About

Rakesh K. Kapania is Norris & Wendy Mitchell Professor of Aerospace and Ocean Engineering at Virginia Tech. He earned his Ph.D. in 1985 from the School of Aeronautics and Astronautics at Purdue University, his M.S. in 1979 from the Department of Aeronautical Engineering at the Indian Institute of Science in Bangalore, India, and his B.S. in 1977 from the Department of Aeronautical Engineering at Punjab Engineering College in Chandigarh, India. His research expertise includes structures and materials, with a focus on computational mechanics, design, and materials and structures. Dr. Kapania has held various academic positions at Virginia Tech since 1985, progressing from Assistant Professor to his current role as Norris & Wendy Mitchell Professor. He has been actively involved in service to the profession and society, including roles on several technical committees, editorial positions, and university committees. His honors include being an Associate Editor for the AIAA Journal and the Composites Engineering journal, as well as receiving the Dean's Award for excellence in research in 2000 and being a Boeing Welliver Fellow in 1996.

Research topics

• Computer Science
• Engineering
• Mathematics
• Structural engineering
• Geometry
• Artificial Intelligence
• Algorithm
• Materials science
• Mathematical optimization
• Mathematical analysis
• Composite material
• Physics

Selected publications

• Unsteady Metric-Based Adaptation via Koopman Expansion

  AIAA Journal · 2026-03-16

  articleSenior author

  Unsteady flowfields are integral to high-speed applications, demanding precise modeling to accurately characterize their dynamic features. The simulation of unsteady supersonic and hypersonic flows is inherently computationally expensive, necessitating a highly refined mesh to capture these dynamic effects. While anisotropic metric-based adaptive mesh refinement has proven effective in achieving accuracy with much less complexity, current algorithms are primarily tailored for steady flowfields. This paper presents a novel approach to address the challenges of anisotropic grid adaptation of unsteady flows by leveraging a data-driven technique called dynamic mode decomposition (DMD). DMD has proven to be a powerful tool to model complex nonlinear flows, given its links to the Koopman operator and also its easy mathematical implementation. This research proposes the integration of DMD into the process of anisotropic grid adaptation to dynamically adjust the mesh in response to evolving flow features. The effectiveness of the proposed approach is demonstrated through numerical experiments on representative unsteady flow configurations, such as a cylinder in a subsonic flow and an oscillating cylinder in a supersonic channel flow. Results indicate that the incorporation of DMD enables an accurate representation of unsteady flow dynamics independently of the remeshing interval. Computational fluid dynamics results obtained with the dynamic anisotropic mesh adaptation achieved a fourfold reduction in drag error compared to static meshing methods.

  PublisherDOI

• Aeroelastic Analysis of a Distributed Propulsor With Rotary Inertia on an Uniform Cantilever Wing

  2026-01-08

  articleSenior author

  This paper investigates the aeroelastic characteristics of a cantilever wing equipped with distributed electric propulsors, with particular attention to the effects of spanwise mass distribution, rotary inertia, and chord-wise center-of-gravity placement. An analytical aeroelastic framework is developed by coupling an Euler-Bernoulli beam with Theodorsen’s unsteady aerodynamic model, and its accuracy is verified using a classical benchmark wing. Several distributed-propulsion configurations are examined to isolate the influence of added mass, tip-mounted and distributed rotary inertia, and changes in propulsor center-of-gravity location on both the natural vibration modes and the onset of flutter. The analysis shows that distributed propulsors alter the dynamic response of the wing by lowering the natural frequencies while increasing the separation between the bending and torsional modes, which has important consequences for aeroelastic stability. Rotary inertia is found to play a secondary role compared with the effects of translational mass, whereas chord-wise center-of-gravity placement has a pronounced influence on the presence or absence of flutter within the investigated range. The results demonstrate that mass and inertia tailoring within distributed propulsion architectures can serve as an effective mechanism for enhancing aeroelastic performance in electrically powered wings.

  PublisherDOI

• Multi-Scale Microstructure-Informed Modeling of Residual Stresses and Distortions in Additive Friction Stir Deposition

