Sensitivity Analysis and Optimization of Mechanical System Design

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Abstract
The paper follows studies on simulation of three-dimensional mechanical dynamic systems with the help of sparse matrix and stiff integration numerical algorithms. For sensitivity analyses and the application of numerical optimization procedures it is substantial to calculate the effect of design parameters on the system behaviour by means of derivatives of state variables with respect to the design parameters. For static and quasi static analyses the computation of these derivatives from the governing equations leads to a linear equation system. The matrix of this set of linear equations shows to be the Jacobian matrix required in the numerical integration process solving the system of governing equations for the mechanical system. Thus the factorization of the matrix perfomed by the numerical integration algorithm can be reused solving the linear equation system for the state variable sensitivities. Some example demonstrate the simplicity of building the right hand sides of the linear equation system. Also it is demonstrated that the procedure proposed neatly fits into a modular concept for simulation model building and analysis.

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