Curved Shell Structures Research Articles

Deformation control of piezoelectric intelligent curved shell structure with multiple actuators based on neural network optimized by genetic algorithm

In aerospace engineering, it is important to achieve precise deformation control of curved shell. In this paper, the piezoelectric intelligent curved shell structure (PICSS) with multiple actuators was selected as the research object. Firstly, a finite element model of the structure was constructed, and the sample data was obtained based on simulation method for the back propagation (BP) neural network. Next, the structure of the BP neural network was determined as ‘6–13-24-3′ with the goal of obtaining the minimum mean square error. Then genetic algorithm was used to optimize the initial weights and thresholds of the BP neural network, and the input voltage of each actuator was predicted. The accuracy of voltage prediction was confirmed through collaborative simulation technology by testing the BP neural network before and after optimization. Finally, the deformation perception and control of the piezoelectric curved shell were verified through the PICSS.

A High-Precision Inverse Finite Element Method for Shape Sensing and Structural Health Monitoring

In the contemporary era, the further exploitation of deep-sea resources has led to a significant expansion of the role of ships in numerous domains, such as in oil and gas extraction. However, the harsh marine environments to which ships are frequently subjected can result in structural failures. In order to ensure the safety of the crew and the ship, and to reduce the costs associated with such failures, it is imperative to utilise a structural health monitoring (SHM) system to monitor the ship in real time. Displacement reconstruction is one of the main objectives of SHM, and the inverse finite element method (iFEM) is a powerful SHM method for the full-field displacement reconstruction of plate and shell structures. However, existing inverse shell elements applied to curved shell structures with irregular geometry or large curvature may result in element distortion. This paper proposes a high-precision iFEM for curved shell structures that does not alter the displacement mode of the element or increase the mesh and node quantities. In reality, it just modifies the methods of calculation. This method is based on the establishment of a local coordinate system on the Gaussian integration point and the subsequent alteration of the stiffness integration. The results of numerical examples demonstrate that the high-precision iFEM is capable of effectively reducing the displacement difference resulting from inverse finite element method reconstruction. Furthermore, it performs well in practical engineering applications.

Fracture modeling of curved composite shell structures using augmented finite element method

This paper presents an augmented finite element method for the fracture modeling of curved composite shell structures considering geometric nonlinear effects. We first derive the composite shell AFEM (CS-AFEM) formulation using a dynamic implicit algorithm, which enhances the numerical convergence when dealing with unstable crack propagations. Besides, the cohesive zone model featuring with shell kinematics is incorporated into the CS-AFEM to describe the quasi-brittle fracture behaviors of composite laminates. Furthermore, a coordinate transformation scheme is proposed to describe both the local material orientation and the crack evolving path in the curved shell structures. Finally, several benchmark examples are numerically investigated, and the capability of the proposed method in modeling the arbitrary evolving cracks in curved composite shell structures has been thoroughly demonstrated.

Knowledge-dominated and data-driven rigid-flexible coupling dynamics for rotating flexible structure

Solving a rigid–flexible coupling nonlinear dynamic equation necessitates updating dynamic quantities in each time step, which is the main factor that hampers computational efficiency. Therefore, this study develops an innovative framework that combines knowledge-based and data-driven solutions, for which a data-driven numerical integration (DDNI) method is established to update the mass matrix and load vector. The DDNI model is obtained from offline training based on a deep neural network model and is embedded in the floating frame of reference formulation for online simulation of rigid–flexible coupling problems. As benchmark cases, planar and curved shell structures are analyzed, and the results show that the DDNI method exhibits excellent performance in terms of accuracy and adaptability. In particular, compared to a fully numeric integration (FNI) scheme, the DDNI method shows significantly improved efficiency, surpassing that of commercial software. These noteworthy characteristics aid the investigation of intricate structures in engineering problems. We utilize the developed DDNI method in a rigid–flexible coupling analysis of a manipulator, which shows that it is highly time-efficient, approximately 20 times faster than the FNI scheme, while producing results that are consistent with those of experiments.

