K. C. Park

Staggered transient analysis procedures for coupled mechanical systems: Formulation

Abstract Coupled-field dynamic problems in mechanics have been traditionally solved by treating the entire system as one computational entity. More recently, increasing attention has been directed to an alternative approach; partition the governing equations into subsystems, which are treated by subsystem analyzers. The selection of the subsystems may be based on weak-coupling considerations, widely different time response characteristics, isolation of nonlinear effects, or more pragmatic reasons such as the availability of analyzer software. In a staggered solution procedure the solution state of the coupled system is advanced by sequentially executing the subsystem analyzers. Subsystem coupling terms are accounted for by temporal extrapolation techniques. This paper focuses on the formulation and computer implementation of staggered solution procedures for two-field problems governed by semidiscrete second-order coupled differential equations. Such equations find application in the modeling of structure-fluid, structure-soil and structure-structure interaction. Following an introductory description of candidate problems and general solution strategies, direct time integration methods are formulated and applied to the coupled system. Staggered solution procedures are constructed through two alternative approaches which are based upon partitioning at the difference and differential equation level, respectively. Characteristic equations that govern the stability of the resulting implementations are derived, and the selection of stable extrapolators discussed. Finally, possible extensions of staggered solution procedures to coupled-field static and eigenvalue problems are suggested.

Partitioned Transient Analysis Procedures for Coupled-Field Problems: Accuracy Analysis

Abstract : A general partitioned transient analysis procedure is proposed, which is amenable to a unified stability analysis technique. The procedure embodies two existing inplicit-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-degree implicit or explicit selections of the solution vector and can be implemented within the framework of the implicit integration packages. A new element-by-element implicit-implicit procedure is also presented which satisfies program modularity requirements and enables the use of single-field implicit integration packages to solve coupled-field problems. (Author)

A Variational Framework for Solution Method Developments in Structural Mechanics

We present a variational framework for the development of partitioned solution algorithms in structural mechanics. This framework is obtained by decomposing the discrete virtual work of an assembled structure into that of partitioned substructures in terms of partitioned substructural deformations, substructural rigid-body displacements and interface forces on substructural partition boundaries. New aspects of the formulation are: the explicit use of substructural rigid-body mode amplitudes as independent variables and direct construction of rank-sufficient interface compatibility conditions. The resulting discrete variational functional is shown to be variationally complete, thus yielding a full-rank solution matrix. Four specializations of the present framework are discussed. Two of them have been successfully applied to parallel solution methods and to system identification. The potential of the two untested specializations is briefly discussed.

DIRECT TIME INTEGRATION METHODS IN NONLINEAR STRUCTURAL DYNAMICS

Abstract This paper reviews some recent developments in direct time integration methods for nonlinear structural dynamics. The developments pertain to the use of linear multistep difference operators in conjunction with the pseudo-force approach. The paper is organized into three main sections. An introductory section provides an overview of the transient response analysis problem. A section on computational aspects deals with the organization of the numerical calculations; this material is largely based on a recent detailed study of linear dynamic calculations [1–2]. A section on integration methods highlights algorithmic aspects that impact the selection of integrator for nonlinear problems and discusses adaptive analysis features such as stepsize control and implicit matrix scaling techniques. An appendix section outlines the functional organization of modular “integration driving” software.

Dynamics of flexible beams for multibody systems: a computational procedure

Abstract A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. The flexible beams are modeled using a nonlinear rod-type theory which accounts for both finite rotations and large deformations. The present formulation incorporates physical measures of conjugate Cauchy stress and covariant strain increments referenced with respect to a convected coordinate system. As a consequence, the beam model can easily be interfaced with real-time strain measurements and feedback control systems. A distinct feature of the present work is the computational preservation of total energy for undamped systems; this is obtained via an objective strain increment/stress update procedure combined with an energy-conserving time integration algorithm which contains an accurate update of angular orientations. The procedure is demonstrated via several example problems.

Are there predominant strains and toxins of Staphylococcus aureus in atopic dermatitis patients? Genotypic characterization and toxin determination of S. aureus isolated in adolescent and adult patients with atopic dermatitis

The colonization of Staphylococcus aureus is one of the most important aggravating factors of atopic dermatitis (AD). Until now, the importance of S. aureus in AD and a positive correlation between colonization with S. aureus and clinical severity/skin barrier function has been demonstrated. The aim of this study was to determine whether there are certain clones of S. aureus which colonize the skin of AD patients. For this purpose, the genotype of S. aureus isolated from AD patients was examined by newly‐developed typing methods. With 36 strains of S. aureus isolated from 35 patients with AD, spa typing, multi‐locus sequence typing (MLST), and staphylococcal toxin gene assay by multiplex polymerase chain reaction, were performed. Clinical severity and skin barrier function were evaluated with eczema area and severity index (EASI) and with transepidermal water loss (TEWL). Among 36 strains of S. aureus, 14 sequence types (ST) and 20 spa types were identified, suggesting a very heterogeneous genetic composition of S. aureus and the absence of a prevailing genotype in S. aureus colonized with AD patients. Furthermore, there was no specific genotype of S. aureus which was associated with the clinical severity of AD or skin barrier dysfunction. A toxin gene assay, however, showed the predominance of S. aureus strains carrying sea and/or tsst‐1. To the best of our knowledge, this is the first report to show the genetic composition of S. aureus strains isolated from AD patients determined by sequence‐based typing methods.

Numerically generated tangent stiffness matrices for nonlinear structural analysis

Accurate tangent stiffness matrices are essential for the solution of nonlinear structural problems via Newton-like methods. The present paper presents an accurate numerical procedure for the generation of tangent stiffness matrices from the internal force generation modules. The present procedure is attractive for problems that require complex constitutive relations and/or kinematic nonlinearities whose models are difficult to linearize and for incorporating Newton-like solution strategies into vectorial-based nonlinear structural analysis codes.

A Classification of Interface Treatments for FSI

This paper proposes a taxonomy of methods for the treatment of the fluid-structure interface in FSI coupled problems. The top-level classification is based on the presence or absence of Additional Interface Variables (AIV) as well as their type. Associated prototype methods: Direct Force Motion Transfer (DFMT), Mortar and Localized Lagrange Multipliers (LLM) are defined. These are later studied in more detail using a specific FSI benchmark problem used in Ross’ 2006 thesis. Desirable attributes of the interfacing methods are stated and commented upon.

A systematic determination of lumped and improved consistent mass matrices for vibration analysis

A systematic procedure for determining the lumped mass matrix and improved consistent mass matrices has been proposed for vibration analyses by the finite element method. The procedure is based on the discrete Fourier analysis which enables one to compare the numerical approximations with the corresponding continuum characteristics. The procedure is applied to vibrations of bar. Euler-Bernoulli beam and plate bending elements. The results obtained by the present procedure clearly indicate that a judicious use of the improved mass matrices offered in the paper can lead to a significant accuracy improvement for intermediate frequencies that can play important roles in modeling of control-structure interaction systems. dynamic localizations and acoustic responses for space structures and underwater vehicles.

Model Based Partitioned Simulation of Coupled Systems

This tutorial paper is extracted from a set of graduate lectures on the time-domain simulation of structural dynamics and coupled systems. This material has also served as a basis for a CISM lecture series on FSI. For the treatment of coupled systems, emphasis is placed on partitioned analysis procedures. Although the subject emerged in the present form over 20 years ago, the time-consuming study of competing formulations and implementations can be streamlined through the use of various tools such as reduction to model equations, and the help of computer algebra systems.