equivalent shell rom

For immersed isogeometric analysis (IGA) of plate and shell problems in explicit dynamics, two key challenges arise: excessively small critical time steps—caused by high-order PDEs, structural slenderness, and ill-conditioned cut elements—and spurious oscillations induced by lumped mass matrices. This paper proposes a polynomial-expansion-based stabilization technique compatible with lumped mass matrices. The method simultaneously increases the critical time step by orders of magnitude and restores boundary-fitted discretization accuracy on physical boundaries. To the best of our knowledge, it is the first approach enabling stable, explicit immersed IGA for plate and shell structures. Numerical experiments demonstrate that the proposed method effectively suppresses spurious high-frequency modes, achieves dynamic response accuracy comparable to conventional boundary-fitted IGA, and significantly enhances the efficiency and robustness of explicit simulations for complex plate and shell geometries.

该研究通过使用POD和ECSW方法在组件级别上生成超简化非线性固体力学模型，解决了复杂装配体高效模拟问题。

This work addresses the challenge of efficiently and accurately estimating quantities of interest (QoI) in multi-query linear problems, where conventional approaches suffer from high computational costs and strong dependence on load configurations. The authors propose a novel reduced-order modeling paradigm based on the adjoint problem, shifting the focus of model reduction from the primal to the adjoint equation for the first time. By introducing a parameterized kernel function to replace the full external load, the method constructs a load-independent surrogate model. Demonstrated on Poisson’s equation and plane-stress elasticity problems, the approach achieves rapid convergence and significantly outperforms traditional primal-based reduction strategies. It enables high-fidelity QoI estimation while supporting fast multi-scenario evaluation and virtual chart generation, thereby greatly enhancing the generality and efficiency of early-stage design optimization.

Existing reduced-order models (ROMs) for solid mechanics face a trade-off between accuracy and usability: intrusive methods require expert knowledge and are computationally expensive, while non-intrusive approaches suffer from insufficient accuracy for nonlinear or non-affine problems. Method: This paper proposes a lightweight intrusive ML-POD co-modeling framework that leverages only black-box outputs from commercial finite element solvers. It employs machine learning to accurately surrogate non-affine terms—particularly the stiffness matrix—enabling ROM construction without expert intervention, extensive snapshot collections, or formal design-of-experiments (DoE). Contribution/Results: For the first time, the stiffness-matrix-driven mechanism is integrated into POD-ML joint modeling, preserving non-intrusive usability while substantially improving nonlinear ROM accuracy. Numerical experiments across multiple benchmark cases demonstrate 40–65% error reduction over conventional non-intrusive methods, confirming superior accuracy, generalizability, and engineering practicality.

Finite-element models of aircraft flexible wings often exhibit discrepancies with experimental measurements due to modeling inaccuracies and parameter uncertainties. Method: This paper proposes an *assembled model updating paradigm*, wherein submodels corresponding to physical components are updated incrementally during hierarchical structural assembly—replacing conventional global, one-shot updating. We introduce a novel framework integrating experimental data-driven calibration, modular substructure modeling, and surrogate-model acceleration. Contribution/Results: The approach preserves high modeling fidelity while significantly improving computational efficiency: experiments demonstrate a 20% reduction in iteration count versus global methods, fewer parameters to estimate, faster convergence, and comparable accuracy. Crucially, the method maintains physical interpretability through component-level updates and offers scalability for high-fidelity modeling of complex aerospace structures.

本文采用物理信息神经网络方法预测薄壁截锥壳的屈曲载荷，并结合基于可靠性的设计，以解决传统设计中对几何形状、制造质量及数据不确定性考虑不足的问题。

This work addresses the high computational cost of traditional finite element analysis and the limited generalizability of existing machine learning surrogates to varying geometries and loading conditions. The authors propose a Mesh Graph Network (MGN) that efficiently predicts von Mises stress fields for arbitrary two-dimensional structures with holes by encoding node types, relative edge features, and global load information. The model inherently satisfies translational and rotational invariance and generalizes to unseen combinations of geometry and loading without retraining. On test cases, it achieves an R² as high as 0.97, substantially outperforming current machine learning approaches, which report R² values ranging from approximately 0.01 to 0.86, thereby demonstrating superior generalization capability and strong potential for practical engineering applications.

Traditional simulation of deformable objects relies on mesh-based representations or neural fields requiring per-shape optimization, struggling to balance geometric complexity and computational efficiency. This work proposes a mesh-free reduced-order simulation method that, for the first time, integrates Reproducing Kernel Particle Method (RKPM) with reduced-order elastic dynamics. By employing RKPM to construct a continuous elastic body model and solving the generalized eigenvalue problem of the elastic energy Hessian matrix, the method automatically computes skinning weights without mesh generation or per-shape optimization. The approach achieves a 40× speedup in training compared to neural field–based methods, yields simulation errors lower than those of converged finite element solutions, and demonstrates successful application across diverse geometric representations and robotic simulation tasks.

This work addresses the instability and low integration efficiency of the virtual element method in large-deformation nonlinear problems by proposing a stabilized approach that combines scaled boundary parameterization with reduced integration. By performing a Taylor expansion of constitutive quantities about the cross-sectional centroid, the weak form is analytically integrated, requiring only a single integration point per cross-section. This strategy drastically reduces the number of integration points while effectively handling hyperelastic anisotropic and elastoplastic large-deformation scenarios. Numerical experiments demonstrate that the method accurately captures structural responses and inelastic behavior across various materials and loading conditions, exhibiting particularly superior performance when physical elements closely resemble their reference configurations.

This work addresses the inability of traditional linear shell models to accurately capture stiffness variations under large deformations, which often leads to distorted shape optimization results. For the first time, a fully geometrically nonlinear Naghdi shell formulation is implemented directly on discrete triangular meshes for shape optimization, eliminating the need for mid-surface parametrization and circumventing limitations inherent in isogeometric analysis. The approach integrates a five-parameter nonlinear shell model—stabilized via selectively reduced integration—with automated residual and tangent operator generation in Firedrake, adjoint-based sensitivity analysis enabled by automatic differentiation, and the Fireshape/ROL trust-region optimizer. The framework successfully reproduces benchmark cases from Sze and Abaqus, accurately capturing stiffness stiffening effects, and achieves an 87% reduction in elastic strain energy for a sheet-metal bracket and a 78% decrease in average deflection for a hemicylindrical shell.