Abstract : Despite numerous well-established algebraic techniques, infusion of the variational approach into computational mechanics is still under way. Among those, the partitioning method has played a pivotal role. It introduced a complicated matrix computation and additional unknowns which should be treated without degrading accuracy. Topics of this mini-symposium will include, but not limited to, the advances in partitioning method and their application; parallel computing, component mode synthesis, non-matching interface, inverse problems, and damage detection. The mini-symposium will bring researchers together working on both fundamental and applied aspects of computational mechanics to provide a forum for discussion, interaction, and assessment of techniques.
[03920] Displacement-only Partitioned Equations for Structures without Lagrange Multipliers
Format : Talk at Waseda University
Author(s) :
K. C. Park (University of Colorado)
Abstract : A new formulation for the Displacement-only Partitioned (DP) equations of motion for linear structures is presented,
which employs: the partitioned displacement and applied force (u, f), the partitioned block diagonal mass and stiffness matrices (M, K); and, the coupling projector (P), yielding the partitioned coupled equations of motion:
M ü =P( f – K u)
The proposed DP formulation contains no Lagrange multipliers and offers wide practical applications as well as
intellectual pleasure.
[04749] Displacement-based dynamic analysis of partitioned structural systems
Format : Online Talk on Zoom
Author(s) :
José Ángel González Pérez (Universidad de Sevilla)
K. C. Park (University of Colorado)
Abstract : An unconditionally stable implicit-explicit time integration algorithm is presented, which employs the displacement-only partitioned formulation for structures. The displacement-only partitioned equations of motion for linear and nonlinear structures are expressed in terms of the partitioned displacements, partitioned velocities, and partitioned accelerations, and are devoid of interface Lagrange multipliers and associated variables. Numerical examples illustrate both unconditional stability of the proposed algorithm, second-order accuracy, as well as computational simplicity and efficiency.
[04659] Partitioned Damage Identification of Structural Systems
Format : Talk at Waseda University
Author(s) :
Hyeon-Jun Kim (KAIST)
Yong-Hwa Park (KAIST)
K. C. Park (University of Colorado)
Abstract : This study proposes a damage identification procedure by employing a recently developed displacement-only partitioned equations of motion for structures. Damage is identified by detecting changes in partitioned or elemental stiffness. Applications of the proposed damage identification procedure to sample problems show that the proposed procedure captures damage locations through numerical examples.
[03098] Development of partitioning method for thermoelastic Interaction Problems with energy flux constraint
Format : Online Talk on Zoom
Author(s) :
Chang-uk Ahn (Kyung Hee University)
Alexandre Cortiella (University of Colorado)
Jin-gyun Kim (Kyung Hee University)
Kwang-chun park (Korea Advanced Institute of Science and Technology)
Abstract : This study presents a partitioned symmetric formulation for transient thermoelastic interaction problems. The thermoelastic interaction problem is a multiphysics problem in which the wave (i.e., hyperbolic type) equation and the diffusion (i.e., parabolic type) equation are coupled. The classical formulation of thermoelastic problems is non-symmetric, and its partitioned form has only been developed in ways that the domains are decoupled in the discrete domain. Based on this motivation, we propose a constraint of energy flux that allows partitioning the thermoelastic problem in a continuum domain. To do this, we construct two separate variational formulations of the uncoupled thermal conduction and uncoupled structural systems. In other words, two separate variational formulations of the uncoupled thermal conduction and uncoupled structural systems are augmented by the constraint of energy exchanges between the elastic body and the thermal conduction body via the method of Lagrange multipliers.
Finally, this study introduces a solution algorithm including implicit-implicit time integration strategies, and the present partitioned formula is verified by well-organized numerical examples.
[04222] A Componenet Mode Synthesis Method Using a Displacement-Based Partitioned Approach
Format : Online Talk on Zoom
Author(s) :
Muhammad Faizan Baqir (Kyung Hee University )
K. C. Park (University of Colorado)
Jin Gyun Kim (Kyung Hee University)
Abstract : A new Partitioned component mode synthesis (P-CMS) is presented, which employs a recently developed Displacement-based Partitioned (DP) formalism. The reduced system matrices are generated via block-by-block substructural matrix computations, directly yielding reduced-order models. The proposed P-CMS method can provide a robust mode selection criterion that remains a challenge in most existing CMS methods. Details of the proposed P-CMS procedure along with numerical examples will be presented in this talk.
[03460] Iterative Algorithm for Quasistatic Structural Problems Employing Only Partitioned Displacements
Format : Talk at Waseda University
Author(s) :
SANGJOON SHIN (Seoul National University)
Seung-Hoon Kang (Seoul National University)
Kwang-Chun Park (University of Colorado Boulder)
Abstract : We report some initial results from the ongoing research on partitioned parallel solution of quasistatic structural problems that employ only partitioned displacements. A notable feature of the present method is the absence of Lagrange multipliers that inevitably manifest in standard partitioned formalisms. Various preconditioning and regularizations that take advantages of the present Displacement-only Partitioned (DP) formulation will be presented and compared with FETI and its allied solution methods.
