ASE 365 - Lecture 42 - Finite element method dx t x v x EI...

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Unformatted text preview: Finite element method dx t x v x EI V dx t x u x EA V L flexural L axial 2 2 ) , ( ) ( 2 1 ) , ( ) ( 2 1 = = , : energy strain finite have must functions admissible that Recall : nts displaceme include must elements, by shared variables, nodal Hence nt. displaceme in continuous be must functions admissible problems, order- second For - 1 choice. simplest the are elements Linear qn q 1 q 6 q 5 q 2 q 4 q 3 u(x,t ) x qn-1 : slopes and nts displaceme both include must variables nodal Hence . nt displaceme in continuous be must functions admissible problems, order- fourth For slope and choice. simplest the are elements cubic Here, qn q 1 q 2 q 4 q 3 v(x,t ) x qn-1 3 2 2 3 1 +- 3 2 2 +- 3 2 2 3 - 3 2 +- : elements within degree polynomial increasing by or version),- (h elements g subdividin by refined be can problems order- second for models element Finite : elements cubic for functions al Hierarchic ) 1 ( - ) 1 )( ( 2 1 -- 2 2 ) 1 ( - 2 2 1 2 ) 1 )( ( -- FEM convergence example* L EA k L x A x A L x EA x EA = - = - = , , : vibration axial in Rod 2 2 2 1 1 5 6 ) ( 2 1 1 5 6 ) ( . , , : s frequencie natural Exact elements. cubic and quadratic linear, using ion eigensolut the e Approximat 2 3 2 2 2 1 11631 . 8 09952 . 5 21552 . 2 L E L E L E = = = u(x,t ) k x 1997. ,...
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This note was uploaded on 09/18/2011 for the course ASE 365 taught by Professor Staff during the Spring '10 term at University of Texas at Austin.

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ASE 365 - Lecture 42 - Finite element method dx t x v x EI...

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