unit6_notes

unit6_notes - ¯ t imposed on the portion of the surface of...

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16.21 Techniques of Structural Analysis and Design Spring 2005 Unit #6 - Boundary value problems in linear elasticity Ra´ul Radovitzky February 27, 2005 Figure 1: Schematic of generic problem in linear elasticity Equations of equilibrium ( 3 equations, 6 unknowns ): σ ji,j + f i = 0 (1) Compatibility ( 6 equations, 9 unknowns): 1 ∂u i ∂u j ± ij = + (2) 2 ∂x j ∂x i 1
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Constitutive Law (6 equations, 0 unknowns) : σ ij = C ijkl kl Boundary conditions of two types: (3) Traction or natural boundary conditions: For tractions
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Unformatted text preview: ¯ t imposed on the portion of the surface of the body ∂B t : n i σ ij = t j = t ¯ j Displacement or essential boundary conditions: For displacements (4) ¯u imposed on the portion of the surface of the body ∂B u , this includes the supports for which we have ¯u = : (5) u i = ¯ u i One can prove existence and uniqueness of the solution ( the ±elds: u i ( x j ) , ij ( x k ) , σ ij ( x k )) in B. 2...
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This note was uploaded on 11/07/2011 for the course AERO 16.21 taught by Professor Dffs during the Fall '10 term at MIT.

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unit6_notes - ¯ t imposed on the portion of the surface of...

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