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4. Vector scale function declaration in C++. 

4. Vector scale function declaration in C++. 

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Figure 2.1. C++ linear algebra API child class definition. 
Figure 2.5. C++ operators API class declaration example: Unconstrained...
Figure 2.6. C++ operators API class definition example: 
Figure 2.19. MATLAB preconditioner API: Full-space PDE-constrained...
+34 Figure 2.12. C++ solution operators API child class dec- 
Design Optimization Toolkit: Users' Manual
Technical Report
Full-text available
  • Jul 2014
The Design Optimization Toolkit (DOTk) is a stand-alone C++ software package intended to solve complex design optimization problems. DOTk software package provides a range of solution methods that are suited for general purpose gradient/nongradient-based optimization, large scale constrained optimization, and topology optimization. DOTk was design...
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... A quasi-Newton optimization algorithm in the Design Optimization Toolkit (DOTk) [3] was employed to minimize the objective function. In quasi-Newton methods, the Hessian is updated by analyzing successive gradient vectors instead of computing the Hessian matrix. ...
Considering DIC Uncertainties in Material Property Identification Using VFM The Virtual Fields Method for Finite Deformation
Conference Paper
Full-text available
  • Jun 2014
Inverse problem methodologies for material property identification often rely on full-field experimen-tal measurements from optical methods. These vital measurements have experimental errors that can lead to large uncertainties in the identified properties, particularly in inverse approaches that utilize nonlinear iterative optimization algorithms where experimental error can lead to spurious local minima. In this paper, the effects of uncertainties associated with Digital Image Correlation (DIC) displacement measurements are investigated for a finite deformation Virtual Fields Method (VFM) approach for plasticity model parameter identification. The complete VFM inverse prob-lem methodology is simulated using computationally derived displacements with superimposed DIC measurement uncertainties, which were quantified for representative DIC experimental setups, as inputs to the identification algorithm. The simulated VFM process that incorporates measurement errors allows for characterizing the impact of DIC uncertainties based on realistic experimental parameters without requiring cost-prohibitive iterative experimental investigations of the full VFM process. This study can help with specimen-geometry and DIC-setup designs so that the real exper-iments provide optimal measurements for lower uncertainties in finite deformation VFM material property identification.
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