Adaptive Computational Mechanics

3D Recovery-based data transfer

Adaptive computational mechanics constitutes the foundation of my research. Rather than employing finite element analysis simply as a numerical tool, my work focuses on advancing the underlying computational methodologies through adaptive mesh refinement, recovery-based error estimation, efficient solution-transfer algorithms, and scalable parallel computing. These developments aim to improve the accuracy, robustness, and computational efficiency of large-scale structural simulations while preserving their practical applicability to engineering analysis.

Particular emphasis has been placed on developing integrated computational frameworks in which adaptive analysis proceeds automatically through successive cycles of error estimation, mesh refinement, solution transfer, and numerical verification. A central component of this research has been the development and extension of the Superconvergent Patch Recovery (SPR) technique for three-dimensional problems, enabling accurate error estimation, reliable adaptive mesh refinement, and efficient data transfer between successive computational meshes.

Error estimation and mesh refinement

As computational models continue to increase in scale and complexity, efficient parallel computing has become an integral part of modern computational mechanics. My research in this area has focused on developing scalable parallel algorithms for finite element analysis, with particular emphasis on computational efficiency, load balancing, communication optimization, and high-performance implementations capable of addressing large-scale engineering simulations.

Parallel computation on CPU

Parallel computation on GPU

The culmination of these research efforts is the development of a Python-based computational framework for adaptive finite element analysis. By integrating adaptive mesh refinement, error estimation, parallel computing, solution-transfer techniques, and scientific visualization within a unified environment, this software provides a practical platform that bridges methodological research with large-scale engineering applications.

Representative Research Topics

• Adaptive Finite Element Analysis
• Error Estimation and Recovery Methods
• Adaptive Mesh Refinement
• Superconvergent Patch Recovery (SPR)
• Parallel Finite Element Computing
• High-Performance Scientific Computing

Optimization & Computational Intelligence

DRBS optimization methodology

Building upon advances in computational mechanics, this research theme investigates how rigorous numerical methodologies can be transformed into practical tools for engineering design and decision-making. Rather than treating structural analysis and optimization as independent processes, my research integrates them within unified computational frameworks capable of improving structural performance while simultaneously satisfying engineering, economic, and computational constraints.

My work in this area encompasses structural optimization, intelligent computational methods, performance-based design, and structural control. The emphasis has consistently been placed on developing robust and transferable computational methodologies whose applicability extends well beyond individual engineering problems. As a result, the proposed approaches provide general computational strategies that can be adapted to a broad spectrum of structural engineering applications requiring reliable decision support.

Performance-based optimum design

Performance-based design provides a natural framework in which computational optimization can be translated into practical engineering solutions. My research has focused on developing computational frameworks capable of automatically identifying optimal structural configurations while satisfying multiple performance objectives under diverse loading conditions.

Intelligent computational strategy

Comparing controlled and uncontrolled responses

Optimal control of structures represents a further extension of these optimization methodologies toward real-time engineering decision-making. My research has investigated both active and semi-active control systems, with particular emphasis on the optimal placement of control devices and the integration of intelligent computational techniques for achieving reliable and efficient structural performance under dynamic loading.

Representative Research Topics

• Structural Optimization
• Optimal Design of Structures
• Intelligent Computational Methods
• Metaheuristic Optimization Algorithms
• Optimal Control of Structures
• Machine Learning & AI

Nonlinear Structural Dynamics

Schematic view of the experiment

Nonlinear structural dynamics represents a natural extension of the computational methodologies developed in the preceding research themes. My research investigates the response of structural systems subjected to dynamic and environmental loading, with particular emphasis on nonlinear behavior, vibration mechanisms, stability, and fluid-structure interaction. These phenomena are studied within a unified computational framework that combines advanced numerical simulation with physical insight into complex dynamic behavior.

My research has extensively investigated nonlinear vibration phenomena, vortex-induced vibrations, chaotic structural response, and dynamic instability. Beyond predicting structural behavior, these studies seek to reveal the fundamental physical mechanisms governing complex dynamic systems. By integrating computational mechanics with nonlinear dynamics, this work contributes to a deeper understanding of structural performance under realistic operational and environmental conditions.

