{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

unit10_notes

# unit10_notes - 16.21 Techniques of Structural Analysis and...

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

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

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

Unformatted text preview: 16.21 Techniques of Structural Analysis and Design Spring 2005 Unit #10 - Principle of minimum potential energy and Castigliano’s First Theorem Ra´ul Radovitzky April 4, 2005 Principle of minimum potential energy The principle of virtual displacements applies regardless of the constitutive law. Restrict attention to elastic materials (possibly nonlinear). Start from the PVD: ¯ ¯ u/ ¯ σ ij ¯ ij dV = t i u i dS + f i u i dV, ∀ ¯ u = 0 on S u (1) V S V Replacing the expression for the stresses for elastic materials: ∂U σ ij = ∂ ij and assuming that the virtual displacement field is a variation of the equili- brated displacement field u = δu , ¯ ¯ ij = δ ij . ∂U 0 δ ij dV = t i δu i dS + f i δu i dV V ∂ ij V S 1 The expression over the brace is the variation of the strain energy density δU : ∂U δU 0 = δ ij ∂ ij Using the properties of calculus of variations δ () = δ (): δU dV = δ U dV = δU = δ t i u i dS + f i u i dV = δ ( − V ) S V where V is the potential of the external loads. is the potential of the external loads....
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

unit10_notes - 16.21 Techniques of Structural Analysis and...

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

View Full Document
Ask a homework question - tutors are online