K C Park

• PhD
• Professor Emeritus at University of Colorado Boulder

A new flexibility-based component mode synthesis method is presented, which is derived by approximating the partitioned equations of motion that employ a localized method of Lagrange multipliers. The use of the localized Lagrange multipliers leads to, unlike the classical Lagrange multipliers, a linearly independent set of interface forces without...

The behavior of linear multistep methods has been evaluated for application to structural dynamics problems. By examining the local stability of the currently popular methods as applied to nonlinear problems, it is shown that the presence of historical derivatives can cause numerical instability in the nonlinear dynamics even for methods that are u...

A general partitioned transient analysis procedure is proposed, which is amenable to a unified stability analysis technique. The procedure embodies two existing implicit-explicit procedures and one existing implicit-implicit procedure. A new implicit-explicit procedure is discovered, as a special case of the general procedure, that allows degree-by...

A partitioned formulation of compressible internal fluid–structure interaction problems is presented by employing a displacement model for both the fluid and structure. Partitioning is effected by a localized version of the method of Lagrange multipliers, which assigns two independent sets of Lagrange multipliers to the structural and fluid interfa...

A theory is presented for transforming the system theory-based realization models into the corresponding physical coordinate-based structural models. The theory has been implemented into a computational procedure and applied to several example problems. The results show that the present transformation theory yields an objective model basis possessi...

In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing equation identification algorithms assuming the state variables are known {\it a priori} and the governing eq...

In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing equation identification algorithms assuming the state variables are known a priori and the governing equation...

This work presents an efficient and accuracy‐improved time explicit solution methodology for the simulation of contact‐impact problems with finite elements. The proposed solution process combines four different existent techniques. First, the contact constraints are modeled by a bi‐penalty contact‐impact formulation1 that incorporates stiffness and...

This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics (SINDy) approach of Brunton et al. (2016), which relies on two main assumptions: the state variables are known a p...

This paper presents a stabilization technique for the finite element modeling of contact-impact problems of elastic bars via a bi-penalty method for enforcing contact constraints while employing an explicit predictor–corrector time integration algorithms. The present proposed method combines three salient features in carrying out explicit transient...

This study proposes a formulation for the dynamics of a flexible multibody heliogyro solar sail undergoing rigid body motion and multi-blade vibration. The heliogyro solar sail consists of a rigid central hub and flexible solar multi-blades. The floating frame approach is applied to describe large translational and rotational motions, as well as bl...

An Iterative Flexibility‐based Component Mode Synthesis (IF‐CMS) is presented for the model reduction of partitioned structural dynamic systems via localized Lagrange multipliers. A distinct IF‐CMS feature is the inclusion of hierarchical residual flexibility at each iteration, resulting in considerably improved accuracy compared with the classical...

This work proposes an iterative sparse-regularized regression method to recover governing equations of non-linear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics (SINDy) approach of [Brunton et al., PNAS, 113 (15) (2016) 3932-3937], which relies on two main assumptions: the...

A partitioned stochastic method (PSM) is proposed for the solution of static structural mechanics problems with uncertainties, whose solution vectors are the displacements for each partition and Lagrange multipliers along with the partition interfaces. The proposed partitioned stochastic method employs three stochastic basis selection steps: an arb...

A method for tailoring mass matrices that allows large time step explicit transient analysis is presented. It is shown that the accuracy of the present tailored mass matrix preserves the low‐frequency contents while effectively replacing the unwanted higher mesh frequencies by a user‐desired cut‐off frequency. The proposed mass tailoring methods ar...

A new frame discretization method for treating non-matching discrete interfaces is presented based on the method of localized Lagrange multipliers, which introduces the frame domain lying between the two interfacing parts. The required interface compatibility conditions are then enforced independently between the master domain interface nodes and t...

Variationally based algorithms for the partitioned solution of structural mechanics problems are presented. Two key features of the present algorithms are the judicious application of the d’Alembert-Lagrange principal equations and the use of dominant substructural deformation modes. The paper includes three developments: 1. Variational derivation...

