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Unformatted text preview: EN0175 09 / 07 / 06 1.2 Introduction to FEM Finite element method is a very powerful tool for numerical analysis in solid and structural mechanics as well as in many other engineering disciplines. Here we present an introduction to the basic concepts of FEM in the simplest context of a one dimensional elasticity of a bar. In lecture 1, we have derived the governing equation for 1D elasticity of a bar as, x L P 2 2 t u f x = + E = x u = We can consider two simple problems, one with traction BC and one with displacement BC. P1: P2: g ( ) = u ( ) P L = P g ( ) = u ( ) = L u ( ) ( ) = = = + P L u E u g u E ' ' ' , ( ) ( ) = = = + ' ' L u u g u E 1 EN0175 09 / 07 / 06 General solution for : ' ' = + g u E 2 1 2 2 C x C x E g u + + = i) Solution for specified boundary conditions of P1: x E gL x E P x E g u + + = 2 2 ( ) x L g P Eu + = = ' Actually, we can simply get this solution by considering the equilibrium below ( ) x L g ( ) x P ii) Solution for specified boundary conditions of P2: ( ) x L x E g Lx E g x E g u = + = 2 2 2 2 ( ) x L g Eu 2 2 ' = =...
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- Spring '06