In this paper, we present an automatic procedure that enhances the solution accuracy of edge-based smoothed 2D solid finite elements (three-node triangular and four-node quadrilateral elements). To obtain an enhanced solution, an adaptive enrichment scheme that uses enriched 2D solid finite elements and can effectively improve solution accuracy by applying cover functions adaptively without mesh-refinement is adopted in this procedure. First, the error of the edge-based finite element solution is estimated using a devised error estimation method, and appropriate cover functions are assigned for each node. While the edge-based smoothed finite elements provide piecewise constant strain fields, the proposed enrichment scheme uses the enriched finite elements to obtain a higher order strain field within the finite elements. Through various numerical examples, we demonstrate the accuracy improvement and efficiency achieved.

The increasing demand for dynamic analysis of large-scale structural systems has highlighted the need for efficient model reduction methods. Reduced order modeling allows large finite element models to be represented with significantly fewer degrees of freedom while retaining essential dynamic characteristics. This paper investigates the Enhanced Craig–Bampton (ECB) method and further explores its application in dynamic analysis. The effectiveness of the ECB method is evaluated by comparing it with the conventional Craig–Bampton (CB) method and the full finite element model using benchmark examples. The numerical results demonstrate that the ECB method provides superior accuracy and computational efficiency, making it a valuable tool for dynamic analysis in complex engineering problems.

This paper presents a novel and efficient solution procedure to improve 3D solid finite element analysis with an enrichment scheme. To this end, we employ finite elements enriched by polynomial cover functions, which can expand their solution space without requiring mesh refinement or additional nodes. To facilitate this solution procedure, an error estimation method and cover function selection scheme for 3D solid finite element analysis are developed. This enables the identification of nodes with suboptimal solution accuracy, allowing for the adaptive application of cover functions in a systematic and efficient manner. Furthermore, a significant advantage of this procedure is its consistency, achieved by excluding arbitrary coefficients from the formulations employed. The effectiveness of the proposed procedure is demonstrated through several numerical examples. In the majority of the examples, it is observed that the stress prediction error is reduced by more than half after applying the proposed procedure.

This study evaluated excessive-acceleration vulnerability based on the Level 1 and Level 2 criteria of the IMO second-generation intact stability framework. A 13K oil chemical tanker was analyzed, incorporating wave-induced dynamic effects into the assessment. The comparison between Level 1 and Level 2 results showed that the Level 2 criterion provided a less conservative evaluation, allowing a wider acceptable range of vertical positions relative to the roll axis. This highlights the necessity of dynamic analysis under realistic wave conditions. To improve the accuracy of the evaluation, the Froude–Krylov roll moment was reformulated by incorporating diffraction effects. Unlike conventional approaches that consider only incident-wave excitation, the proposed method accounts for both incident- and diffracted-wave components. This results in a smoother frequency-dependent effective wave slope function and a more consistent representation of hydrodynamic excitation. The results demonstrate that including diffraction effects extends the allowable range satisfying the Level 2 criterion, thereby increasing the design margin associated with the vertical center of gravity. Although the proposed approach requires additional computational effort, it provides a basis for examining the influence of diffraction on excessive-acceleration assessment.