The Finite Element Method for the Analysis of Non-Linear and ...

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Structural Elements Truss and Cable Elements A Truss Element is a structural element capable of transmitting stresses only in the direction normal to the cross-sectional area Consider a truss element that has an arbitrary orientation. It is usually described by two to four nodes and is subjected to large displacements and large strains. Institute of Structural Engineering Method of Finite Elements II 14
Truss and Cable (Bar) Elements The nodal point coordinates determine the spatial configuration of the bar at time 0 and t using: n∑ n∑ n∑ 0 x 1 (r) = N 0 k x k 1 0 x 2 (r) = N 0 k x k 2 0 x 3 (r) = N 0 k x k 3 and t x 1 (r) = Shape Functions k=1 n∑ N t k x k 1 k=1 t x 2 (r) = n = 2 nodes at r 1 = −1, r 2 = 1 k=1 n∑ N t k x k 2 k=1 N1 a = 1 2 (1 − r), N 2 a = 1 (1 + r) 2 n = 3 nodes at r 1 = −1, r 2 = 1, r 3 = 0 t x 3 (r) = N b 1 = N a 1 − 1 2 (1 − r2 ), N b 2 = N a 2 − 1 2 (1 − r2 ), N b 3 = (1 − r 2 ) k=1 n∑ N t k x k 3 k=1 n = 4 nodes at r 1 = −1, r 2 = 1, r 3 = − 1 3 , r4 = 1 3 N c 1 = N b 1 + 1 16 (−9r3 + r 2 + 9r − 1), N c 2 = N b 2 + 1 16 (9r3 + r 2 − 9r − 1), N c 3 = N b 3 + 1 16 (27r3 + 7r 2 − 27r − 7), N c 4 = 1 16 (−27r3 − 9r 2 + 27r + 9) Institute of Structural Engineering Method of Finite Elements II 15
Page 1 and 2: The Finite Element Method for the A
Page 3 and 4: Setting up the governing equations
Page 9 and 10: Element Matrices B) TL Formulation
Page 11 and 12: Element Matrices where the followin
Page 13: Element Matrices where the followin
Page 17 and 18: Truss and Cable Elements Matrix Equ
Page 19 and 20: Truss and Cable Elements - Example
Page 25: Truss and Cable Elements - Example

The Finite Element Method for the Analysis of Non-Linear and ...

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