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MIT2_092F09_lec04

# MIT2_092F09_lec04 - 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 4 - The Principle of Virtual Work Prof. K. J. Bathe MIT OpenCourseWare S u = Surface on which displacements are prescribed S f = Surface on which loads are applied S u S f = S ; S f S u = Given the system geometry ( V , S u , S f ), loads ( f B , f S f ), and material laws, we calculate: Displacements u, v, w (or u 1 , u 2 , u 3 ) Strains, stresses We will perform a linear elastic analysis for solids. We want to obtain the equation KU = R . Recall our truss example. There, we had element stiﬀness AE . To calculate the stiﬀnesses, we could proceed this way: L i 1

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Lecture 4 The Principle of Virtual Work 2.092/2.093, Fall ‘09 u Every diﬀerential element should satisfy EA d 2 = 0. To obtain F, we solve: dx 2 ; u = 1 . 0 ; u d 2 u = 0 = 0 EA dx 2 x =0 x = L i Consider a 2D analysis: In this case, the method used for the truss problem to get the stiﬀness matrix K would not work. In general 3D
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MIT2_092F09_lec04 - 2.092/2.093 Finite Element Analysis of...

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