This book centers on the principle of virtual work and its related method for mechanical modeling. It demonstrates and enhances the polyvalence and versatility of the virtual work approach to the mechanical modeling process.
Virtual work is set as the principle at the root of a force modeling method that can be implemented on any geometrical description. Building on experimentally grounded hypotheses, the method provides a unifying framework for building up consistently associated force models where external and internal forces are introduced through their virtual rates of work.
Systems described as three-dimensional, curvilinear or planar continua are considered and force models are established with the corresponding equations of motion. The validation process reveals that enlarging the domain of relevance of a mechanical model, when needed for practical applications, calls for an enrichment of its geometrical description that takes into account its underlying microstructure.
1. The Emergence of the Principle of Virtual Velocities.
2. Dualization of Newton’s Laws.
3. Principle and Method of Virtual Work.
4. Geometrical Modeling of the Three-dimensional Continuum.
5. Kinematics of the Three-dimensional Continuum.
6. Classical Force Modeling for the Three-dimensional Continuum.
7. The Curvilinear One-dimensional Continuum.
8. Two-dimensional Modeling of Plates and Thin Slabs.
Appendix 1. Introduction to Tensor Calculus.
Appendix 2. Differential Operators.
Appendix 3. Distributors and Wrenches.
Jean Salençon is a Member of the French Academy of Sciences and the Academy of Technologies. He works as a Senior Fellow of the Institute for Advanced Study at the City University of Hong Kong and his research interests include continuum mechanics, structure analysis and soil mechanics.
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