Thin-walled cylindrical shells in launch-vehicle structures are sensitive to geometric imperfections, making reliable lower-bound knockdown factor (KDF) prediction a requirement in preliminary design. Existing numerical approaches, including perturbation-based analyses and direct imperfection modeling, are applied on a case-by-case basis and require computational effort for each new geometry or tolerance level, which limits their efficiency in early-stage design. In parallel, widely used empirical KDF curves derived from historical databases, such as NASA SP-8007, were established under manufacturing and testing conditions that differ from those of aerospace structures, motivating complementary investigations. To address these challenges, this study develops a framework for predicting the lower-bound KDF of axially compressed cylindrical shells. The framework combines perturbation-driven sampling of imperfection-sensitive buckling responses using the Worst Multiple Perturbation Load Approach with surrogate-assisted finite element evaluations, followed by the construction of explicit KDF envelope relations through multi-gene genetic programming. This process enables generation of tolerance-aware datasets and their transformation into compact analytical expressions describing KDF variations across wide ranges of radius-to-thickness ratios, length-to-radius ratios, and imperfection amplitudes. Comparisons with benchmark experiments indicate that the proposed framework captures conservative lower-bound trends while maintaining consistency with test observations, providing a scalable and cost-effective tool for preliminary shell design.

The gradient optimizer plays a crucial role in topology optimization for updating design variables. However, the existing optimizers have deficiencies in terms of efficiency and effectiveness. To address this, a novel optimizer called explicit stable interval iteration optimizer (ESIIO) is proposed, in which a new constraint interval transformation method is established to construct the density constraint. Subsequently, the interval iterative formulation is strictly elucidated based on the Karush-Kuhn-Tucker optimality conditions. The directional stability transformation method is used to promote the convergence, in which a new adaptive boundary-crossing update strategy is proposed to evaluate the chaos control factor. The effectiveness of ESIIO is verified by five different types of mechanical problems, i.e. compliance, stress, heat conduction, fluid-thermal coupling, and multi-frequency problems. It is found that ESIIO is effective and its efficiency is significantly higher than that of traditional methods. Moreover, a 33-line MATLAB code and relevant explanations of ESIIO are provided in Appendix B. The source code of ESIIO is publicly available at: https://github.com/TOESIIO/Explicit-Stable-Interval-Iteration-Optimizer.

In practical engineering reliability analysis, it is common to encounter both probability and non-probability uncertain parameters (UPs) coexisting within the same system. However, the traditional double-loop hybrid reliability analysis method incurs high computational costs, especially for high-reliability problems. In this paper, a single-loop hybrid reliability analysis method for rare events based on a novel hybrid reliability model with uniform distribution (SHRA-UD) is proposed with the following key innovations. (i) The traditional method for calculating failure probability involves integrating a nonlinear probability density function over a complex, unknown failure domain. This calculation is not only difficult to perform but also has poor engineering applicability. To address this problem, the Box–Muller transformation is employed. Thus, the probability parameters are accurately characterized by two uniform distribution parameters, and the solution of the failure probability is transformed into the ratio of the failure domain to the feasible domain. (ii) A hybrid reliability analysis framework is established based on the intelligent directional search with constraint feedback (IDS). The reliability index related only to probability parameters is set as the optimization objective, and the limit state function (LSF) related to both probability and non-probability parameters is used as the constraint. The solution of non-probability parameters is carried out in the form of constraint feedback to obtain the combination of non-probability and probability parameters that maximizes the failure probability. (iii) In order to improve computational efficiency and handle irregular failure domains more effectively, the improved null-hypothesis approximation (iNHA) method is proposed by introducing an adaptive step size mechanism and replacing the original failure domain cutting method with the Delaunay triangulation (DT). Finally, the effectiveness of the proposed method is validated through three numerical examples and two engineering case studies.

The mechanical properties of polycrystalline materials are determined not only by the geometric shape and crystal orientation of individual grains but also by other grains within the neighborhood. Here, we propose a graph convolutional neural network model for rapidly predicting the thermomechanical coupling response of polycrystalline materials. We adopt the Voronoi method for grain geometry modeling. By taking the degradation of the elastic modulus of the nickel-based superalloy GH4169 under unidirectional axial pressure in different temperature fields and orientation angles, we verify that the GCN model effectively learned the node characteristics and propagation laws of heterogeneous graphs. The prediction results show a strong linear fitting relationship, the root mean square errors are all less than 5%. In addition, the gradient integration method was employed to quantify the contribution of each feature parameter to the model’s prediction, the effects of different hyperparameters on the performance of the GCN model and the future application prospects of the framework are also discussed.

