What is complementary energy in structural analysis?

Complementary energy is the expanse encompassed by the sloping formation, and the upright axis is called the complementary strain energy. The area under the stress-strain curve towards the point of deformation and the strain energy per unit volume is known as strain energy density.

What is complementary strain energy?

Complementary Strain Energy : The area enclosed by the inclined line and the vertical axis is called the complementary strain energy. For a linearly elastic materials the complementary strain energy and elastic strain energy are the same.

What are energy methods in structural analysis?

Energy methods: These are methods based on linear elastic behavior and conservation of energy, i.e. the work done by external forces equals the energy stored in the structure under load.

What is complementary internal energy density?

The complementary strain energy U∗ in the rod is defined by. (2.1.24) Therefore, the complementary strain energy density corresponds to the area above the stress-strain curve. For a linearly elastic material, the two areas are equal, and U∗ = U.

What is the relation between work done and complementary work done *?

9. What is the relation between work done and complementary work done? Explanation: They are equal only when Hooke’s law is applicable i.e. the material is linearly elastic.

What is principle of complementary virtual work?

A deformable system satisfies all kinematical requirements if the sum of the external complementary virtual work and the internal complementary virtual work is zero for all statically admissible virtual stresses Saj. …

What is the principle of energy methods?

In energy methods, the principles of virtual work or their derivatives, such as the principles of minimum potential energy or complementary energy, are used to obtain the equations.

What is the energy method?

The Energy Method is a general modeling technique, any multidisciplinary dynamic system can be captured by the Energy Method (kinetic energy, potential energy, work). Before diving into the energy method we should recall the definition of potential and kinetic energy.

What is the meaning of energy density function?

A strain energy density function or stored energy density function is a scalar valued function that relates the strain energy density of a material to the deformation gradient.

What is the relation between work done and complementary work done a they are always equal b They are always equal C can’t say D depends upon loading?

What principle that shows the relationship between work and energy?

the work-energy theorem
The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.

What is complementary energy method?

The complementary energy method may be used to considerable advantage in the solution of problems of bending of straight and thin curved beams. In general we suppose that the moment—curvature relationship for an element of a beam is of the form shown in Figure 17.9.

What is the principle of minimum complementary energy?

The principle of minimum complementary energy can be stated as follows: ‘Of all possible stress states which satisfy the equilibrium equations and the stress boundary conditions, the state which satisfies the compatibility conditions will make the complementary energy assume a minimum value’.

How do you write the complementary strain energy?

The complementary strain energy can be written, in the presence of known initial strains ɛ0, as: where the strain–stress relations are assumed to be of the form: The work done by the applied loads during stress change, also known as the complementary work, is given by:

What is complementary work done by applied loads during stress change?

The work done by the applied loads during stress change, also known as the complementary work, is given by: where S2 is the part of the surface of the body on which the values of displacements are prescribed as: Eqns [28] and [30] can be used to express the complementary energy of the body as: