This division of my research focuses on the development of alternative numerical methods that enable the users to analyze complex systems with high accuracy and low computational cost.
Packing Optimization Techniques
Packing optimization is an important problem class that concerns various disciplines including warehouse management, shipping, and design of engineering products. Despite their versatility in treating irregular geometries, the raster methods have received limited attention in solving packing problems. To address this gap, I introduced the COMPACT: Concurrent or Ordered Matrix-based Packing Optimization Technique. It can be used to rotate the objects by arbitrary angles and efficiently obtain raster approximations with loop-free operations. It also includes a novel performance metric that aids effective filling of the available space by maximizing the internal contact within the domain. Moreover, the introduced techniques enable the exploitation of the objective functions for discarding the overlap and overflow constraints.
Rayleigh-Ritz based Methods
Rayleigh-Ritz method is a well-established meshless technique, which has been prevalently used for the vibration analysis of engineering structures. Our novel models extend the use of this method beyond the analysis of classical structures.
We developed a Rayleigh-Ritz based methodology for vibration analysis of laminated composite plates with surface-bonded piezo-patches. Piezoelectric transducers can be integrated into laminated composite structures for a variety of vibration control and energy harvesting applications. Analyzing the dynamics of these structures requires precise modeling tools that properly consider the coupling between the piezoelectric elements and the laminates. Our model can be utilized for accurate and efficient analysis and design of such electromechanical systems.
We proposed another novel semi-analytical method for the dynamic analysis of plates having discrete and/or continuous non-uniformities. Dynamic properties of the plate structures can be enhanced by introducing discontinuities of different kinds such as surface-bonded discrete patches or spatially varying stiffness and mass properties of the plate. Our method can be utilized for accurately predicting the dynamic response of such non-uniform structures. Different from the similar existing numerical methods, our novel can tackle the discontinuities that are not aligned with the plate axes.
The spectral-Tchebychev method is a state of the art meshless modeling technique. We unified the spectral-Tchebychev method with the lamination parameters formulation for analyzing doubly curved laminates as well as variable-stiffness composites.