We introduce a strongly coupled model reduction method recently developed for well-known vibro-acoustic interaction, which is a standard (u, p) formulation. The key principle of the scheme is a sequential reduction process from the structure to fluid domains. The sequential projection allows for a strong connection between two different physical do...

This paper presents a new formulation of the coupled reduced-order modeling technique for fluid–structure interaction problems. The problem addressed here is a classical vibro-acoustic issue, which is a coupled vibration of an acoustic fluid in an elastic structure. Discretization of the problem yields a model having many degrees of freedom, which...

An iterative algorithm of component mode synthesis for a rational reduced-order modeling is proposed. The present algorithm consists of three steps: initial mode selection with a priori criterion, model reduction using the selected modes, and a posteriori error evaluation. The algorithm is based on the Craig–Bampton method, which is one of the most...

A multistep explicit time integration algorithm is presented for tracking the propagation of discontinuous stress waves in heterogeneous solids whose subdomain to subdomain critical time step ratios range from tens to thousands. The present multistep algorithm offers efficient as well as accurate computations for tracking discontinuous waves propag...

This study introduces a new version of a virtual tetrahedral gap element to connect partitioned structures which are independently discretized with tetrahedral elements. Tetrahedral meshes are widely used for practical engineering problems due to their simplicity. The proposed interface method employs the localized Lagrange multiplier method. The v...

Nonlinear hysteresis from the piezoelectric tripod manipulator integrated with a compliant mechanism obstructs precise motion. To accurately control the piezoelectric tripod manipulator, in article number 1800298, Hyeong‐Geon Kim, Jong‐Nam Kim, Il‐Kwon Oh and co‐workers successfully apply a feedforward hysteresis compensator based on the rate‐depen...

Flexibility-based component mode synthesis (F-CMS) is one of the most popular free-interface component mode synthesis (CMS) methods. In the F-CMS method, localized Lagrange multipliers are employed along the interface boundary as a constraint condition between substructures; thus, it offers various advantages, including the perfect independence of...

A variational framework is employed to generate inverse mass matrices for isogeometric analysis. As different dual bases impact not only accuracy but also computational overhead, several dual bases are extensively investigated. Specifically, locally discontinuous bi‐orthogonal basis functions are evaluated in detail for B‐splines of high continuity...

In this study, a precise motion control strategy for a piezoelectric tripod manipulator integrated with compliant mechanisms based on feedforward hysteresis compensation and feedback control is reported. The piezoelectric tripod platform is designed with three piezoelectric legs to produce large transverse stroke and angular motions with three degr...

In this work, we consider the dynamic interaction of incompressible fluids with flexible structures. Due to the particular characteristics of fluid and solid systems, different formulations are usually applied to each medium producing non-matching interfaces. Also the movements of the fluid on the free surface due to sloshing motions are usually bi...

Electroactive polymers such as dielectric elastomers (DEs) have attracted significant attention in recent years. Computational techniques to solve the coupled electromechanical system of equations for this class of materials have universally centered around fully coupled monolithic formulations, which while generating good accuracy requires signifi...

Electroactive polymers such as dielectric elastomers (DEs) have attracted significant attention in recent years. Computational techniques to solve the coupled electromechanical system of equations for this class of materials have universally centered around fully coupled monolithic formulations, which while generating good accuracy requires signifi...

The topology optimization for practical engineering problems is computationally expensive owing to the complexity of the entire system. Therefore, most of the topology optimization is currently being conducted on simplified decomposed subsystems, which are then assembled in order to reduce the computational cost. Under these circumstances, there is...

A proper imposition of interface compatibility condition is important for issues in interface coupling, especially when the interface contains nonmatching meshes. For precise handling of interface coupling, a localized mortar method is widely used by introducing a fictitious frame domain to impose interface constraint. The performance of the method...

