MIT2_094S11_lec21

MIT2_094S11_lec21 - 2.094 Finite Element Analysis of Solids...

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Unformatted text preview: 2.094 Finite Element Analysis of Solids and Fluids Fall 08 Lecture 21- Plates and shells Prof. K.J. Bathe MIT OpenCourseWare Timoshenko beam theory, and Reissner-Mindlin plate theory For plates, and shells, w , x , and y as independent variables. w = displacement of mid-surface, w ( x,y ) A = area of mid-surface p = load per unit area on mid-surface w = w ( x, y ) (21.1) w ( x, y, z ) = w ( x, y ) The material particles at any z move in the z-direction as the mid-surface. (21.2) u ( x, y, z ) = x z = x ( x, y ) z v ( x, y, z ) = y z = y ( x, y ) z (21.3) (21.4) xx = u x = z x x yy = v y = z y y (21.5) (21.6) xy = u + v = z x + y (21.7) y x y x x x xx = z (21.8) y yy y xy x + y y x 90 MIT 2.094 21. Plates and shells w u w xz = x + z = x x...
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This note was uploaded on 12/29/2011 for the course ENGINEERIN 2.094 taught by Professor Prof.klaus-jürgenbathe during the Spring '11 term at MIT.

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MIT2_094S11_lec21 - 2.094 Finite Element Analysis of Solids...

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