Jaehun Lee

In this paper, we propose a two-step sequential hyper-reduction method to significantly enhance computational efficiency for both macro- and micro-level analyses in concurrent nonlinear FE² multiscale simulations. In general, one of the major computational burdens of nonlinear FE² problems is the repetitive micro-level analysis, which must be performed at all integration points of the macroscopic structure. We propose adopting the discrete empirical interpolation method (DEIM) for both macroscopic and microscopic problems, achieving a significant reduction in the number of integration points in both models. The proposed two-step sequential framework aligns with reduced-order modeling, enabling an efficient multiscale procedure for concurrent nonlinear FE² analysis in the online stage. We verified the accuracy and efficiency of FE² analysis using the proposed method through a simple example.

This paper proposes a simple yet accurate finite element (FE) formulation for the thermomechanical analysis of laminated composites and sandwich plates. To this end, an enhanced first-order shear deformation theory including the transverse normal effect based on the mixed variational theorem (EFSDTM_TN) was employed in the FE implementation. The primary objective of the FE formulation was to systematically interconnect the displacement and transverse stress fields using the mixed variational theorem (MVT). In the MVT, the transverse stress field is derived from the efficient higher-order plate theory including the transverse normal effect (EHOPT_TN), to enhance the solution accuracy, whereas the displacement field is defined by the first-order shear deformation theory including the transverse normal effect (FSDT_TN), to amplify the numerical efficiency. Furthermore, the transverse displacement field is modified by incorporating the components of the external temperature loading, enabling the consideration of the transverse normal strain effect without introducing additional unknown variables. Based on the predefined relationships, the proposed FE formulation can extract the C0-based computational benefits of FSDT_TN, while improving the solution accuracy for thermomechanical analysis. The numerical performance of the proposed FE formulation was demonstrated by comparing the obtained solutions with those available in the literature, including 3-D exact solutions.

This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been suggested to obtain a satisfactory size for the reduced systems. Although previous hybrid-level interface-reduction approaches have addressed major issues associated with conventional interface-reduction methods—in terms of accuracy and efficiency through considering partial substructure synthesis—this method can be applied to limited modeling conditions where interfaces and substructures are independently defined. To overcome this limitation, an interface localizing algorithm is developed to ensure an enhanced performance in the conventional hybrid-level interface-reduction method. The interfaces are discriminated through considering the Boolean operation of substructures, and the interface reduction basis is computed at the localized interface level, which is constructed by a partially coupled system. As a result, a large amount of computational resources are saved, achieving the possibility of efficient design modifications at the semi-substructural level.