A mode selection method is presented for the reduced-order modeling (ROM) of structural systems in conjunction with the Craig-Bampton component mode synthesis technique. The proposed method is derived by using a consistent expansion of the interface displacement in terms of a frequency-dependent small parameter as applied to a Craig-Bampton-like RO...

A method for three-dimensional non-matching interface treatment with a virtual gap element is developed. When partitioned structures contain curved interfaces and have different brick meshes, the discretized models have gaps along the interfaces. As these gaps bring unexpected errors, special treatments are required to handle the gaps. In the prese...

An efficient method for generating the mass matrix inverse of structural dynamic problems is presented, which can be tailored to improve the accuracy of target frequency ranges and/or wave contents. The present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditio...

Model reduction methods increase the effectiveness of dynamic analysis in various engineering fields such as aerospace, electronic and even in biomechanial engineering. The component mode synthesis (CMS) technique, especially the Craig-Bampton (CB) method is one of the most popular and widely used model reduction method. The CB method selects a few...

A mixed displacement-pressure formulation of the Stokes problem for incompressible fluids with free surfaces is developed for modeling the propagation of gravity waves in liquids and their interaction with structures using a Lagrangian approach. We assume that fluid displacements are small, making convective effects negligible and approximate the f...

We report a hierarchical piezoelectric tripod manipulator based on a reverse bridge-type displacement amplifier. The reverse bridge-type amplification mechanism is pre-strained by each piezo-stack actuator up to 60 μm and is cross-stacked in a series arrangement to make a compact and high-stroke manipulator having load-bearing characteristics. The...

This paper reports a comparison study of several mode selection strategies for the Craig-Bampton (CB) component mode synthesis method which is one of the most widely used CMS methods. We analyze various mode selection strategies and compare the pros and cons of each strategy. Mode selection strategies can be divided into two categories: a priori an...

Component mode synthesis is a popular reduced-order modeling technique with a substructuring strategy in structural dynamics. The ideal goal of component mode synthesis is to construct compact reduced models with adequate accuracy for specific intended applications. In this paper, five a priori mode selection methods plus an a posteriori mode selec...

The transition piece of a fixed offshore wind turbine is a reinforced part of the support structure that is connected to the wind turbine tower. These structural elements present unique features and are critical components of offshore wind turbines; designed to resist strong bending moments, shear forces and axial loads coming from cyclic environme...

The paper complements and extends the previous works on partitioned explicit wave propagation analysis methods, which were presented for discontinuous wave propagation problems in solids. An efficient implementation of the partitioned explicit wave propagation analysis methods is introduced. The present implementation achieves about 25% overall com...

In this work, a partitioned scheme for the numerical simulation of the surface-coupled problem of a fluid interacting with a saturated porous medium (fluid-porous-media interaction) is proposed by adopting the method of localised Lagrange multipliers, which facilitates an automatic spatial partitioning of the problem and a parallel treatment of the...

We propose a new class of acoustic waveguides with tunable bandgaps (TBs) by using vibro-acoustic metamaterials with shunted periodic piezoelectric unit cells. The unit metamaterial cells that consist of a single crystal piezoelectric transducer and an electrical shunt circuit are designed to induce a strong vibro-acousto-electrical coupling, resul...

A family of gap elements are developed for treating non-matching interfaces occurring in partitioned analysis of mechanical systems. The proposed gap elements preserve linear and angular momentum and can be specialized to equivalent dual mortar methods, if desired. The proposed gap elements continue to be applicable when the interface gaps disappea...

A major challenge in component mode synthesis (CMS) remains the absence of a robust mode selection algorithm which can provide a measure of accuracy of the reduced model compared to the full model. In order to address this challenge, two concepts have been proposed in tandem: mode selection and error estimation methods. In this paper, we reassess p...

We report a two-dimensional acoustic cloak designed with axisymmetric cylindrical lattices. The proposed axisymmetric lattice layers are optimized such that acoustic cloaking can be effectively realized within realistic material properties regardless of the incoming direction of plane waves. The cylindrical shape of lattice structures consists of f...

