Energy principles in structural mechanics express the relationships between
stresses,
strains or
deformations,
displacement
Displacement may refer to:
Physical sciences
Mathematics and physics
*Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
s, 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
Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation (mechanics), deformation under the action of forces, temperature chang ...
. 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
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to how ...
.
General principles
*
Virtual work
In mechanics, virtual work arises in the application of the '' principle of least action'' to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different fo ...
principle
**Principle of virtual displacements
**Principle of virtual forces
***
Unit dummy force method
The Unit dummy force method provides a convenient means for computing displacements in structural systems. It is applicable for both linear and non-linear material behaviours as well as for systems subject to environmental effects, and hence more g ...
* Modified variational principles
Elastic systems
*
Minimum total potential energy principle
* Principle of stationary total complementary potential energy
*
Castigliano's first theorem (for forces)
Linear elastic systems
*
Castigliano's second theorem (for displacements)
*
Betti's reciprocal theorem
*
Müller-Breslau's principle
Applications
* Governing equations by variational principles
* Approximate solution methods
*
Finite element method in structural mechanics The finite element method (FEM) is a powerful technique originally developed for the numerical solution of complex problems in structural mechanics, and it remains the method of choice for analyzing complex systems. In FEM, the structural system is ...
Bibliography
*Charlton, T.M.; ''Energy Principles in Theory of Structures'', Oxford University Press, 1973.
*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.
*Langhaar, H. L.; ''Energy Methods in Applied Mechanics'', Krieger, 1989.
*Moiseiwitsch, B. L.; ''Variational Principles'', John Wiley and Sons, 1966.
*Mura, T.; ''Variational Methods in Mechanics'', Oxford University Press, 1992.
*
Reddy, J.N.; ''Energy Principles and Variational Methods in Applied Mechanics'', John Wiley, 2002.
*Shames, I. H. and Dym, C. L.; ''Energy and Finite Element Methods in Structural Mechanics'', Taylor & Francis, 1995,
*Tauchert, T.R.; ''Energy Principles in Structural Mechanics'', McGraw-Hill, 1974.
*Washizu, K.; ''Variational Methods in Elasticity and Plasticity'', Pergamon Pr, 1982.
*Wunderlich, W.; ''Mechanics of Structures: Variational and Computational Methods'', CRC, 2002. {{ISBN, 0-8493-0700-7
Structural analysis
Calculus of variations