  2026-01-08

  article

  The objective of this study is to develop a multi-scale framework for thermo-mechanical analysis of Ti-6Al-4V structures manufactured using the Additive Friction Stir Deposition (AFSD) technique. During the AFSD process, the structure undergoes repeated heating and cooling cycles as hot layers are deposited continuously over previously cooled material, leading to a large thermal gradient that can result in residual stresses and structural distortions. The proposed framework aims to predict such residual stresses and distortions efficiently and accurately. To capture the microstructural evolution during the process, Düsseldorf Advanced Material Simulation Kit (DAMASK), an open source Crystal Plasticity model, is used to determine the slip parameters needed to simulate the plastic deformation based on the experimental stress-strain data. Since crystal plasticity simulations are computationally expensive, a surrogate Forward Neural Network (FNN) is trained using DAMASK to predict the elasto-plastic stress-strain response of Ti-6Al-4V microstructure as a function of strain rate and temperature. The trained surrogate model is shown to significantly reduce the computational time for a low fidelity analysis to just 1 minute as compared to 71 hours when using the full physics-based DAMASK crystal plasticity simulations. The ANN architecture is then integrated with the macro scale model in Simulia Abaqus. Process simulation for AFSD is done through a sequential thermo-mechanical analysis. A transient heat transfer analysis is conducted first and the obtained temperature profiles, varying in both time and space, are used as predefined temperature field boundary conditions for the following thermo-mechanical analysis on the same mesh. The material properties such as Young’s Modulus, coefficient of thermal expansion, etc. are defined as a function of temperature. Framework capabilities are demonstrated using a ring stiffened panel example with Stainless Steel 304L substrate and Ti-6Al-4V stiffener.

  PublisherDOI

• Affine decomposition of structural stiffness matrices and their application in metaheuristic design optimization of fiber composite structures

  Structural and Multidisciplinary Optimization · 2026-02-19

  articleOpen accessSenior author

  Abstract A novel affine decomposition strategy for the finite element linear and geometric stiffness matrices of a fiber composite plate structure is presented here. The main goal of this decomposition is to express the stiffness matrices as an affine summation of terms formed by parameter-independent matrices and parameter-dependent scalars. Such a grouping has applications in improving efficient finite element analysis and improved performance of metaheuristic optimization algorithms used in structural optimization. The linear stiffness matrix is decomposed using lamination parameters and invariant matrices from classical lamination theory. The decomposition of the geometric stiffness matrix is more complicated due to the involvement of the in-plane load-induced transverse stiffness. First, the static response of the structure is approximated using a set of projection basis vectors, and the coefficient associated with each vector has an implicit dependence on the fiber composite configuration. The design-independent components of the geometric stiffness matrix are computed in terms of the projection basis vectors of the static response, and the coefficients are computed on the fly using least squares approximation. The application of these decompositions in a parametric model order reduction-based two-step optimization framework is demonstrated. The proposed approach resulted in a significant reduction in the time and resource requirement needed to carry out this optimization.

  PublisherOA PDFDOI

• Mechanical cues guide the formation and patterning of 3D spheroids in fibrous environments

  PNAS Nexus · 2025-08-12 · 7 citations

  articleOpen access

  Multicellular spheroids have shown great promise in 3D biology. Many techniques exist to form spheroids, but how cells take mechanical advantage of native fibrous extracellular matrix (ECM) to form spheroids remains unknown. Here, we identify the role of fiber diameter, architecture, and cell contractility on spheroids' spontaneous formation and growth in ECM-mimicking fiber networks. We show that matrix deformability revealed through force measurements on aligned fiber networks promotes spheroid formation independent of fiber diameter. At the same time, larger-diameter crosshatched networks of low deformability abrogate spheroid formation. Thus, designing fiber networks of varying diameters and architectures allows spatial patterning of spheroids and monolayers simultaneously. Forces quantified during spheroid formation revealed the contractile role of Rho-associated protein kinase in spheroid formation and maintenance. Interestingly, we observed spheroid-spheroid and multiple spheroid mergers initiated by cell exchanges to form cellular bridges connecting the two spheroids. Unexpectedly, we found large pericyte spheroids contract rhythmically. Transcriptomic analysis revealed striking changes in cell-cell, cell-matrix, and mechanosensing gene expression profiles concordant with spheroid assembly on fiber networks. Overall, we ascertained that contractility and network deformability work together to spontaneously form and pattern 3D spheroids, potentially connecting in vivo matrix biology with developmental, disease, and regenerative biology.

  PublisherDOI

• Rapid Coupled Loads Analysis and Trade Studies Using Norton-Thevenin Receptance Coupling

  2025-01-03

  article

  Coupled loads analysis (CLA) is a complex and time-consuming process, and successful adjudication of the results is required to certify a spacecraft for launch. Currently, spacecraft finite element models (FEMs) are reduced using component mode synthesis (CMS) methodology, and are submitted to the launch vehicle provider, with the expectation that CLA results will be delivered in 3-6 months. As further flexibility is demanded from payload providers, better intermediate methods of CLA are required to examine the impact of changes to the dynamic system. This research will investigate the feasibility of utilizing Norton-Thevenin Receptance Coupling (NTRC) to determine vehicle loads outside of the formal verification process. NTRC is a frequency-response-based sub-structuring (FBS) method, which uses impedance techniques to characterize subcomponents, netting significant time and complexity savings over CMS. Previous research has derived and validated NTRC – this work will further develop the scripting and inputs to generate an optimization tool for space vehicles consisting of a host spacecraft and interchangeable payloads.

