Finite element modeling for stress analysis. (English) Zbl 0837.73001

Cook, Robert D.

New York, NY: Wiley. xi, 320 p. (1995).

This book is intended for beginning courses in finite elements (FE) that are oriented toward users of the method. The presentation presumes a knowledge of elementary matrix algebra and the level of physical understanding that a good student should have after completing a first course in mechanics of materials. After an introductory chapter 1, chapter 2 considers elements for bar and beam problems and discusses the mathematical structure of the FE method (the “stiffness method”). Plane problems are treated in chapter 3. Chapter 4 discusses special methods for elements formulation and linear static analysis. After studying chapters 1 through 4, the reader should have enough background to profit from a thorough discussion of how to use the FE method properly, with attention to planning the model, detecting errors, and verifying results. This material appears in chapter 5 and is an elaboration of section 1.3. Chapters 6 and 7 discuss general solids, solids of revolution, plates, and shells. Temperature distribution is considered in chapter 8, with emphasis on its use in thermal stess analysis. Vibration and other dynamic problems occupy chapter 9. Chapter 10 is devoted to nonlinear problems and buckling. Example applications of the FE method appear near the ends of most chapters.

MSC:

74-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74S05	Finite element methods applied to problems in solid mechanics
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

stiffness method; bar; beam; linear static analysis; solids of revolution; plates; shells; thermal stess analysis; dynamic problems; buckling