Free vibration analysis of barrel-shaped sandwich shells with auxetic honeycomb core using modified thick shell theory

Modern engineering extensively employs complexly curved shell structures, presenting mathematical challenges in analyzing their mechanical behavior due to geometric intricacies. The recent trend of incorporating advanced lightweight materials into these structures drives the need to develop improved theories and methods. This study presents an investigation into the free vibration analysis of barrel-shaped sandwich (BSS) shells using a modified thick shell theory (MTST). These sandwich shells feature functionally graded (FG) ceramic-metal layers on both inner and outer surfaces, with a lightweight honeycomb core. Notably, the honeycomb layer's thickness surpasses that of the inner and outer layers, necessitating the application of thick shell theory for accurate analysis. However, previous studies have often used classical theories for thin shells, and those applying thick shell theory sometimes neglected the curvature effects in the fundamental equations and rotary inertia components. Thus, this research employs the MTST to overcome these limitations. The study includes comparative validations and explores the impact of material parameters and curvature radii on the natural frequencies of these barrel-shaped sandwich shells through numerical examples.

A Universal Quadrilateral Shell Element for the Absolute Nodal Coordinate Formulation

Abstract A simple quadrilateral shell element is proposed in this work to study large deformations and large rotations of membrane/plate/shell structures. There are three merit characters in this element: locking-free; immune to mesh distortions; and robust to surface tessellations. Numerical issues in plates/shell elements such as shear-locking and thickness-locking problems are resolved, and quadrilateral area coordinates are adopted to solve the mesh distortion issues. This element can be adopted to curved shell structures, and warped deformations can be well described. Moreover, even if a shell structure cannot be easily tessellated by high quality quadrilateral polygons, it can still be discretized by a mesh consisting of high-quality triangular and quadrilateral elements, then this element can work together with a corresponding triangular element to provide accurate results on this combined mesh, and the degree-of-freedom for the discretized system is no more than several times of the number of nodes. Numerical tests validate the effectiveness, efficiency, and universality of this element in engineering scenarios.

Nonlinear deflection characteristics of damaged composite structure theoretical prediction and experimental verification

This research derived a nonlinear computational model for the prediction of deflection responses of the damaged layered composite structures. The model validity was verified using in-house experimentation. The composite panel model has been derived mathematically using the higher-order polynomial kinematics without non-zero shear stress conditions and Green’s strain for the geometrical nonlinearity. The nonlinear deflection responses of combined damage curved shell structures are evaluated numerically utilizing the nonlinear isoparametric finite element technique in conjunction with the direct iterative method. By setting the necessary convergence criteria, the model accuracy has been explored by comparing the deflections of the published literature (the maximum deviation observed is 6.97%). Additionally, the experimentation is done on damaged laminated shell structures, and results are compared to show the proposed model’s efficacy (maximum deviation observed is 2.17%). Finally, a number of numerical examples are solved to assess the effects of the material, geometry and damage-related parameters on the nonlinear deflections of the shell structure.

Machine learning-based optimization design of bistable curved shell structures with variable thickness

The mechanical performance of curved shell structures is difficult to predict due to their complex geometric nonlinearity. There have been many efforts to improve the mechanical property of curved shell structures by designing the thickness distributions. However, due to the nonlinear characteristics of variable-thickness shells, it is impossible to exhaust all possible structural forms through experimental and theoretical approaches. In this paper, we report a new machine learning (ML)-based approach to design and optimize bistable curved shell structures. The ML model is used to establish the underlying mapping relationship between structural parameters and specific performance. Nonlinear shell structures are efficiently and accurately designed and optimized with optimal backward snapping forces (B). The results demonstrate an effective approach for the design and optimization of curved shell structures and provide a valuable reference for future study of nonlinear structures. Moreover, this approach presents an efficient means of designing advanced metamaterials. The modular design of meta-atoms based on ML has the potential to construct metamaterials with specific properties and functionalities, which will lead to extensive applications in different fields.

