This paper derives the analytical solution for the buckling load of extension-twist multicoupled laminates. The optimization targets both the buckling load and coupling effect, with verification through simulations and experiments. Using the double trigonometric series method, the analytical solution for the buckling load of the extension-twist multicoupled laminate, simply supported on all four sides and subjected to in-plane compressive loads, is obtained. Based on this, a multi-objective optimization design model for the extension-twist multicoupled laminate is established, with the optimization objectives of maximal buckling load and coupling effect. The optimization is achieved using the sequential quadratic programming (SQP) algorithm, and the laminate with enhanced coupling effect and buckling load is designed. Based on the ply angle sequence of the optimal laminate, numerical simulations and robustness analyses confirm the buckling model. Compared to the simulation results, the analytical solution error for the buckling load of the laminate is within 5%, validating the theoretical framework. Experimental measurements using a multi-directional loading test machine reveal that the discrepancy between measured and theoretical buckling loads is within 3%, further verifying the theory's accuracy. This research provides valuable insights for improving the load-bearing capacity of structures such as wings and wind turbine blades.

Shallow spherical shells are widely used in large structures, such as launch vehicles, nuclear containments, and gasholders. Studying scaled models of geometric and material distortion in the free vibration of large, thin-walled clamped shallow spherical shells is essential. First, frequency equations and natural frequency solutions for clamped shallow spherical shells are utilized to apply similarity transformation, leading to the derivation of generalized similarity conditions and scaling laws for the free vibration of these shells. The numerical approach is then validated by comparing the theoretical natural frequencies of clamped shallow spherical shells. Finally, geometric and material distortion similarity predictions for the free vibration of clamped shallow spherical shells with different rise-to-thickness ratios are investigated by numerical simulations. Results indicate that scaled models for clamped shallow spherical shells with different rise-to-thickness ratios, designed according to similarity conditions and incorporating the corresponding generalized similarity condition of mode shape and the natural frequency scaling relationship, can accurately predict the free vibration characteristics of the prototypes. For the free vibration of clamped shallow spherical shells with medium, small, and large rise-to-thickness ratios, in addition to meet the same mode shape, the distorted scaling laws also need to ensure that the scaling factors of rise-to-thickness ratio and Poisson's ratio equal 1, the scaling factor of Poisson's ratio is 1, and the rise-to-thickness ratios of scaled models and the prototype are no less than 25. The method and results of this study offer valuable insights for the design and experiments of scaled models for similar shells with thickness and material distortion.

Sandstone is a typical discontinuous and heterogeneous material characterized by a significant presence of pores. Porosity is a crucial factor that influences the complex characteristics of sandstone, notably affecting its compressive strength and deformation parameters. It is of considerable theoretical significance and engineering value to investigate the impact of porosity on the fracture behavior of sandstone under compressive loading. In this paper, we apply both the Intermediately-Homogenized PeriDynamic (IH-PD) model and the Fully-Homogenized PeriDynamic (FH-PD) model to examine the fracture behavior of sandstone containing a single oval flaw subjected to uniaxial compression. The IH-PD model incorporates porosity as pre-existing PD damages, wherein mechanical bonds connected to PD nodes are randomly pre-broken to achieve the desired porosity. The IH-PD model considers the heterogeneous characteristics of sandstone without detailing the explicit geometry of the actual pores. Simulation results from the IH-PD model indicate that both pore size and particle size influence the fracture mode of sandstone under uniaxial compression. A comparative analysis of fracture modes and stress-strain curves from IH-PD simulations, FH-PD simulations, and experimental measurements confirms the accuracy and superiority of the IH-PD model in simulating compressive fracture behavior. The results indicate that only the IH-PD model, which accounts for the inherent heterogeneities of sandstone, can adequately reflect the variations in crack paths caused by changes in pore distribution. Moreover, the IH-PD model successfully reproduces tortuous crack paths, captures transverse cracks in sandstone under compression, and exhibits asymmetric fracture modes, which markedly differ from the FH-PD simulation outcomes. This work employs the IH-PD model to investigate the fracture behavior of sandstone containing a single oval flaw with varying porosity levels under uniaxial compression, elucidating the influence of porosity on the failure modes of sandstone. The findings underscore the significant impact of porosity on the paths, roughness, and tortuosity of cracks. As porosity increases, the cracks exhibit greater tortuosity and roughness, and the symmetry of fracture modes becomes more easily disrupted.

Large-area and tunable strain gradients arise from inhomogeneous deformation in wrinkled thin films, making them promising for flexoelectric applications. Consequently, the structure and buckling modes of these films have garnered significant attention. In this paper, an electromechanical coupling model is developed to study the buckling behavior of thin-film-and-finite-thickness-substrate structures with flexoelectric effects. First, the influence of flexoelectric effects on the buckling evolution of thin-film-substrate structures is assessed using the minimum energy method. Two buckling modes, i.e., global buckling and local wrinkling, are distinguished by changing structural parameters and the flexoelectric coefficient. Results show that stronger flexoelectric effects lead to slenderer films and an increased likelihood of global buckling. Additionally, a stronger flexoelectric effect raises the critical strain required for buckling and significantly impacts local wrinkling mode. In local wrinkling, as the amplitude increases, the maximum strain in thin films decreases; sparser wrinkles with greater amplitude occur with a more pronounced flexoelectric effect. When the flexoelectric effect reaches a certain threshold, the buckling mode of the thin film shifts from local wrinkling to global buckling. The flexoelectric effect enhances structural stiffness and stretchability. Moreover, flexoelectric polarization can be continuously adjusted with compressive strain, highlighting its controllability in wrinkled thin films for generating and managing material polarity. These findings will aid in the design and application of micro and nanoscale electromechanical devices.

