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Method of Finite Elements I: Shape Functions

Adrian EggerMethod of Finite Elements I: Shape FunctionsWhy Shape Functions ? Discretization leads to solution in the nodes, but no information concerning the space in between Shape Functions required to approximate quantities between nodes Underlying assumption of how quantities are distributed in an element (stiffness, mass, element loads; displacements, strains, stress, internal forces, etc.) Geometry transformation3/24/20152 Adrian Egger | FEM I | FS 2015 ?What can Shape Functions be used for? to interpolate between discrete nodal quantities continuous across element = ( ) = 1( ) 1+ 2( ) 23/24/20153 Adrian Egger | FEM I | FS 2015 What can Shape Functions be used for? to discretize continuous quantities to nodal continuous across element discrete nodal quantities3/24/20154 = =0 ( ) = =0 011 111 021 121 ( ) = 2 212 2 212 1 1 2 2 Adrian Egger | FEM I | FS 2015 Alternative way to derive loading vector Recap: We calculate the solution in the nodes What is the influence of element loading in the nodes We must fix the el

Used to discretize continuous quantities to nodal DOF i.e. continuous across element discrete nodal quantities 3/24/2015 4

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