Uncertainties in material properties and geometric dimensions are inherent in the fabrication of stiffened panels, which significantly influence the structural mechanical performance and reliability. To ensure structural safety, these factors need to be incorporated into the structural stochastic analysis. Therefore, this study proposes a perturbation stochastic isogeometric analysis (PSIGA) method based on a nested geometric model to predict the stochastic responses of stiffened panels under these uncertainties. The nested geometric model is adopted to ensure model accuracy and watertightness, securing numerical analysis precision. On this basis, a random field modeling method for stiffeners under the nested geometric model is developed. Uncertainties of skin and stiffeners are represented as random fields via the Karhunen-Loe`ve (K-L) expansion, which are then assembled into the stochastic static and buckling equations and incorporated into the stochastic isogeometric analysis framework. A first-order perturbation method is employed to solve these stochastic equations and derive the statistical characteristics of stiffened panel responses. Moreover, a sensitivity analysis is conducted to quantify the relative influences of individual uncertainties on the structural behavior. Five numerical examples validate the proposed method by comparing the predicted random displacement, buckling responses, and the computational efficiency with Monte Carlo simulation (MCS) results. The outcomes demonstrate that the proposed PSIGA method efficiently and accurately captures the stochastic behavior of stiffened panels, providing a robust tool for engineering structural safety evaluations.

Stiffened thin-walled structures are widely used as load-bearing components in engineering due to their excellent mechanical properties. When modeling complex stiffened shells, traditional spline models face issues with piecewise splicing and difficulties in ensuring watertightness. While subdivision modeling provides an effective solution, in dealing with non-manifold stiffened surface structures, it both requires highly detailed meshes and is prone to mesh distortion. To address these challenges, this paper proposes a novel modeling method for stiffened arbitrary surfaces using the subdivision-based nested model (SNM) and extends subdivision-based isogeometric analysis (IGA) to this model. In terms of model representation, the SNM proposed based on the nested idea adopts Catmull-Clark subdivision surfaces to describe the skins and spline control curves explicitly defined on the control meshes to represent stiffeners. Additionally, through its implicit mapping, SNM enables intuitive modeling and precise description of complex stiffened surfaces. In particular, to satisfy the continuity requirements, a geometric continuity correction algorithm is proposed to ensure G1 continuity of stiffener curves on complex surfaces. In terms of numerical analysis, built on the IGA framework, a degenerate shell element formulation based on the Catmull-Clark subdivision is implemented. To achieve automatic strong coupling analysis, a degenerate stiffener element suitable for SNM is implemented, which integrates modeling and analysis while reducing the degrees of freedom (DOFs). Three common linear analysis formats for stiffened thin-walled structures, including static, buckling, and free vibration, are established. The effectiveness and robustness of the proposed method are fully verified by two benchmarks and three engineering examples.

Stiffener layout is critical to the structural efficiency of lightweight stiffened thin-walled shells. Principal stress trajectory (PST)-guided approaches provide a rapid, mechanics-informed initialization by aligning stiffeners with load-transfer paths. While NURBS-based isogeometric analysis (IGA) preserves exact CAD geometry and supports skin-conforming stiffener modeling via parametric-domain mappings, extending this workflow to geometrically and topologically complex shells remains challenging. In particular, trimmed and multi-patch representations fragment the parametric domain, making it difficult to maintain inter-patch consistent stress and principal stress direction (PSD) fields and to trace PSTs reliably across patch boundaries, which impedes globally coherent layouts. To address this limitation, this paper extends PST-guided stiffener design to Catmull-Clark subdivision shells and develops a patch-independent subdivision parameterization (PISP) by integrating computational conformal mapping with control-mesh connectivity. PISP maps the control mesh onto a single connected planar domain and establishes an explicit piecewise mapping between global PISP coordinates and sub-patch parameter domains, thereby linking independent local domains through control-mesh adjacency and forming a globally connected 2D working domain. This enables interface-consistent transport of stresses and derived PSDs from the physical shell to PISP and allows uninterrupted PST tracing over complex shells. Dense PSTs are traced on PISP and hierarchically clustered to extract representative force flow members (FFMs) as initial stiffeners. For further lightweighting, low-dimensional stiffener-height optimization with Shepard-type smoothing is performed. Four representative examples demonstrate CAD/CAE-consistent stiffener layouts on complex shell geometries. Comparisons with equal-volume reference layouts and ABAQUS/TOSCA benchmarks demonstrate the effectiveness of the proposed framework and show consistent load-path and stiffness-improvement trends.