Free Vibration Analysis of Curved Shell Structures with Various Boundary Conditions by Using A Meshfree Method

In this paper, the free vibration of curved shell structures with various boundary conditions is examined by using a meshfree method. The meshfree method in this study is based on the radial point interpolation method (RPIM). The RPIM shape function is chosen because it satisfies the Kronecker delta property allowing for the direct imposition of essential boundary conditions. The field variables and the geometry of the curved shell are interpolated through the RPIM shape function. The curved shell formulation is constructed based on the first-order shear deformation theory (FSDT), which considers the transverse shear strain. In a meshfree approach to investigate curved shell structures, a convected coordinate system is employed. This convected coordinate system is tied to the curved surface and used to map an arbitrary curved shell in 3D space into 2D space. To obtain the numerical solution, the calculation is performed first in this convected coordinate system and then mapped back to the global coordinate system. The accuracy and ability of the meshfree method have been shown through many numerical examples. The natural frequencies of curved shells with different geometry and boundary conditions are in good agreement with other available reference solutions.

Numerical investigation of transient thermo-mechanical loading effect on combined damaged (crack and delamination) curved shell structure: An experimental verification

The transient responses of the curved shell panels are examined under thermo-mechanical loading and verified experimentally. The damaged shell model is formulated mathematically considering polynomials of higher-order based on isoparametric finite element (FE) steps. The dynamic (time-dependent deflection) responses are evaluated numerically using developed computer code in MATLAB, utilizing Newmark's constant average acceleration method. The accuracy of the present model is proven by equating the consequences with the available data in the published literature. Additionally, a few experimentations have been accomplished and outcomes are equated with the numerical solution to show the effectiveness of the present developed numerical model. Further, the impact of damages (debond and/or crack), numerous structural input parameters (curvature ratio, shell geometry) and temperature on the curved shell panel is demonstrated and presented through a wide variety of numerical examples.

Numerical simulation of fracture in layered and sandwich structures: A systematic literature review

A systematic literature review on numerical strategies suitable to simulate defects and discontinuities in layered and sandwich structures is presented here. Particular care is given to studies whose scope concerns the so-called Moving Mesh (MM) or Isogeometric Analysis (IGA) methods. A general overview of the peculiarities of each approach is also provided. A total of fifteen and twenty-six journal/conference articles were summarised and categorised for MM and IGA methods, respectively. Based on the available literature, it can be stated that MM approaches generally allow a lower computational burden due to the reduced number of re-meshing steps required when compared to standard finite element approaches. Conversely, IGA approaches bring strong advantages in the geometric description of curved shell structures and, due to a non-uniform rational b-spline interpolation function, ensure higher numerical accuracy in stress analysis problems.

Dynamic Deformation and Perforation of Ellipsoidal Thin Shell Impacted by Flat-Nose Projectile.

Experimental and theoretical studies were carried out on the dynamic deformation and penetration response characteristics of metal ellipsoidal thin curved shells under impact loads. The deformation characteristics of the impacted ellipsoid shell was investigated via the use of a light gas gun to carry out impact loading experiments at different speeds. Ten cases of experiments were conducted with the impact velocities distributed between 25.69 m/s and 118.97 m/s. Stereo digital image correlation (3D-DIC) technology was applied to capture the dynamic deformation and penetration process of the impacted shell. The recovered shells were measured, and the deformation characteristics were analyzed, along with the dynamic evolution, as observed through 3D-DIC analysis. Based on the experimental results, the displacement mode was summarized and the displacement distribution of the locally impacted ellipsoid shell was proposed. The governing equations were derived for the dynamic deformation and penetration of the impacted ellipsoid shell by means of the Lagrange equation. The proposed theoretical model was verified based on the experimental results. Finally, the influence of the curvature distribution on the impact resistance of ellipsoidal shells is discussed. The results indicated that the proposed theoretical model was effective in analyzing the large deformation and the penetration speed. Stretching the axial length of the ellipsoid shell in the impact direction improved its resistance to penetration. Stretching the axial length of the ellipsoid shell perpendicular to the impact direction improved its resistance to deformation, but reduced its resistance to penetration. Maintaining the triaxial ratio and appropriately reducing the size of the ellipsoidal shell improved its resistance to both deformation and penetration. The above research provides a reference for the analysis of the impact resistance of thin-walled curved shell structures in engineering.

