Finite Elements in Solids and Structures

This book is an introduction to finite elements in their specific and elementary application to solid mechanics and structural analysis. It is written for use as an advanced undergraduate text and is designed to find application in mechanical, aeronautical and civil engineering departments. The book deals mainly with static linear analysis but also includes a brief introduction to dynamic problems. It is intended either as a prescribed text for a final year course in finite element methods or computational solid mechanics, or as an accompanying text for more conventional solid mechanics/advanced strength of materials courses which incorporate aspects of the finite element approach, or simply as a self-contained course of private study for students or graduate engineers who need to become familiar with the finite element method for one reason or another. The subject matter is presented in a logical sequence which starts with a brief introduction to the finite element method in general followed by a review of the necessary relationships from linear elasticity and from beam and plate theory. Variational statements for the continuum problem are then presented and the displacement energy method is selected as a basis for solid and structural applications of the finite element approach. Various categories of continuum and structural element are then discussed roughly in order of increasing complexity. One- and two- dimensional bar elements are dealt with first. These are followed by linear two- and three- dimensional continuum elements, higher-order continuum elements, mapped elements, beam elements, plate elements and shell elements. En route, there are brief digressions into solution methods and convergence criteria. The book concludes with a brief introduction to dynamic analysis.