The conventional standard regression models often struggle to accurately predict the residual stiffness of Carbon Fiber Reinforced Polymers (CFRP), while data-driven approaches typically lack interpretability. To address these challenges, we introduce a novel method that integrates Back Propagation Neural Network (BPNN) with Symbolic Regression (SR). A stiffness degradation dataset is constructed using static and fatigue test data from T800. Key features, including stress level, normalized life, and strength, are selected through methods such as Pearson Correlation Coefficient (PCC), Max-Relevance and Min-Redundancy (mRMR), and SHAP analysis. SR is employed to uncover clear physical principles, while BPNN effectively captures complex relationships among multiple parameters. The results indicate that SR significantly outperforms traditional models in predicting the combined effects of stress level and normalized life. Additionally, BPNN demonstrates greater accuracy in predicting the interactions among stress level, normalized life and strength, maintaining low prediction errors across varying conditions. This integrated framework successfully merges physical interpretability with the capacity to model intricate relationships, offering a valuable tool for precise and transparent fatigue damage assessment in composite materials.

This work attempts to optimize Graphene nanoplatelets (GPLs) distribution in the face sheet of sandwich plates to pursue the minimum thermal deflection and transverse shear stresses at interfaces. Thus, an Improved Legendre Higher-order plate Theory combined with Isogeometric Analysis (ILHT-IGA) is, first, proposed to accurately predict thermomechanical behaviors of GPLs-reinforced sandwich plates, which can ensure the reliability of the optimized results. Then, an accelerated multi-objective optimization approach is proposed to optimize thermomechanical behaviors. The trained machine learning algorithm based on ILHT-IGA is employed as a surrogate model to accelerate the optimization process. Finally, X-shaped GPLs distribution can provide the maximum stiffness to resist thermal expansion. However, X-shaped GPLs distribution on face sheets will result in large difference of stiffnesses at adjacent surfaces of face sheets and core layer. Thus, transverse shear stresses at interfaces are obviously increased. To avoid a sudden increase of transverse shear stresses at interfaces, an alternative optimized GPLs distribution has been obtained, where GPLs gradually increase toward the upper and lower surfaces of face sheets and suddenly decrease near the surface of face sheets. Such distributions can effectively enhance the stiffness of sandwich plates to resist thermal expansion behaviors and decrease transverse shear stresses at interfaces.

Using the plate/shell elements in commercial software, accurate analysis of interlaminar initial damage in typical composite structures is still a challenging issue. To propose an accurate and efficient model for analysis of interlaminar initial damage, the following work is carried out: (A) A higher-order theory is firstly proposed by introducing the local Legendre polynomials, and then a novel shell element containing initial damage prediction is developed, which can directly predict transverse shear stresses without any postprocessing methods. Unknown variables at each node are independent of number of layers, so the proposed model is more efficient than the 3D-FEM. (B) Compression experiment is carried out to verify the capability of the proposed model. The results obtained from the proposed model are in good agreement with experimental data. (C) Several examples have been analyzed to further assess the capability of the proposed model by comparing to the 3D-FEM results. Moreover, accuracy and efficiency have been evaluated in different damage criterion by comparing with the selected models. The numerical results show that the proposed model can well predict the initial interlaminar damage as well as other damage. Finally, the model is implemented with UEL subroutine, so that the present approach can be readily utilized to analyze the initial damage in typical composite structures.

Sandwich structures have been widely applied in the wing and the horizontal tail of the aircraft, so face sheets of such structure might occur wrinkling deformation in the process of service, which will largely decrease capability of sustaining loads. As a result, this paper aims at proposing a reasonable strategy resisting wrinkling deformation of sandwich structures. To this end, an enhanced higher-order model has been proposed for wrinkling analysis of sandwich structures. Buckling behaviors of a five-layer sandwich plate are firstly analyzed, which is utilized to assess performance of the proposed model. Subsequently, wrinkling behaviors of four sandwich plates are further investigated by utilizing present model, which have been evaluated by using quasi three-dimensional (3D) elasticity solutions, 3D Finite Element Method (3D-FEM) results and experimental datum. Finally, the present model is utilized to study the buckling and the wrinkling behaviors of sandwich plates reinforced by Carbon Nano Tubes (CNTs). In addition, influence of distribution profile of CNTs on wrinkling behaviors has been analyzed, and a typical distribution profile of CNTs has been chosen to resist wrinkling deformation. Without increase of additional weight, the present strategy can effectively resist wrinkling deformation of sandwich plates, which is rarely reported in published literature.

The transverse stretching vibration of thick sandwich plates, which is attributed to largely different stiffness at the adjacent layers, is a challenging issue, and efficient approach for such issue is less reported in the published literature. Thus, natural frequencies corresponding to stretching vibration modes are generally neglected in engineering design, which might impact structural safety as frequencies of the exciting force are close to transverse stretching vibration frequencies. This paper proposes an alternative higher-order model for dynamic analysis corresponding to the higher-order vibration modes. The proposed model is classified in the displacement-based equivalent single-layer theory, as the number of displacement parameters in the proposed model is independent of the layer number. The continuity of displacements and transverse shear stresses can be fulfilled at the interfaces between the adjacent layers of structures. To demonstrate the capability of the proposed model, typical examples are analyzed by utilizing the proposed model, the three-dimensional finite element method and the chosen higher-order models. By comparing with the exact three-dimensional elasticity solutions, it is found that the proposed model can yield more accurate natural frequencies corresponding to the higher-order displacement modes than the selected models. Moreover, the factors influencing reasonable prediction of the higher-order frequencies are investigated in detail, which can provide a reference for the accurate prediction of the higher-order frequencies.

Apertures generally exist in the sandwich structures attributing to mechanical connection and lightweight, which might induce failure of such structures. Thus, it is required to realize the impact of aperture on mechanical behaviors of sandwich structures. If transverse shear deformations are unable to be described accurately, the reasonable prediction of dynamic behaviors of the form-core sandwich plates with apertures will meet severe challenges due to a large difference of transverse shear modulus at the adjacent layers. Thereby, such issue is less studied by using the efficient models and experimental testing, so an alternative sinusoidal-type finite element formulation is to be proposed to precisely predict dynamic response of the form-core sandwich structures with apertures. The proposed finite element formulation can meet beforehand compatible conditions of transverse shear stresses at the interfaces of adjacent laminates. In order to appraise strictly capability of the proposed model, experimental tests on natural frequencies of three groups of specimens with different apertures have been carried out. Moreover, four specimens in each group are tested to reduce the testing errors, which is less reported in the published literature. In addition, three-dimensional Finite Element Method (3-D FEM) is also selected to account for the good performance of the present model. Finally, the impact of aperture diameter on the natural frequencies of the sandwich structures is both experimentally and numerically investigated, which can serve as a reference for other researchers.