A Primer for Finite Elements in Elastic Structures

A thorough guide to the fundamentals--and how to use them--of finite element analysis for elastic structures For elastic structures, the finite element method is an invaluable tool which is used most effectively only when one understands completely each of its facets. A Primer for Finite Elements in Elastic Structures disassembles the entire finite element method for civil engineering students and professionals, detailing its supportive theory and its mathematical and structural underpinnings, in the context of elastic structures and the principle of virtual work. The book opens with a discussion of matrix algebra and algebraic equation systems to foster the basic skills required to successfully understand and use the finite element method. Key mathematical concepts outlined here are joined to pertinent concepts from mechanics and structural theory, with the method constructed in terms of one-dimensional truss and framework finite elements. The use of these one-dimensional elements in the early chapters promotes better understanding of the fundamentals. Subsequent chapters describe many two-dimensional structural finite elements in depth, including the geometry, mechanics, transformations, and mapping needed for them. Most chapters end with questions and problems which review the text material. Answers for many of these are at the end of the book. An appendix describes how to use MATLAB(r), a popular matrix-manipulation software platform necessary to perform the many matrix operations required for the finite element method, such as matrix addition, multiplication, inversion, partitioning, rearrangement, and assembly. As an added extra, the m-files discussed can be downloaded from the Wiley FTP server.

Finite Element Method Prerequisites. The Finite Element Method. Element Stiffness Equations by Direct Methods. Global Stiffness Equations. Element Stiffness Equations by Displaced State Virtual Work Applications. General Approach to Element Stiffness Equations. Plane Stress and Plane Strain. Plane Stress Structural Triangular Finite Elements. Isoparametric Plane Stress Structural Quadrilateral Finite Elements. Flat Plate Flexural Finite Elements. Axisymmetric Structural Finite Elements. Structural Finite Elements in Perspective. Appendix. Answers to Selected Problems. Index.