We present a similarity law for form drag coefficients, which is obtained by a judicious utilization of an energy dissipation equation due to eddy viscosity for incompressible turbulent flow, the steady-state κ –ω turbulence model, and the Kolmogorov turbulence dissipation length scales. It is shown that the form drag coefficients of three geometri...

This paper presents a state-of-the-art in the use of localized Lagrange multipliers (LLMs)for 3D frictional contact problems coupling the Finite Element Method (FEM) and the BoundaryElement Method (BEM). Resolution methods for the contact problem between non-matching mesheshave traditionally been based on a direct coupling of the contacting solids...

This work presents a partitioned finite element formulation for flexible multibody systems, based on the floating frame (FF) approach, under the assumption of small deformations but arbitrarily large rotations of the bodies. In classical FF of reference methods, deformational modes are normally computed by modal analysis. In this approach, free-flo...

Wake effects of a horizontal-axis wind-turbine blade on aeroelastic characteristics were investigated under normal operational conditions. A structural analysis was performed employing a nonlinear beam model based on the large deflection beam theory. For inflow analysis on rotor blades, a free-vortex wake method was employed. An advantage of the pr...

This paper presents a complete formulation for three‐dimensional hydrodynamic analysis of floating flexible structures subjected to surface regular waves, as well as other excitation forces, by employing a direct tight coupling method. The continuum mechanics‐based finite element method is employed to model floating structures with arbitrary geomet...

Horizontal axis wind turbines operate under yawed conditions for a considerable period of time due to the power control mechanism or sudden changes in the wind direction. This in turn can alter the dynamic characteristics of a turbine blade because the flow over the rotor plane may trigger complicated induced velocity patterns. In this study, an ae...

An explicit integration algorithm for computations of wave propagation in solids is presented, which is designed to trace extensional and shear waves in accordance with their respective propagation speeds. This has been possible by an orthogonal decomposition of the total displacement into extensional and shear components. The two decoupled wave eq...

Computer implementation of the new algorithm developed in [1, 2, 3] and its numerical performance is presented, with detailed discussions of the element-by-element decomposition of the extensional and shear components and step-by-step algorithmic procedures. Numerical results as applied to wave propagating through cracked plane stress problems, thr...

An explicit integration algorithm for computations of discontinuous wave propagation in two‐dimensional and three‐dimensional solids is presented, which is designed to trace extensional and shear waves in accordance with their respective propagation speeds. This has been possible by an orthogonal decomposition of the total displacement into extensi...

Aeroelastic instability problems have become an increasingly important issue due to the increased use of larger horizontal axis wind turbines. To maintain these large structures in a stable manner, the blade design process should include studies on the dynamic stability of the wind turbine blade. Therefore, fluid-structure interaction analyses of t...

SUMMARY The finite element tearing and interconnecting (FETI) method is recognized as an effective domain decomposition tool to achieve scalability in the solution of partitioned second-order elasticity problems. In the boundary element tearing and interconnecting (BETI) method, a direct extension of the FETI algorithm to the BEM, the symmetric Gal...

The wave propagation characteristics of an acoustic metamaterial composed of periodically repeated one-dimensional Helmholtz resonator array was investigated considering the effects of dimensional changes of the resonator geometry on the transmission coefficient and band gap. The effective impedance and transmission coefficient of the acoustic meta...

Active disturbance rejection control method that can actively compensate nonlinear model uncertainties and unpredictable external disturbances is proposed for an accurate position tracking of an ionic polymer-metal composite actuator. An empirical model of the electroactive polymer actuator is constructed by fitting the step response of the actuato...

The effect of clamping pressure on the actuation performance of ionic polymer–metal composite (IPMC) actuators is newly investigated by carefully considering changes of mechanical stiffness and electrical resistance due to the interfacial contacts between the IPMC and clamping devices. During the clamping process, the soft ionic exchangeable polyme...

