Geometric Continuum Mechanics and Induced Beam Theories, 2015 Lecture Notes in Applied and Computational Mechanics Series, Vol. 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.

Introduction.- Part I Geometric Continuum Mechanics.- Part II Induced Beam Theories.

Devoted to fundamental questions on the foundations of continuum mechanics

Presents application of the fundamental concepts of continuum mechanics to beam theories

All classical beam theories, where the cross sections remain rigid and plain, are presented

Augmented beam theories, where cross section deformation is allowed, are derived as well

Includes supplementary material: sn.pub/extras