fundamenta! knowledge of strength of materlals (elementary and advanceć) and dynamlcs.

The flrst of 14 chapters Introduces shell theory. Toplcs łn Chapter 2 include dlfferentlal geometry on and neer a reference surface and an explanatłon of and appllcatłons of tensor theory. Chapter 3 has to do wlth klnematlcs of the shell, Includlng base vectors and compatłbłllty conditlons. Chapter 4 is concerned wlth the generał balance equation and includes equatlons of motlon and conservation of energy and a method for expandlng stress compo-nents. Chapter 5 treats constitutlve relatlons for elastic shełls; three-dimensional hypereiastlc bodies; and generał constitutive equatlons for hypereiastlc bodies and hypereiastlc shełls. Chapter 6 has to do wlth kinematics: approx|matłons. equatłons of motlon, and boundary condltions.

Chapter 7 describes various aspects of membranę theory includlng linear theory of statics of elastic membranes. dlfferentlal equatłons of deformatlon In linear theory, bending tensors. expliclt forms of linear constitutive equatlons, the membranę equation in Carteslan coordlnates. Caughy-Rlemann equatłons, boundary conditlons, and nonllnear theory of the first order. Chapter 8 focuses on bending theories. linearized equations of motlon, constitutłve equations of linear bending theory. Trefftz's method, and the well known Love-Kirchoff hypothesis. The con-cluding sections cover direct integration of stresses, mjxed tensor formulation of linear theory. boundary conditlons, and nonllnear bending theories.

Chapter 9 is concerned wlth the theory of shełls. Shełls are considered to be bounded regłons of some deformable two-dimensional manifold and include polyhedra and Isometric surfaces. Openings and slits that can prevent the shell from malntaining its form are described by rlgldlty theories and rigid point Cosserat and Cosserat surfaces. The chapter concludes wlth a generał discussion of constltutive equations. Chapter 10 explałns classical Solutions to equilibrium probłems, Solutions for linear probłems, and constitutive equations in generał as well as those applłed to shallow shełls.

The next chapter contałns an excellent discussion of the stability of shełls, includlng branchlng theory and