Local modal reduction in explicit dynamics with domain decomposition. Part 2: specific interface treatment when modal subdomains are involved

SUMMARYFor a few decades, various approximate techniques have been developed to calculate the eigenvalues in a reduced manner. In order to construct reliable reduced systems it is essential to select the proper primary degrees of freedom (PDOFs). Unless the PDOFs are selected properly, the selection of PDOFs might be localized and the eigenvalue prediction might emphasize excessively the lower modes or lose the important modes. Moreover, sometimes, it takes considerable amount of computing time to construct a reduced system in large-scale problem. These troubles in constructing reduced system can be avoided by applying reduction scheme in sub-domain level. After dividing global system into a number of subdomains, reduced system which has only the PDOFs is constructed in each sub-domain. This paper presents new algorithms to construct efficient reduction system through three different schemes. They are version 1, version 2 and version 3 systems. The version 3 system is constructed by combining the advantages of the version 1 and the version 2 systems. Numerical examples demonstrate that the proposed version 3 method saves computational cost effectively and provides a reduced system which can predict accurate eigenvalues of global system.

show abstract

“…where we can set From Equation (40), the relation of SDOFs and PDOFs is arranged as shown in Equation (41).…”

Section: Formulation Of the Versionmentioning

confidence: 99%

Improvement of reduction method combined with sub‐domain scheme in large‐scale problem

Kim

Cho

2006

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Anyhow, as pointed out in [46], associating the singular values to the actual elastic and kinetic energies of the system is "incorrect in principle and may yield misleading results." So, to ensure the stability and invertibility of the interface operator (16), see also [47], in the snapshot matrix nodal displacements are gathered, and a weak continuity across subdomains is enforced through the local stiffness k, see Eq. (15).…”

Section: Reduced-order Modelling Approachmentioning

confidence: 99%

Coupled domain decomposition–proper orthogonal decomposition methods for the simulation of quasi-brittle fracture processes

Corigliano

Confalonieri

Dossi

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

View full text Add to dashboard Cite

In this paper, we discuss a strategy to reduce the computational costs of the simulation of dynamic fracture processes in quasi-brittle materials, based on a combination of domain decomposition (DD) and model order reduction (MOR) techniques. Fracture processes are simulated by means of three-dimensional finite element models in which use is made of cohesive elements, introduced on-the-fly wherever a cracking criterion is attained. The body is initially subdivided into sub-domains; for each sub-domain MOR is obtained through a proper orthogonal decomposition (POD) of the equations governing its evolution, until when it starts getting cracked. After crack inception within a sub-domain, the solution is switched back to the original full-order model for that sub-domain only. The computational gain attained through the coupled use of DD and POD thus depends on the geometry of the body, on the topology of sub-domains and, on top of all, on the spreading of cracking induced by load conditions. Numerical examples concerning well-established fracture tests are used for validation, and the attainable reduction of the computing time is discussed at varying decomposition into sub-domains, even in the absence of a full exploitation of parallel computing potentialities.

show abstract

“…Many engineering applications of this method are available for transient nonlinear dynamics, FSI, non‐matching interfaces, co‐computations, simulation of automobile crashes, hybrid experimental/numerical real‐time testing, earthquake loading, impact on concrete structures, microsystems, coupled electro‐mechanical problems, and fracture in polysilicon micro electro‐mechanical systems, with two or more subdomains with their own integrator and timescale , , (see for instance for an example with nine subdomains, nine different time integrators, and a maximum ratio of time steps close to 1000).…”

Section: Heterogeneous Asynchronous Time Integratorsmentioning

confidence: 99%

Heterogeneous asynchronous time integrators for computational structural dynamics

Gravouil

Combescure

Brun

2014

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYComputational structural dynamics plays an essential role in the simulation of linear and nonlinear systems. Indeed, the characteristics of the time integration procedure have a critical impact on the feasibility of the calculation. In order to go beyond the classical approach (a unique time integrator and a unique timescale), the pioneer approach of Belytschko and co-workers consisted in developing mixed implicit-explicit time integrators for structural dynamics. In a first step, the implementation and stability analyses of partitioned integrators with one time step have been achieved for a large class of time integrators. In a second step, the implementation and stability analyses of partitioned integrators with different time steps were studied in detail for particular cases. However, stability results involving different time steps and different time integrators in different parts of the mesh is still an open question in the general case for structural dynamics. The aim of this paper is to propose a state-of-the art of heterogeneous (different time schemes) asynchronous (different time steps) time integrators (HATI) for computational structural dynamics. Finally, an alternative approach based on energy considerations (with velocity continuity at the interface) is proposed in order to develop a general class of HATI for structural dynamics.

show abstract

Local modal reduction in explicit dynamics with domain decomposition. Part 2: specific interface treatment when modal subdomains are involved

Cited by 8 publications

References 7 publications

Improvement of reduction method combined with sub‐domain scheme in large‐scale problem

Improvement of reduction method combined with sub‐domain scheme in large‐scale problem

Coupled domain decomposition–proper orthogonal decomposition methods for the simulation of quasi-brittle fracture processes

Heterogeneous asynchronous time integrators for computational structural dynamics

Contact Info

Product

Resources

About