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

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