This study elucidates a multi-applicability mechanism of elastomer-toughened brittle thermoplastics polymers through experimental methods and multiscale analysis. Polyolefin elastomer (POE) and glycidyl methacrylatemodified POE (POE-GMA) were used to toughen thermoplastic polymers polyphenylene sulfide (PPS) and polybutylene terephthalate (PBT). It was found that small amounts of POE-GMA could enhance the fracture energy of PBT and PPS by 167 % and 415 %, while only sacrificing 5.3 %-11.6 % of strength or rigidity, and the lower the inherent toughness of the polymer, the better the toughening effect, whereas POE showed no significant effect. Molecular dynamics simulations indicate that the GMA groups enhance interactions between POE-GMA and polymers, promoting POE-GMA diffusion into the polymer matrix and improving dispersion. Further finite element modeling indicates that smaller and more dispersed elastomer particles can induce more microcracks, enhancing energy absorption and consequently increasing the fracture energy, thereby improving toughness. This multi-applicability mechanism provides crucial insights for designing polymer composites that balance toughness and rigidity.

This study focuses on the effects of impact energy combinations and layup configurations on the residual compressive performance and failure evolution mechanisms of carbon fiber reinforced composite laminates under multiple impacts. The compressive after impact properties were examined under four distinct impact energy levels. Laminates with layup configurations of [02/902]4s, [0/90] 4s, and [02/902]2s were designed to investigate the influences of ply orientation, ply thickness and ply clustering effects. Delamination after impact and after compression failure was characterized using C-scan techniques. The results indicate that under multiple impacts, higher energy impacts occurring later in the sequence lead to greater total energy absorption and larger delamination areas, resulting in lower residual compressive strength. The uniform distribution of impact energy resulted in the highest residual compressive performance. Quasi-isotropic laminates exhibited superior residual compressive strength after repeated impacts compared to cross-ply laminates. The use of thinner plies and an increased number of interleaved ply arrangements can enhance the residual compressive performance of composites subjected to repeated impacts. This study provides insights into the effect of impact energy sequencing on damage progression and reveals its implications for the residual compressive behavior of composite laminates.

Composite structures in service are susceptible to repeated low-velocity impacts, where the distribution of impact energy critically influences damage evolution. This study systematically investigates how different Impact Energy Distribution (IED) modes-under a constant total energy of 30 J-govern the failure response of carbon/epoxy laminates. Three IED scenarios were examined: 10 J x 3, 15 J x 2, and 30 J x 1. Experimental results reveal that for the same total energy, an increased number of impacts elevates peak force and maximum displacement but reduces total absorbed energy. A high-fidelity finite element model, incorporating the Puck failure criterion, was developed and validated, demonstrating excellent agreement with experiments. Crucially, the study unveils three fundamental ways in which IED mode dictates damage behavior: first, it activates certain failure mechanisms only at higher single-impact energy levels; second, it controls the propagation extent of specific damage types, such as fiber and matrix cracking, as well as delamination area; third, it alters the very morphology of damage, as evidenced by the transition of impact-surface fiber compression failure from an elongated linear band in IED10/ IED15 to a peanut-shaped distribution in IED30. These findings provide novel, mechanistic insights into cumulative damage, essential for designing composite structures against repeated impacts.

Interfacial delamination is a common failure mode in fiber fabric/flexible polymer composites. Using aramid fiber fabric/thermoplastic polyurethane composites as a representative system, this study develops a multiscale model to predict interface peel strength. Guided by the model, an interface mechanical interlock structure is designed and geometrically optimized. Experiments demonstrate that the optimized mechanical interlock structure increases the interfacial peel strength by a factor of 9.6. The proposed multiscale modeling framework and mechanical interlock design strategy provide guidance for the interfacial strengthening of fiber fabric/flexible polymer composites.

