Numerical Integration Methods for Multibody Dynamics

Numerical Integration Methods for Multibody Dynamics Lesson 8. Numerical Integration Methods for Multibody Dynamics Accuracy of Explicit Euler Method By Taylor series expansions, Explicit Euler Method 2 3. +1 = + + + . 2 6 . 2. +1 = + + + Truncation error 2. +1 = + + Truncation error 3. Truncation error ( ) < ( : user defined error tolerance). 6. 3 6 . Allowable step size .. must be estimated). ( . 3. Accuracy of Implicit Euler Method By Taylor series expansions, Implicit Euler Method 2 3. +1 = + + + . 2 6 . 2 2 3. +1 = + + +1 + Truncation error = + + +1 + . 2 2 3. where, +1 = + +1 + Truncation error 2 . = =. 2 . + +. 2. + . 2 +1 +1. 2 . 2 . 2 . = +1 + . 2. 3. Truncation error ( ) < ( : user defined error tolerance). 3. 3 3 . Allowable step size .. must be estimated). ( . 4. Stability of Euler Methods . Explicit Method.

Preconditioned Conjugate Gradient (PCG) iterative solver. This solver performs well for small deformation models. This solver generally takes longer than general linear solver for shell element or large deformation problems. Preprocessing time is required to find a good preconditioner.

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