HW2 - =- -f dx du a dx d for the case of linearly varying...

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MCE 561 Computational Methods in Solid Mechanics Homework Assignment 2 Due Feb. 14, 2011 1. Using the Ritz method, determine the one and two-term approximate solutions of a cantilever beam of length L that carries an end load of P . For this case, use polynomial approximating functions 1 + = φ i i x , and note that the essential boundary conditions 0 0 ) 0 ( ) 0 ( = φ = = o w w . Make note of the material in the passed out notes and text (Example 2.5.2). Compare your approximate results with the exact solution (see any mechanics of materials text). Ans. 3 2 ) 2 ( 2 ) 1 ( 6 2 , 4 x EI P x EI PL w x EI PL w - = = 2. Consider the two-noded linear element h x 0 . Explicitly develop the local element equation for the one-dimensional, second order equation
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Unformatted text preview: =- -f dx du a dx d for the case of linearly varying properties given by: x f f f x a a a o o 1 1 , + = + = . Partial Ans. -- + = 1 1 1 1 2 ] [ 1 a h a K o 3. Problem 3.5, page 152 in text. Note the suggested scheme should not require you to set up four equations for four unknowns. Partial Ans. - - -= h x h x h x x 1 2 3 1 3 1 ) ( 1 , where ) , ( h x is the local coordinate. 4. Problem 3.9, page 153 in text. L P x w...
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