MIT2_092F09_lec05

MIT2_092F09_lec05 - 2.092/2.093 — Finite Element Analysis...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: 2.092/2.093 — Finite Element Analysis of Solids & Fluids I Fall ‘09 Lecture 5- The Finite Element Formulation Prof. K. J. Bathe MIT OpenCourseWare In this system, (X, Y, Z) is the global coordinate system, and (x, y, z) is the local coordinate system for the element i . We want to satisfy the following equations: τ ij,j + f i B = 0 in V Equilibrium Conditions τ ij n j = f i S f on S f → u i = u i S u Compatibility Conditions (A) S u → τ ij = f ( ε kl ) Stress-strain Relations → Then we have the exact solution. Principle of Virtual Displacements ε T Cε dV = u T f B dV + u S f T f S f dS f (B) V V S f Here, real stresses ( Cε ) are in equilibrium with the external forces ( f B , f S f ). Note that Eq. (B) is equivalent to Eq. (A). Recall that we defined ε T = ε xx ε yy ε zz γ xy γ yz γ zx ∂u ε T = ε ¯ xx ε ¯ yy ε ¯ zz γ ¯ xy γ ¯ yz γ ¯ zx = . . . ∂x Basic assumptions: ⎡ ⎤ ( m ) u ( x, y, z ) u ( m ) = ⎣ v ( x, y, z ) ⎦ = H ( m ) u ˆ (1) w...
View Full Document

{[ snackBarMessage ]}

Page1 / 4

MIT2_092F09_lec05 - 2.092/2.093 — Finite Element Analysis...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online