MIT2_092F09_lec10

# MIT2_092F09_lec10 - 2.092/2.093 Finite Element Analysis of...

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2.092/2.093 Finite Element Analysis of Solids Fluids I Fall ‘09 Lecture 10 - Nonlinear Finite Element Analysis of Solids Structures Prof. K. J. Bathe MIT OpenCourseWare Reading assignment: Sections 6.1, 8.4.1 Discretization of the variational formulation leads to the following equilibrium statement: t t F = t t R (1) t t F = nodal forces corresponding to element stresses at time t + Δ t t t R = external loads applied at the nodes at time t + Δ t It is assumed that the solution is known up to time t . The problem is to ±nd t t F , given t t R where: ² V ( m ) t t F ( m ) = B ( m ) T t t τ ( m ) dV ( m ) In linear analysis, V ( m ) , B ( m ) are constant. In general nonlinear analysis, V ( m ) , B ( m ) are functions of time. Types of Analysis I. Linear analysis (e.g. response of an airplane, car under operating loads) (a) Δ = strain < 0 . 04 L (b) τ = , E is a constant (c) Δ also small t t F ( m ) = K ( m ) t t U ( m ) K t t U t t R = K = Σ K ( m

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MIT2_092F09_lec10 - 2.092/2.093 Finite Element Analysis of...

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