  PublisherDOI

• Computational Solid Mechanics and Fluid–Structure Interaction

  American Institute of Aeronautics and Astronautics, Inc. eBooks · 2025-08-05

  book-chapter
  PublisherDOI

• Integrated structural design optimization of space vehicles with multidisciplinary constraints

  Aerospace Science and Technology · 2025-09-17 · 1 citations

  article
  PublisherDOI

• Confinement in fibrous environments positions and orients mitotic spindles

  PNAS Nexus · 2025-06-16 · 2 citations

  articleOpen access

  Accurate positioning of the mitotic spindle within the rounded cell body is critical to physiological maintenance. Mitotic cells encounter confinement from neighboring cells or the extracellular matrix (ECM), which can cause rotation of mitotic spindles and tilting of the metaphase plate (MP). To understand the effect of confinement on mitosis by fibers (ECM confinement), we use flexible ECM-mimicking nanofibers that allow natural rounding of the cell body while confining it to differing levels. Rounded mitotic bodies are anchored in place by actin retraction fibers (RFs) originating from adhesions on fibers. We discover that the extent of confinement influences RF organization in 3D, forming triangular and band-like patterns on the cell cortex under low and high confinement, respectively. Our mechanistic analysis reveals that the patterning of RFs on the cell cortex is the primary driver of the MP rotation. A stochastic Monte Carlo simulation of the centrosome, chromosome, membrane interactions, and 3D arrangement of RFs recovers MP tilting trends observed experimentally. Under high ECM confinement, the fibers can mechanically pinch the cortex, causing the MP to have localized deformations at contact sites with fibers. Interestingly, high ECM confinement leads to low and high MP tilts, which we mechanistically show to depend upon the extent of cortical deformation, RF patterning, and MP position. We identify that cortical deformation and RFs work in tandem to limit MP tilt, while asymmetric positioning of MP leads to high tilts. Overall, we provide fundamental insights into how mitosis may proceed in ECM-confining microenvironments in vivo.

  PublisherOA PDFDOI

• Optimization of a Tapered Deployable Space Structure

  2025-01-03

  articleSenior author

  Modern spacecraft utilize deployable structures for many applications to strike a balance between functionality and size within a launch vehicle. Due to volume restrictions in a launch vehicle these deployable structures are stowed in a collapsed configuration during launch and deployed when the spacecraft successfully reaches a stable orbit. In this study, an optimization of a tapered composite beam deployable structure is performed to find an optimally performing design, minimizing wrapped strain energy and deployment dynamics. The beam will consist of a compressible, lenticular section that will include a taper ratio from the beam’s root to its tip in a chord-wise manner. Material selection of the composite layup will also be included in the optimization with the ability to choose different composite mixtures, layup directions and ply thicknesses. Abaqus CAE, a commercial finite element analysis software, is used to conduct two analyses that make up the optimization architecture. The first is to obtain the fundamental frequency of a beam design in its deployed state. The second will find stresses along the beam as it is wrapped examining the stored strain energy of the beam in the wrapped state. The second analysis will then continue to deploy the structure from the wrapped state and examine the rotational velocity and beam’s oscillatory behavior during deployment. HEEDS MDO, a commercial optimization software, is utilized to conduct the optimization. Design variables will include beam dimensions and taper ratio, as well as material properties of the composite layup. The objective function will minimize the beam’s weight, stored strained energy in the wrapped state and beam tip displacements during deployment. Constraints will be assigned on design variables and objectives, but transient stresses during wrapping will be checked for material failure using Hashin Damage Criterion. Finding a design that satisfies mission requirements and maintains structural integrity during wrapping and deployment will be challenging and computationally expensive. The optimization simulation presented in this paper aims to generate the best possible design that satisfies all requirements.

  PublisherDOI

Frequent coauthors

• Joseph A. Schetz

  Virginia Tech

  72 shared

• Sameer B. Mulani

  United States Air Force Research Laboratory

  58 shared

• Wei Zhao

  Sichuan University

  46 shared

• Raphael T. Haftka

  31 shared

• Mohamed Jrad

  25 shared

• Rikin Gupta

  Toyota Motor Corporation (Switzerland)

  22 shared

• Amrinder S. Nain

  Virginia Tech

  18 shared

• Ali Y. Tamijani

  18 shared

Labs

• Kevin T. Crofton Department of Aerospace and Ocean EngineeringPI

Education

• Ph.D., Aeronautics and Astronautics

  Purdue University West Lafayette

Awards & honors

• Dean's Award for excellence in Research (2000)
• Boeing Welliver Fellow (1996)
• Associate Editor, AIAA Journal (2007)
• Associate Editor, AIAA Journal (1994-1997)