SUMMARYA partitioned, continuum‐based, internal fluid–structure interaction (FSI) formulation is developed for modeling combined sloshing, acoustic waves, and the presence of an initial pressurized state. The present formulation and its computer implementation use the method of localized Lagrange multipliers to treat both matching and non‐matching...

An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. The essence of the present method is a combination of two wave capturing characteristics: a new integr...

Fiber Bragg Grating (FBG) sensor arrays can be used to monitor the mechanical behavior of large composite structures. However, brittle FBG sensors, especially multiplexed FBG sensors can be easily damaged when they are installed in flexible structures. As a protection for brittle FBG sensors, epoxy packaged FBG sensors have been suggested. Packaged...

The viability of the previously presented flexibility-based component mode synthesis (FCMS) of structural dynamical systems1 is reassessed. The present paper offers a historical perspective on the fore method and various CMS methods, and then reexamines the FCMS method against this backdrop. The FCMS method involves two-level model reductions: cons...

The viability of the previously presented flexibility-based component mode synthesis (FCMS) of structural dynamical systems1 is reassessed. The present paper offers a historical perspective on the fore method and various CMS methods, and then reexamines the FCMS method against this backdrop. The FCMS method involves two-level model reductions: cons...

SUMMARYA simple explicit–implicit finite element tearing and interconnecting (FETI) algorithm (AFETI‐EI algorithm) is presented for partitioned transient analysis of linear structural systems. The present algorithm employs two decompositions. First, the total system is partitioned via spatial or domain decomposition to obtain the governing equation...

The Boundary Element Tearing and Interconnecting (BETI) method is an efficient parallel domain decomposition methodology that emerged as a direct extension of the Finite Element Tearing and Interconnecting (FETI) method to the Boundary Element Method. In the BETI method, a symmetric Galerkin boundary element formulation is used in order to obtain s...

We report here a facile synthesis of high performance electro-active polymer actuator based on a sulfonated polyimide with well-defined silver electrodes via self-metallization. The proposed method greatly reduces fabrication time and cost, and obviates a cation exchange process required in the fabrication of ionic polymer-metal composite actuators...

This paper proposes a time-discontinuous and space-continuous variational integration (TDSC-VI) method for accurate elastic stress wave propagation computations in one-dimensional bar. The algorithm employs a limiter, akin to classical artificial viscosity treatment, to mitigate the deleterious Gibbs jumps across the stress discontinuities, and a p...

An explicit integrator for wave propagation analysis of heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. Hence, the present method can be applied to multi-physics and multi-scale problems in which discontinuous spatial and temporal discont...

This paper presents a partitioned modeling of internal and gravity fluid waves that interact with flexible structures. The governing interaction model consists of three completely partitioned entities: fluid model, structural model, and interface model that acts as an internal constraint on the fluid–structure interface boundary. Thus, the proposed...

This paper proposes a numerical algorithm of a time-discontinuous variational integrator based on the Hamiltonian in order to obtain more accurate results in the analysis of elasto-plastic stress wave. The algorithm proposed adopts both a time-discontinuous variational integrator and space-continuous Hamiltonian so as to capture discontinuities of...

This paper addresses the dynamics and quasi-statics of floating flexible structures as well as extensions to unconstrained substructures and partitions of coupled mechanical systems. The principal solution is defined as the state of self-equilibrated forces obtained as the particular solution of the rigid motion and interface equilibrium equations....

A method is proposed for identifying the location of an open transverse crack in flexible rotor systems by modeling the crack as a localized element with rotating asymmetry. It exploits the strong correlations between the modal constants of the reverse directional frequency response functions (r-dFRFs) and the degree and location of asymmetry. A ma...

a b s t r a c t New approximate models for external acoustics interacting with flexible structures are developed. The basic form of the present models is obtained by a combination of the Laplace-transformed retarded and advanced potentials with the weighting parameter as part of the model equation. It is shown that the maximum attainable time-deriv...

