06_PlateTheory_09_StrainEnergy

# 06_PlateTheory_09_StrainEnergy - Section 6.9 6.9 Strain...

This preview shows pages 1–3. Sign up to view the full content.

Section 6.9 Solid Mechanics Part II Kelly 179 6.9 Strain Energy in Plates 6.9.1 Strain Energy due to Plate Bending and Torsion Here, the elastic strain energy due to plate bending and twisting is considered. Consider a plate element bending in the x direction, Fig. 6.9.1. The radius of curvature is 2 2 / x w R = . The strain energy due to bending through an angle θ Δ by a moment y M x Δ is () x x w y M U x Δ Δ = Δ 2 2 2 1 (6.9.1) Considering also contributions from y M and xy M , one has y x y w M y x w M x w M U y xy x Δ Δ + = Δ 2 2 2 2 2 2 2 1 (6.9.2) Figure 6.9.1: a bending plate element Using the moment-curvature relations, one has y x y x w y w x w y w x w D y x y w y x w y w x w x w D U Δ Δ + = Δ Δ + + + = Δ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 ν (6.9.3) This can now be integrated over the complete plate surface to obtain the total elastic strain energy. x Δ R

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Section 6.9 Solid Mechanics Part II Kelly 180 6.9.2 The Principle of Minimum Potential Energy
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/20/2012 for the course ENGINEERIN 2 taught by Professor Staff during the Fall '11 term at Auckland.

### Page1 / 4

06_PlateTheory_09_StrainEnergy - Section 6.9 6.9 Strain...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online