18a-Beams-and-Frames

18a-Beams-and-Frames - v and v , x at ends. William Klug...

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© William Klug MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 18a Beams & Frames
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© William Klug Beams • Euler-Bernoulli beam theory: – Governing Equation: – Weighted residual
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© William Klug Euler-Bernoulli Beam Theory
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© William Klug BC’s & Weak Form • E.B.C • N.B.C Interpolation must satisfy these
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© William Klug Properties of Weak Form • Highest derivatives are of order 2. • Admissibility conditions: v , xx must be bounded v , x continuous C 1 smoothness is required. • Displacements and derivatives must be continuous. – EBC’s:
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Unformatted text preview: v and v , x at ends. William Klug Euler-Bernoulli Beam Theory Single element: End deflections and slopes are DOF To satisfy E.B.C. polynomial must have 4 parameters William Klug Shape Functions Write (1) in terms of using interpolation conditions: (1) William Klug Shape Functions William Klug Stiffness, Nodal Forces William Klug Stiffness, Nodal Forces William Klug Beams with Axial Flexibility Bar Beam William Klug Summary and Review Beam element: Strong form: Weak form: Shape functions: Stiffness and loads:...
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This note was uploaded on 08/09/2011 for the course MAE 168 taught by Professor Klug during the Spring '11 term at UCLA.

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18a-Beams-and-Frames - v and v , x at ends. William Klug...

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