But where w strain energy lambda w potential of

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

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