A Consistent Design Sensitivity Analysis Formulation for Systems With History-Dependent Response
Vidal, Creto Augusto
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https://hdl.handle.net/2142/72191
Description
Title
A Consistent Design Sensitivity Analysis Formulation for Systems With History-Dependent Response
Author(s)
Vidal, Creto Augusto
Issue Date
1992
Doctoral Committee Chair(s)
Haber, Robert B.
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Engineering, Civil
Engineering, Mechanical
Abstract
Design sensitivity analysis is the determination of the rate of change with respect to design parameters of a given performance measure which generally can be cast in the form of a functional. The functional typically exhibits both explicit dependence and implicit dependence (via the response) on the design. Sensitivity analysis is used in structural optimization, identification problems, and reliability analysis.
There has been considerable recent progress in developing mechanics theory for analytical sensitivity analysis methods. Current interest in composite materials, polymers and other materials with history-dependent response makes design sensitivity analysis for such materials a topic of considerable practical importance. Only limited progress has been reported in developing analytical sensitivity analysis methods for this class of problems, for which finite difference sensitivity methods are extremely expensive and unreliable. The present work uses the concept of the algorithmic constitutive relation and the corresponding consistent tangent operator concept to construct simulation models for history-dependent creep and elastoplasticity. Then, it uses the direct differentiation method of sensitivity analysis while maintaining consistency with the underlying simulation model, to obtain accurate sensitivity expressions for these two classes of problems. The sensitivity expressions can be evaluated with only a modest increase in computational expense beyond the cost of simulation. This represents a significant improvement over the methods published to date.
First-order sensitivity expressions involving the complete set of design variables, including shape design variables, are derived for a generic response functional. The reduced form of the consistent tangent stiffness matrix obtained at the end of each time or load step in the finite element procedure is used to update the response sensitivities for that time step. Therefore, no iterations are needed in the sensitivity computations.
Numerical examples demonstrate the new sensitivity analysis method for a power-law creep model and a rate-independent elastoplasticity model. Explicit sensitivities from the new method are confirmed by finite difference estimates that were obtained using careful convergence studies.
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