Search results
The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for stored energy will then be used to solve some elasticity problems using the energy methods mentioned in the previous section.
When a material does obey Hooke's law, the elastic strain energy, E can be calculated with an equation. The equation is the area of a right-angled triangle under the force-extension graph; Where: E = elastic strain energy (or work done) (J) F = average force (N) ΔL = extension (m)
Learn how to use the concept of potential energy and the principle of virtual work to derive solutions for elastic problems. The lecture covers the energy methods for beams, plates and 3-D bodies, with examples and formulations.
Strain energy is the potential energy absorbed by the body due to the deformation or strain effect. It is denoted by the symbol uppercase letter ‘U’. The strain energy absorbed by the material is equal to the work required to create the deformation in the object.
In the general case, elastic energy is given by the free energy per unit of volume f as a function of the strain tensor components ε ij = + where λ and μ are the Lamé elastic coefficients and we use Einstein summation convention.
then the total strain energy can be written compactly as U= 2 V {σ}T{ }dV. (5) This equation is a general expression for the internal strain energy of a linear elastic structure of any type. It can be simplified significantly for structures built from a number of prismatic members, such as trusses and frames. CC BY-NC-ND H.P. Gavin
Strain energy. The area under the \(\sigma_e - \epsilon_e\) curve up to a given value of strain is the total mechanical energy per unit volume consumed by the material in straining it to that value. This is easily shown as follows: \[U^* = \dfrac{1}{V} \int P\ dL = \int_0^L \dfrac{P}{A_0} \dfrac{dL}{L_0} = \int_{0}^{\epsilon} \sigma d\epsilon\]