This study presents a two-dimensional (2D) bond-based peridynamics (BBPD) model based on the incompressible neo-Hookean (NH) constitutive model for simulating the tensile large deformation and failure behavior of incompressible hyperelastic membranes. First, the force density vector and micropotential function of the PD bond are derived by equating the strain energy density of the 2D BBPD model with that of the NH hyperelastic constitutive model. The model parameters are found to be related to the ratio of principal stretches in the neighborhood of the PD bond. Then a bond-associated horizon is introduced, and principal stretches are calculated based on the calculation of the deformation gradient within this horizon. A 2D BBPD model for NH hyperelastic materials is thus established. To validate the model, the nominal stress-stretch curves for a square hyperelastic membrane under uniaxial tension and biaxial tension with different biaxial tension speed ratios are calculated using the proposed BBPD model, and compared with theoretical curves. The deformation and load-displacement curves of a hyperelastic membrane with a central circular hole under uniaxial and biaxial tensile loads are also calculated and compared with finite element method (FEM) predictions. Finally, the deformation and failure processes of the hyperelastic membrane with a central circular hole under different tensile loads are calculated, and the influences of loading conditions on the mechanical properties and failure behavior of the NH hyperelastic membrane are analyzed based on the evolution analysis of strain energy density and damage of material points at the crack tip. It is found that the proposed BBPD model achieves less than 10% error in calculations. The failure load of the hyperelastic membrane with a central circular hole decreases while the failure displacement increases with rising biaxial tension speed ratios. Crack bifurcation occurs in the hyperelastic membrane with a central circular hole, with the bifurcation angle increasing alongside the biaxial tension speed ratio.

The negative Poisson's ratio honeycomb structure is widely used in the field of impact protection because of its unique mechanical properties and excellent energy absorption capacity. The evolution of local dynamic stress in this structure is closely related to changes in its cellular microstructure under dynamic impact. Current research on negative Poisson's ratio structures mainly focuses on improving overall energy absorption capacity of the structure by designing cells with concave deformation mechanism, often ignoring the structural optimization of existing models and lacking exploration of other energy absorption mechanisms of rotary deformation. To further improve the dynamic response of star-shaped honeycomb structures with negative Poisson's ratio under in-plane impacts, the rotation characteristics of cells are studied in this paper. Building on traditional designs, the star-shaped honeycomb structure is further optimized, and the deformation energy absorption mechanism of star-shaped honeycomb cell is endowed with the coupling idea. Based on the principle of relative density equality, two types of rotating star-shaped cellular cells with double negative Poisson's ratio effect are obtained by internal rotation and external rotation: internal star-shaped cellular cells and external star-shaped cellular cells. The energy absorption characteristics of different honeycomb structures under in-plane impact loads are studied using numerical simulations, and the influences of both concave and rotating deformation mechanisms on the energy absorption characteristics of honeycomb structures are investigated. Based on one-dimensional shock wave theory and energy absorption efficiency method, empirical formulas for dynamic platform stress and dense strain of star-shaped honeycomb structures are given, and the formulas for calculating their relative density are established. According to the theory of critical velocity, the first and second critical velocities of the star-shaped honeycomb structure are determined. The dynamic response of the rotating star-shaped honeycomb structure under different impact velocities is analyzed using the explicit dynamic finite element method. Simulation results are compared and analyzed with the evaluation indexes of model macro and micro deformation modes, platform stress, and specific energy absorption. The results show that when the new structures are impacted, their cells first rotate and then recess, exhibiting a stronger negative Poisson's ratio effect. Under the impact at a medium speed of 20 m/s, the platform stress of the internal honeycomb structure is higher and the stress stability is better. In the platform stage, the stress fluctuation of the external spiral honeycomb structure is more severe, but it has higher specific absorption energy under the impact at a high speed of 120 m/s. This study shows the relationship between the concave mechanism and rotation mechanism of the star-shaped honeycomb structure and its energy absorption characteristics, providing new insights for optimizing the impact dynamic performance of honeycomb structures.

