A Variational Approach to Structural Analysis (PDF)

An insightful examination of the numerical methods used to developfinite element methods
A Variational Approach to Structural Analysis provides readers withthe underpinnings of the finite element method (FEM) whilehighlighting the power and pitfalls of virtual methods. In aneasy-to-follow, logical format, this book gives complete coverageof the principle of virtual work, complementary virtual work andenergy methods, and static and dynamic stability concepts.
The first two chapters prepare the reader with preliminarymaterial, introducing in detail the variational approach used inthe book as well as reviewing the equilibrium and compatibilityequations of mechanics. The next chapter, on virtual work, teacheshow to use kinematical formulations for the determination of therequired strain relationships for straight, curved, and thin walledbeams. The chapters on complementary virtual work and energymethods are problem-solving chapters that incorporate Castigliano'sfirst theorem, the Engesser-Crotti theorem, and the Galerkinmethod. In the final chapter, the reader is introduced to variousgeometric measures of strain and revisits straight, curved, andthin walled beams by examining them in a deformed geometry.
Based on nearly two decades of work on the development of theworld's most used FEM code, A Variational Approach to StructuralAnalysis has been designed as a self-contained, single-sourcereference for mechanical, aerospace, and civil engineeringprofessionals. The book's straightforward style also providesaccessible instruction for graduate students in aeronautical,civil, mechanical, and engineering mechanics courses.