The non-probabilistic reliability-based topology optimization (NRBTO) method offers a powerful tool for achieving high-performance and high-safety layout designs under uncertain-but-bounded (UBB) parameters. However, the practical application of NRBTO is limited by unaffordable computational burden associated with repeated non-probabilistic reliability iterations. To address this issue, a new non-iterative reliability-based topology optimization method for static and dynamic problems with UBB parameters is established to avoid the non-probabilistic reliability iteration, in which a novel non-iterative method (NIM) is proposed by strict proving the monotonicity conditions with respect to UBB parameters. The complex NRBTO model is transformed into an equivalent deterministic topology optimization model, thereby reducing computational costs. Moreover, the sensitivities with respect to design variables are derived using the adjoint method. The effectiveness of proposed NIM for NRBTO is validated through two static and two dynamic examples, where the compliance, displacement, stress, frequency, and frequency-band problems are addressed.

Carbon fiber-reinforced poly (ether ether ketone) (CF/PEEK) composites exhibit excellent comprehensive properties, but their performance is often restricted by weak interfacial bonding between chemically inert carbon fibers and the PEEK matrix, which limits efficient load transfer. To overcome this limitation, a hexagonal boron nitride/polyetherimide (hBN/PEI) composite sizing agent was developed to modify the carbon fiber surface and regulate the CF/PEEK interface. The uniformly decorated hBN/PEI sizing layer increased the surface roughness of carbon fibers and improved interfacial adhesion with the PEEK matrix. As a result, the interlaminar shear strength (ILSS) of the sized CF/PEEK composites increased by up to 45.07%. To elucidate the underlying reinforcement mechanism, molecular dynamics (MD) simulations were conducted to investigate molecular-scale interfacial interactions. The simulation results showed that the hBN/PEI sizing interlayer strengthened the interactions between carbon fibers and PEEK. This enhancement was mainly attributed to intensified mechanical interlocking, which changed the interfacial failure mode and enabled more effective load transfer. This study provides an effective interfacial regulation strategy for CF/PEEK composites and offers theoretical guidance for designing high-performance thermoplastic composites.

This paper innovatively proposes a novel sub-fold annular Miura-tapered origami tube (MTOT), enclosed by six Miura origami units with sub-folds incorporated at the ends of each unit. Under compression, the load triggers the initial instability of the sub-folds, generating moving plastic hinge lines and achieving a progressive energy absorption mode. Experimental 3D-printed samples were tested under quasi-static axial compression and analyzed using high-fidelity finite element simulations of axial compression and low-velocity oblique impact to systematically investigate its energy absorption characteristics. The results indicate that through the sweeping of moving plastic hinge lines activated by sub-folds the MTOT absorbs the energy, resulting in superior energy absorption performance. Further parameter analysis shows that the MTOT achieves the most active energy absorption performance with the specific energy absorption (SEA) of 21.0 J/g and the stableness of load-carrying capacity (SLC) of 93.2%, representing 23.4% and 80.3% improvements over the CTT (conventional tapered tube), and maintains a high load level under oblique impact loading. Moreover, a force prediction model has been developed for the MTOT that accurately estimates its energy absorption characteristics. The MTOT activates moving plastic hinge lines through sub-folds, featuring low peak force, high average force and strong stability, providing a new solution for the crashworthiness design in aerospace and other fields.

As electronic devices rapidly evolve toward higher power density and integration, the importance of efficient thermal management grows significantly. In the context of nano-reinforced thermoplastic composites, establishing effective thermal path through the filler network is crucial. In this study, by optimizing the ratios of two sizes of hexagonal boron nitride (h-BN) nanosheets in the poly (ether ether ketone) (PEEK) matrix, a significant enhancement of the thermal conductivity of PEEK/h-BN composites was achieved. The thermal conductivity of a PEEK/h-BN composite containing a 3:7 weight ratio of the two sizes of h-BN(with 15 wt% overall h-BN content) achieved the highest thermal conductivity of 0.87 W/m & centerdot;K due to the formation of more complete thermal paths. Additionally, based on the structural distribution of boron nitride nanosheets (BNNSs) observed in scanning electron microscopy (SEM), the influence of heat transfer direction along single-layer BNNSs, as well as the interlayer relative displacement and torsional angle of bilayer BNNSs, on the thermal conductivity of BNNSs/PEEK composites was investigated through molecular dynamics simulations. The results show that when heat flow is transmitted along the armchair direction of BNNSs, the BNNSs/PEEK composites exhibit higher thermal conductivity. Furthermore, by regulating the microstructure of BNNSs, the interface scattering in BNNSs/PEEK composites can be effectively reduced, and the interfacial coupling of BNNSs/PEEK composites can be improved, leading to an enhancement in thermal conductivity. This study provides experimental data and theoretical support for the further development of high-performance thermal management materials.