Purpose The purpose of this paper is to describe reduced order modelling based on dynamic flexibility approximation and applied to transient analyses. Design/methodology/approach This work is based on a recently proposed flexibility‐based component modes synthesis (CMS) approach which was shown to be very efficient for solving large eigenvalue pro...

This paper proposes a numerical algorithm of a time-discontinuous variational integrator based on the Hamiltonian in order to obtain more accurate results in the analysis of elasto-plastic stress wave. The algorithm proposed adopts both a time-discontinuous variational integrator and space-continuous Hamiltonian so as to capture discontinuities of...

A continuum-based modeling of coupled electrostatics-structure interactions is presented for the frequency computations of MEMS devices. The present general formulation of electrostatics accounting for free space is validated first by specializing it to one-dimensional uniform motion of conducting surfaces and comparing the resulting electrostatics...

An implicit partitioned transient analysis algorithm is presented for linear structural systems whose model consists of partitioned substructures. A key property of the present algorithm is the judicious application of the d'Alembert-Lagrange principal equations. The present implicit transient analysis algorithm can be reduced to solve quasi-static...

Variationally based solution algorithms for the partitioned analysis of transient and quasi-static struc-tural mechanics problems are presented. A key property of the present algorithms is the judicious appli-cation of the d'Alembert-Lagrange principal equations. The paper includes three developments: (1) an implicit transient analysis algorithm th...

A new concept is presented for modeling the dynamic interaction between an acoustic fluid and an elastic structure. The coupling of this multiphysics system is done by inserting a kinematic interface frame between the fluid and the structure, and using node-collocated Lagrange multipliers to connect the frame to each subsystem. The time-domain resp...

This paper presents a unified formulation for the combination of the finite element method (FEM) and the boundary element method (BEM) in 3D frictional contact problems that is based on the use of localized Lagrange multipliers (LLMs). Resolution methods for the contact problem between non-matching meshes have traditionally been based on a direct c...

This paper is a sequel on the topic of localized Lagrange multipliers (LLM) for applications of fluid–structure interaction (FSI) between finite-element models of an acoustic fluid and an elastic structure. The prequel paper formulated the spatial-discretization methods, the LLM interface treatment, the time-marching partitioned analysis procedures...

Identification of location of an incipient crack along a shaft in rotating machinery is critical for maintenance and repair because the crack, if allowed to grow, can cause not only malfunction but also a catastrophic disaster. In this paper, a simple method for the crack identification is suggested. To this end, we employ the modal constants of th...

A simple computer implementation of membrane wrinkle behaviour is presented within the classical elastic plane stress constitutive model. In the present method, a projection technique is utilized for modelling of the wrinkle mechanisms, in which the total strains in wrinkled membranes are decomposed into elastic and zero-strain energy parts, and a...

A design challenge in large membrane space structures is to apply pretension as uniformly as possible throughout the membrane, without increasing structural mass and volume. The present paper begins with a brief review of existing designs of membranes surrounded by catenary cables and shear compliant borders. The paper then introduces weblike cable...

A numerical structural model of a thin-film sail that simulates the deformation caused by solar-radiation pressure is developed, using a geometrically nonlinear finite element method (FEM). By using the finite element presented in this study, the force and moment exerted on an arbitrarily shaped solar sail subjected to solar pressure can be calcula...

The present study aims at improving a solar sail quadrant design concerning three objective quantities: mass, fundamental frequency, and wrinkled sail area. For the analysis, a parametric finite-element sail model is constructed, which is described by a set of seven design variables. In addition, the support boom is modeled using an analytical beam...

A flexibility-based component mode synthesis (CMS) is proposed for reduced-order modelling of dynamic behaviour of large structures. The approach employs partitioning via the localized Lagrange multiplier method. The use of the localized Lagrange multipliers leads to, unlike the classical Lagrange multipliers, a linearly independent set of interfac...