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The conventional representative volume element approach may not be accurate enough in examining stress distribution near singularity in a composite. However, enormous number of degrees of freedom (DOFs) is usually required to discretize the subcomponents within the composite structure; hence, it may not be handled in a single CPU. In this study, the finite element tearing and interconnecting algorithm, a domain decomposition method, is proposed to address the challenges posed by such enormous number of DOFs via parallel computation. Owing to the message passing interface, analyses in this study will be conducted on the parallel computing environment. Furthermore, the METIS algorithm is adopted to automatically divide the solid domain into certain number of subdomains. Consequently, the fiber-reinforced polymer which possesses either a crack or notch discretized by over 10 million DOFs will be readily analyzed. The computational time is reduced significantly compared against the original one. Also, the stress and stiffness predictions show good agreement with those by the other existing analyses or experiments. Therefore, this study is expected to be fast and accurate in analyzing composite structures with enormous number of DOFs.

This paper presents an all-direct domain decomposition approach for large-scale structural analysis. The proposed approach achieves computational robustness and efficiency by enforcing the compatibility of the displacement field across the subdomain boundaries via local Lagrange multipliers and augmented Lagrangian formulation (ALF). The proposed domain decomposition approach was compared to the existing FETI approach in terms of the computational time and memory usage. The parallel implementation of the proposed algorithm was described in detail. Finally, a preliminary validation was attempted for the proposed approach, and the numerical results of two- and three-dimensional problems were compared to those obtained through a dual-primal FETI approach. The results indicate an improvement in the performance as a result of the implementing the proposed approach.

This paper presents development of an improved domain decomposition method for large scale structural problem that aims to provide high computational efficiency. In the previous researches, we developed the domain decomposition algorithm based on augmented Lagrangian formulation and proved numerical efficiency under both serial and parallel computing environment. In this paper, new computational analysis by the proposed domain decomposition method is performed. For this purpose, reduction in computational time achieved by the proposed algorithm is compared with that obtained by the dual-primal FETI method under serial computing condition. It is found that the proposed methods significantly accelerate the computational speed for a linear structural problem.

Finite element based formulations for flexible multibody systems are becoming increasingly popular and as the complexity of the configurations to be treated increases, so does the computational cost. It seems natural to investigate the applicability of parallel processing to this type of problems; domain decomposition techniques have been used extensively for this purpose. In this approach, the computational domain is divided into non-overlapping sub-domains, and the continuity of the displacement field across sub-domain boundaries is enforced via the Lagrange multiplier technique. In the finite element literature, this approach is presented as a mathematical algorithm that enables parallel processing. In this paper, the divided system is viewed as a flexible multibody system, and the sub-domains are connected by kinematic constraints. Consequently, all the techniques applicable to the enforcement of constraints in multibody systems become applicable to the present problem. In particular, it is shown that a combination of the localized Lagrange multiplier technique with the augmented Lagrange formulation leads to interesting solution strategies. The proposed algorithm is compared with the well-known FETI approach with regards to convergence and efficiency characteristics. The present algorithm is relatively simple and leads to improved convergence and efficiency characteristics. Finally, implementation on a parallel computer was conducted for the proposed approach.

This paper presents an improved structural analysis for a bearingless helicopter rotor. The bearingless rotor usually features a significantly large elastic twist in the flexbeam and additional unique structural characteristics. Thus, it will require sophisticated structural analysis and relevant numerical validation procedures due to its multiple load paths, as induced by the single or multiple flexbeams and the torque tube. In this paper, an extended finite element formulation was derived to consider the multiple components as individual beam elements. A geometrically exact beam formulation was adopted to describe the nonlinear behavior of these major components in the rotor precisely. To implement the interconnecting kinematic relationship with the major components, Lagrange multipliers were used. The present static analysis was validated through comparisons with the existing multi-body dynamics analysis DYMORE. Additional results were obtained for rotating conditions in both a vacuum and a set atmosph...

This paper describes application of an improved computational approach based on domain decomposition technique for a large scale structural analysis. We compared computational algorithms corresponding to the original and an improved FETI approach. In the original FETI approach, Lagrange’s multipliers were introduced to enforce compatibility at the interface DOF’s. Specifically, we adopted local Lagrange’s multipliers with an augmented Lagrangian formulation (ALF) as penalty formulation of the problem to improve computational robustness and efficiency. For validation of the present approach, we compared its results with those obtained by the original FETI. Practical performances of the present approach were demonstrated through several 2-D plane and 3-D shell static analysis results.