Design optimization and sensitivity analysis on time-domain sound radiation of laminated curved shell structures

Design optimization and sensitivity analysis on time-domain sound radiation of laminated curved shell structures

Topology optimization of bi‐material curved shell structures for minimizing time‐domain sound radiation

AbstractSo far, the research on topology optimization against noise has mainly addressed frequency‐domain problems, while time‐domain analysis is also widely used in practical engineering. Nonetheless, the topology optimization work on the latter was rarely reported due to its complexity. This article presents a new topology optimization scheme of bi‐material curved shell structure to reduce the time‐domain noise generated by transient vibration. A finite element formulation for an eight‐node curved shell element is presented. The Newmark integral method is employed to calculate transient responses, and the obtained results are input into the time‐domain boundary element method to predict transient sound pressure. In the optimization model, the volumetric densities of material in a bi‐material interpolation model constructed by the solid isotropic material with penalization model are chosen as the design variables; the time integral of the squared sound pressure on structural surfaces or prescribed reference points in acoustic medium over a specified time interval of interest is taken as the objective function; and the constraint on material volume is considered. A volume‐preserving Heaviside penalization is introduced to suppress gray elements. Furthermore, the calculation of time‐domain sound radiation sensitivity is transformed into the following two processes: (a) the derivation of transient response based on the Newmark integral method; (b) the derivation of transient sound pressure based on the discrete time‐domain boundary integral equation. Numerical examples demonstrate the validity of the approach proposed in this article. The influences of volume‐preserving Heaviside penalization, volume constraint, loading position and form, and selection of objective function on the optimal design are discussed.

Influences of elastic foundations on the nonlinear free vibration of composite shells containing carbon nanotubes within shear deformation theory

In this work, the solution of nonlinear free vibration problem of composite shells structures containing carbon nanotubes (CNTs) resting on elastic soils within shear deformation theory (ST) is presented. After modeling the mechanical properties of nanocomposite shell structures containing CNTs and elastic soils, the basic relations, and governing equations of double curved shell structures within the ST are established considering the geometric nonlinearity. The frequencies of nonlinear and linear free vibrations and their ratios for inhomogeneous nanocomposite structures on the soils within the ST are obtained using perturbation method for the first time. After checking the methodology of the research, the effects of soils, nonlinearity, shear strains and patterns of CNT on the frequency-amplitude dependence of nanocomposite shell structures for various geometric parameters are carried out.

Flexural wave mitigation in metamaterial cylindrical curved shells with periodic graded arrays of multi-resonator

This paper aims to present a theoretical model of flexural wave bandgaps in locally resonant cylindrical curved shell and investigates a technique for broadband wave mitigation using a metamaterial cylindrical curved shell. Firstly, cartesian coordinates are converted to cylindrical coordinates in the cylindrical curved shell structure to construct periodic conditions in the circumferential direction. Then, governing equations are derived by using the extended Hamilton principle, and plane wave expansion (PWE) method is implemented to calculate the band structures of acoustic metamaterial cylindrical curved shells with different multi-resonator parameters. In addition, a periodic graded arrays technique is also utilized to broaden the frequency range of bandgap. Lastly, finite element method (FEM) is used to calculate the band structures and vibration transmission characteristics to verify the accuracy of PWE results. The results disclose that the proposed structure has a good attenuation effect on flexural wave and the periodic graded arrays technique can effectively splice bandgaps of each resonator to enlarge frequency range of the flexural wave mitigation. Hence, the proposed structure can be used to achieve a good attenuation effect on flexural wave in the future.