The structural stability and stiffness are both crucial for maintaining aerodynamic profiles of stiffened thin-walled structures, especially in aerospace applications when subjected to extreme thermal loading. One of the challenges arises from significant compression loads induced by the restricted thermal expansion, leading to thermally induced buckling issues and severe thermal deformation. Existing methods lack choice and inevitably rely on room-temperature optimization models in thermal buckling designs, leading to an irreconcilable contradiction between the optimized thermal buckling and thermal stiffness performances. This study focuses on the collaborative design of buckling resistance and stiffness reinforcement for mitigating deformation failure in stiffened thin-walled structures and proposes a novel collaborative optimization model that maximizes the critical buckling load factor (BLF) under volume and regional strain energy constraints, namely BVR model. Compared with the conventional model that maximizes the critical BLF under volume and compliance constraints (BVC), the comparison results demonstrate the advantage of the proposed method in ensuring structural clarity, stability, and stiffness of optimal designs through typical and complex numerical examples. The failure reason for the conventional model is also given. For an aft deck structure under thermal loading, the proposed method increases the critical BLF by 98.7% and reduces the thermal deformation by 63.6%.

Calibration is vital to estimate unknown parameters and update the model, while the multiple solution problem makes it difficult to obtain accurate and robust calibrated models. Besides, blindly pursuing the minimum discrepancy between the computer model and experimental data may lead to results deviating from the true values. In this paper, we propose a novel multi-objective calibration method to solve these two problems. First, an adaptive weighted multi-objective method is provided, which considers the preference level for the response function and the uncertainty of the calibration results for each response. The sample number and Gaussian model prediction variance for different objective functions are used to evaluate the weights. Second, a calibration method based on Brownian distance correlation is proposed, which focuses on the similarity between the computer model and the physical process. The Brownian distance correlation preserves the inherent discrepancy between the computer model and the physical process, and mitigates the confounding effect between parameter estimation and model discrepancy, thereby enhancing the physical interpretability of the calibrated parameters. The proposed method is verified by four numerical examples and one engineering example. The results show that the proposed method can obtain an accurate inversion of the model parameters, which also improves the prediction accuracy of the model.

Variable-stiffness (VS) panels have shown significant potential for improving structural load-bearing performance. Inspired by natural cellular morphologies, this study proposes a Voronoi-driven partitioned combinatorial variable-stiffness (VPCVS) design framework for stiffened panels. A unified characterization method is developed to parameterize Voronoi-based stiffener unit cells, enabling continuous control of cell geometry and stiffness. The characterization is integrated with a surrogate-based optimization strategy to efficiently explore manufacturable stiffener layouts. Under non-uniform boundary conditions, the optimized VPCVS configuration achieves up to 47.93% improvement in load-bearing capacity compared to an orthogrid stiffened panel optimized for the same mass. By combining partitioned design and field-modulation techniques, the framework enables rational spatial distribution of stiffener morphology across the panel. The proposed method is further validated through nonlinear finite element simulations and full-scale axial compression experiments. The VPCVS panel exhibits a significantly higher critical buckling load while achieving a 36.54% reduction in stiffener weight relative to the conventional orthogrid baseline. Both numerical and experimental results confirm the effectiveness of the proposed approach for structural design and manufacturing of high-performance variable-stiffness stiffened panels.

The paper proposes an isogeometric integrated framework for geometrically nonlinear analysis and optimization based on a shell model with embedded stiffness of stiffeners. A shell model with embedded stiffness of stiffeners is established for stiffened shells, in which stiffeners are defined in the shell parametric space, and their deformation is described by the shell degrees of freedom through mapping relationships, thereby reducing the analytical degrees of freedom. For structural analysis, the total Lagrangian formulation is employed, extending the model to the isogeometric geometrically nonlinear analysis of stiffened shells based on Reissner-Mindlin shell theory and Timoshenko beam theory. To achieve connection with stiffener elements, the 6-degree-of-freedom isogeometric Reissner-Mindlin shell element is established, thereby eliminating the need for additional coupling matrices to connect shell and stiffener elements. Furthermore, Rodrigues’ rotational tensor is adopted to accurately describe the finite rotations of both shell and beam elements. Analytical sensitivities for the shape and size of the stiffeners are derived in detail by exploiting the functional relationship between the stiffeners and the skin. The gradient-based optimization approach is employed to solve the structural compliance minimum and volume minimum optimization problems. Finally, several numerical examples are presented to verify the effectiveness.