Mathematical model for rigid cylinder with nonlinear snapping support

Vortex-induced vibrations represent one of the most challenging fluid-structure interaction problems in engineering. My research has investigated the complex dynamic behavior of cylindrical structures subjected to flow, with particular emphasis on the transition from periodic to chaotic response and the influence of support conditions on vibration characteristics.

Fluid-structure interaction forms an essential component of many nonlinear engineering systems. My research has focused on developing efficient partitioned computational strategies that combine advanced fluid solvers with robust structural models, enabling accurate simulation of vortex-induced vibrations and other complex coupled dynamic phenomena.

Hilbert transform trajectories of the displacement (left) and lift force (right) for the system with γ = 0.2

Chaotic behavior, although often associated with undesirable structural response, provides valuable insight into the fundamental mechanisms that govern nonlinear dynamic systems. My research explores the detection, characterization, and interpretation of chaotic behavior as a means of advancing the understanding of complex structural dynamics and supporting more reliable engineering predictions.

Representative Research Topics

• Nonlinear Dynamics
• Fluid-Structure Interaction
• Vortex-Induced Vibrations
• Dynamic Stability
• Chaotic Structural Response
• Snap-Through Systems

Engineering Applications

Ultimate lateral strength in the models with V braces

Engineering applications represent the culmination of my research rather than its starting point. They are not presented merely as numerical examples or validation studies, but as demanding environments in which newly developed computational methodologies are evaluated against the complexity of real engineering systems. Their purpose is to demonstrate that rigorous mathematical models and numerical algorithms remain reliable when nonlinear behavior, uncertainty, deterioration, and large-scale computation become dominant features of practical engineering problems.

Although these applications span diverse branches of structural and computational engineering, they share a common methodological foundation built upon adaptive finite element analysis, nonlinear simulation, probabilistic modeling, structural reliability, optimization, and high-performance scientific computing. Rather than developing isolated application-specific procedures, my objective has been to establish computational methodologies whose validity extends across a broad spectrum of engineering systems while preserving both mathematical rigor and practical engineering relevance.

Finite element model of jackets

Overview of reliability analysis

Steel structural systems have provided one of the principal platforms for validating these methodologies. My research has addressed nonlinear seismic behavior of steel moment-resisting and dual systems, staged-construction effects, innovative shear fuse systems for energy dissipation, optimization of steel connections, and performance-based structural evaluation. Collectively, these studies demonstrate how computational mechanics can support both structural understanding and informed engineering decision-making under severe loading conditions.

A complementary line of research concerns offshore steel infrastructure, where uncertainty becomes an inherent component of engineering practice. My work integrates probabilistic corrosion models, Bayesian reliability updating, and reliability-based inspection planning into unified computational frameworks for jacket platforms. These methodologies provide quantitative tools for predicting structural deterioration, optimizing inspection strategies, and improving life-cycle management under uncertain environmental conditions.

Scientific software development represents a natural extension of this research philosophy. Rather than implementing isolated numerical algorithms, projects such as PyAdMesh and SUT-DAM have been developed as integrated computational platforms through which advanced engineering methodologies become accessible for large-scale scientific computing and multidisciplinary engineering analysis. These software environments translate mathematical concepts into practical technologies that support both academic research and professional engineering practice.

Pastor-Zienkiewicz model in SUT-DAM

The Mahabad dam, the nodal displacement vectors at 50 s after beginning of the earthquake using Pastor-Zienkiewicz model

Viewed collectively, these engineering investigations are united by a single objective: transforming rigorous computational methodologies into dependable engineering technologies. Whether the problem involves seismic performance of steel structures, offshore infrastructure, reliability-based engineering decisions, or high-performance scientific software, the underlying philosophy remains unchanged. Engineering applications are not simply the destination of computational research—they are the ultimate demonstration that sound mathematical methodologies can reliably describe, predict, and support decisions in complex real-world engineering systems.

Representative Engineering Research Areas

• Performance-Based Seismic Engineering
• Steel Structural Systems
• Structural Reliability and Probabilistic Engineering
• Bayesian Reliability Updating
• Offshore Steel Structures
• Scientific Software Development
• High-Performance Engineering Computing
• Computational Geotechnics