Nonlinear frequency prediction of cutout borne multi-layered shallow doubly curved shell structures

This is the first time two different geometrical nonlinear strain–displacement relationships are adopted to model the laminated shell structure with the cutout to predict the eigenvalues considering a higher-order displacement model. The nonlinear solution for the natural frequency value is obtained using Picard's iterative method in association with the isoparametric finite element method. The present research mainly indicates the inevitability of Green-Lagrange's nonlinear strain in the framework of higher-order displacement kinematics instead of von-Karman's nonlinear strain including all of the nonlinear higher-order strain. The predicted nonlinear solution consistency is verified by solving a series of examples, as same as the source data. The influences of the cutout (shape and size) related data and the corresponding geometrical parameters of the multilayered structure are expressed in the final output form. Lastly, the inclusive inferences are highlighted to recommend the nonlinear model to analyze a flexible laminated structural component with and without cutout.

Combined Damage Influence Prediction of Curved Composite Structural Responses Using VCCT Technique and Experimental Verification

The influences of crack and delamination on the natural frequency and strain energy release rate of the laminated doubly curved shell structure are computed via a commercial finite element tool (ABAQUS). The effect of individual damages (crack and delamination) is modeled using the virtual crack closure technique (VCCT), considering the curvature effect. Initially, the model validity is established by comparing the results with the available results in the open domain. Additionally, the model validity has been verified via in-house experimentation for frequency responses. Further, the natural frequency and strain energy release rate (SERR) have been calculated for the structure to examine the influences of the individual or combined effect of damages by varying the design-dependent input geometrical parameters. The inclusive characteristics of the current model in conjunction with geometrical configurations are summarized for subsequent references.

Pressure-induced instability and its coupled aeroelasticity of inflated pillow

A floating air weapon system (such as airborne floating mines) plays an important role in modern air defense operations. This paper focuses on aeroelastic characteristics of airborne floating mine named inflated pillow. Firstly, the dynamic deployable process of the pillow and characteristics of the local instability of the edge are studied, and the evolution mechanism of wrinkles and kinks is analyzed. Secondly, in the cruising stage, the fluid-structural-thermal coupling analysis is performed on the pillow, and the aeroelastic characteristics are studied. Thirdly, the shape-preserving effect of the inflated pillow during the “negative pressure” slow landing stage is evaluated. It is found that when the wind velocity is higher, the pillow has a collapsed instability (surface extrusion and contact), and when the wind velocity is lower, snap-through instability occurs. Finally, for the collapsed instability, a carbon fiber skeleton is added to discrete the large global collapsed fold into small local folds, thus achieving shape-preserving effect of pillow. For snap-through instability, the critical internal pressure and different shape evolution under different wind velocity are evaluated. Through the analysis of the mechanical mechanism and control of the structural morphological evolution, it provides theoretical guidance for the application of the curved shell structure in floating air weapon system.

Integrated design optimization of actuator layout and structural ply parameters for the dynamic shape control of piezoelectric laminated curved shell structures

Compared with static shape control, dynamic shape control is more difficult due to its time-varying nature. To improve the control precision and reduce the number of actuators needed, an integrated design optimization model of structure and control is proposed. The following three sets of design variables are considered to minimize the time domain variance between the controlled and desired dynamic shapes: the time-varying actuator voltages, the actuator layout and the structural ply parameters. To satisfy the engineering performance requirements to the greatest extent possible, constraints on the structural mass, the energy, the maximum transient voltage and the number of actuators are considered. Because the control voltages are varying in time, a two-level optimization strategy is adopted. In the inner optimization problem, the Newmark integral method is applied to derive discrete time domain expressions for the shape control equations, and then, the Kuhn-Tucker condition is introduced to calculate the optimal time-varying voltage distribution. To solve the outer optimization problem, because of the coexistence of discrete variables and continuous variables, a simulated annealing algorithm is used. To address the shape control of complicated curved shells, a finite element formulation for an eight-node laminated curved shell element with piezoelectric actuators is derived. Numerical examples show that the proposed integrated design optimization method can significantly improve the control effect and that the optimization of the structural ply parameters plays an important role. Moreover, the control system can be simplified by taking the minimum number of actuators as the objective function when the control accuracy allows.