Metal structures are widely used in modern industrial fields, but their manufacturing and service processes often produce composite defects that affect the mechanical properties and service life. Defects can appear both on the surface and beneath the structure, making it challenging for a single nondestructive testing (NDT) method to address all issues. Furthermore, using multiple NDT methods can result in low efficiency and high costs. To address this, a novel electromagnetic-acoustic integrated testing method, called PECT-EMAT, has been developed in this study, with its detection capability evaluated based on the theory of probability of detection (POD). Firstly, we established a simulation method and experimental system for PECT-EMAT to test aluminum alloy specimens with both surface cracks and bottom thinning defects, and explored a signal separation method using spectrum analysis. Next, we built a POD model based on statistical methods and created a signal database for composite defects. Finally, we conducted a statistical analysis of this database to determine the minimum detectable size of the PECT-EMAT hybrid testing method. The research findings indicate that: (1) For metal structures with both surface cracks and bottom thinning defects, the proposed PECT-EMAT method can effectively identify composite defects through signal separation. (2) The PECT signals and EMAT signals separated from the original detection signals exhibit distinct characteristics for detecting surface cracks and bottom thinning defects, respectively, leading to the establishment of a signal features' database for composite defects. (3) POD analysis reveals that the minimum detectable lengths for surface cracks are 2.72 mm in simulation and 2.12 mm in experiments, while for bottom thinning defects, they are 4.13 mm and 1.92 mm, respectively. This study provides a theoretical foundation for the adoption of the PECT-EMAT hybrid testing method and offers a reliable technical means for detecting complex defects in engineering structures.

Simulating three-dimensional (3D) crack propagation in solid structures poses significant challenges due to the unpredictability of crack paths, complicating both computation and solution strategies. Traditional methods often face difficulties in accurately capturing arbitrary crack propagation during large deformations. The finite particle method (FPM), based on vector mechanics, offers a novel numerical approach for analyzing complex behaviors in solid mechanics. Different from conventional continuum-based methods, FPM discretizes the solid domain into a collection of finite particles, each governed by Newton's second law of motion. This particle-based formulation enables seamless transitions between continuum and non-continuum behaviors by dynamically adding or removing particles, providing significant advantages for crack propagation analysis in both static and dynamic scenarios. In this study, the FPM is extended to address the dynamic fracture in 3D solids, focusing on the challenges related to crack initiation, propagation, and branching. The FPM is combined with an extrinsic cohesive zone model (CZM) to capture the complex behaviors of fractures, avoiding the need to pre-define crack paths and effectively managing discontinuities caused by crack propagation. A discriminant criterion is developed to identify the onset of crack initiation, and an automated embedding process for cohesive elements is implemented to enable real-time simulation of fracture surfaces. To manage the evolving topologies that arise from crack propagation, we propose a general strategy based on an ergodic search algorithm, which updates the connectivity of the discretized solid model dynamically as cracks evolve. In addition, we develop a GPU-based parallel solver using the CUDA toolkit to significantly accelerate fracture computations. The accuracy and applicability of the proposed method are validated through several numerical examples, including fracture simulations of plates and beams subjected to dynamic loading. The results demonstrate the capability of the method to accurately capture the intricate details of crack initiation, growth, and interaction in 3D solids. This extended FPM framework serves as a robust tool for analyzing dynamic fractures in engineering applications, providing a versatile framework for studying delamination, material failure, and structural collapse in both research and practical settings.

The study of data-driven predictions for constraint-related fracture toughness is an interdisciplinary scientific problem relevant to mechanics, mechanical engineering, as well as computer science and technology, and is of great significance for accurate structural integrity assessment. This research focused on nuclear power steel A508. The predictive capabilities of four algorithms, namely the K-nearest neighbors (KNN) regression, kernel regression (KR), linear regression (LR), and random forest (RF) regression, for constraint-related fracture toughness predictions were investigated. The RF algorithm outperformed the others, while the KR algorithm had the least effective predictions. The prediction accuracy ranked as follows: RF>LR>KNN>KR. Furthermore, based on the RF algorithm, data under plane strain conditions were added for data enhancement, enabling the prediction and verification of constraint-related fracture toughness for single-edge notch bending (SENB) specimens. The validated model was successfully transplanted to single-edge notch tension (SENT), compact tension (CT), and central crack tension (CCT) specimens. Results indicated that the RF algorithm with data augmentation improved prediction accuracy and capability, particularly at boundary points. The RF-based model, enhanced with additional data strategies, demonstrated strong generalization across different specimen types. For SENB and CT specimens, bending loads dominate at the crack tip; thus, altering a/W and B/W enhances restraint. For SENT and CCT specimens, where shear loads predominate at the crack tip, adjusting a and B proves more effective. Finally, a unified, high-accuracy prediction model was developed by incorporating sample category features using the RF algorithm and data enhancement strategies.

Traditional methods for analyzing the P-Δ effect in tall structures often fail to adequately account for time-varying axial forces, which can lead to an underestimation of its impact on structural safety. This paper introduces a high-order accurate analysis method based on the weak-form quadrature element method (QEM). We develop Hermite-type quadrature element models for both distributed and concentrated mass structures. The proposed method is capable of addressing dynamic P-Δ effects caused by arbitrary axial loads without iterative computations, yielding precise solutions. Its efficacy and accuracy are validated through comparative analysis involving three distinct case studies. Numerical results confirm that the proposed approach delivers highly accurate P-Δ effect analyses, achieving exceptional precision in dynamic response with a single quadrature element, even in complex structural systems. Overall, this method offers a novel and efficient solution for detailed analysis of P-Δ effects in tall structures.