Nonlinear Example

Nonlinear Example - 2 4 6 8 10 12 14 16 18 20 5 10 15 20 25...

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Unformatted text preview: 2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30 35 40 u K m=0.6 Softening m=1.0 Linear m=1.2 Hardening 2 4 6 8 10 12 14 16 18 20 0.5 1 1.5 2 2.5 3 3.5 4 4.5 u Ku Nonlinear Behavior of Ku = K o u m+1 with m = -0.5 One Degree of Freedom Nonlinear Example Consider the basic finite element equation } { } ]{ [ F u K = for the one degree of freedom case with a specific nonlinear stiffness m o u K u K K = = ) ( . Particular examples of this stiffness response for different values of m are shown in the following figure. We now consider two examples, including both convex and concave behaviors for } )]{ ( [ u u K . For the convex case, we choose m = -0.5 and take F = 4 as shown in the figure below. The highlighted dot indicates where } { } ]{ [ F u K = . 5 10 15 20 25 30 2 4 6 8 10 12 14 16 Number of Iterations u-Value Direct Iteration Method with m = -0.5 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 Number of Iterations u-Value Newton-Raphson Method with m = -0.5 In order to find the solution for this case, we employ both the Direct Iteration and Newton-...
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Nonlinear Example - 2 4 6 8 10 12 14 16 18 20 5 10 15 20 25...

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