Ch_22

# But where w strain energy lambda w potential of

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: te: these are total strains & not elastic strains Let us define [B] such that {e}6×1 = [B] 6×n { (e ) U }n×1 depends on elem. type Each eqn. in a is used to generate one row of [B] ∂u (i.e. 1st row, . . . etc.) ∂x Chapter 22 Page 10 K. Haghighi Element Matrices: [k(e )]& {f (e)} by minimizing the We obtain Potential Energy of the system or body (Π ). But where Π =Λ−W Λ = Strain energy (Lambda) W = Potential of forces acting on the body. Chapter 22 Page 11 K. Haghighi Strain Energy Equation: For a 3 - D elastic body, Λ is Λ (e) 1⌠ = ⎮ ( σ xx ε xx + σ yy ε yy + σ zz ε zz + σ xy ε xy 2⌡ V + σ xz ε xz + σ yz ε yz ) dV or (e ) = 1 {σ}T {ε}dV Λ ∫ 2V Chapter 22 Page 12 K. Haghighi but recall that {σ} = [D]{ε} so generaliz...
View Full Document

## This document was uploaded on 01/29/2014.

Ask a homework question - tutors are online