Geometric Continuum Mechanics and Induced Beam Theories (Lecture Notes in Applied and Computational Mechanics Book 75)

This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories. Front Matter....Pages i-ix Introduction....Pages 1-13 Front Matter....Pages 15-15 Kinematics....Pages 17-32 Force Representations....Pages 33-42 Front Matter....Pages 43-43 Preliminaries....Pages 45-53 Classical Nonlinear Beam Theories....Pages 55-73 Classical Linearized Beam Theories....Pages 75-81 Classical Plane Linearized Beam Theories....Pages 83-99 Augmented Nonlinear Beam Theories....Pages 101-115 Conclusions and Outlook....Pages 117-121 Back Matter....Pages 123-146