Energy principles in structural mechanics
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Energy principles in structural mechanics express the relationships between stresses, strains or deformations, displacements, material properties, and external effects in the form of energy or work done by internal and external forces. Since energy is a scalar quantity, these relationships provide convenient and alternative means for formulating the governing equations of deformable bodies in solid mechanics. They can also be used for obtaining approximate solutions of fairly complex systems, bypassing the difficult task of solving the set of governing partial differential equations.
General Principles
- Virtual work principle
- *Principle of virtual displacements
- *Principle of virtual forces
- **Unit dummy force method
- Modified variational principles
Elastic systems
- Minimum total potential energy principle
- Principle of stationary total complementary potential energy
- First Castigliano's theorem (for forces)
Linear Elastic Systems
- Second Castigliano's theorem (for displacements)
- Betti's reciprocal theorem
- Muller-Breslau's principle
Applications
- Governing equations by variational principles
- Approximate solution methods
- Finite element method in structural mechanics
Bibliography
Charlton, T.M. Energy Principles in Theory of Structures, Oxford University Press, 1973. ISBN 0197141021
Dym, C. L. and I. H. Shames, Solid Mechanics: A Variational Approach, McGraw-Hill, 1973.
Hu, H. Variational Principles of Theory of Elasticity With Applications, Taylor & Francis, 1984. ISBN 0677313306
Langhaar, H. L. Energy Methods in Applied Elasticity, Krieger, 1989.
Moiseiwitsch, B. L. Variational Principles, John Wiley and Sons, 1966. ISBN 0470612800
Mura, T. Variational Methods in Mechanics, Oxford University Press, 1992. ISBN 0195068300
Reddy, J.N. Energy Principles and Variational Methods in Applied Mechanics, John Wiley, 2002. ISBN 047117985X
Shames, I. H. and Dym, C. L. Energy and Finite Element Methods in Structural Mechanics, Taylor & Francis, 1995, ISBN 0-89116-942-3
Tauchert, T.R. Energy Principles in Structural Mechanics, McGraw-Hill, 1974. ISBN 0070629250
Washizu, K. Variational Methods in Elasticity and Plasticity, Pergamon Pr, 1982. ISBN 0080267238
Wunderlich, W. Mechanics of Structures: Variational and Computational Methods, CRC, 2002. ISBN 0849307007
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