Thin-walled Shells Research Articles

Frequency analysis of longitudinal-radial vibrations of a cylindrical shell

The article solves the problem of harmonic longitudinal-radial vibrations of a circular cylindrical shell with freely supported ends. To solve the problem, we used the refined equations of oscillation of such a shell, derived earlier from the exact three-dimensional formulation of the problem and its solution in transformations. An extensive review of works devoted to the study of harmonic and nonstationary processes in elastic bodies on the basis of classical (Kirchhoff-Love, Flyugge) and refined Timoshenko type (Hermann-Mirsky, Filippov-Khudoinazarov) theories is given. Four frequency equations are obtained for the main parts of the longitudinal and radial displacements of the cylindrical shell. These frequency equations admit, as special cases, frequency equations and a thin-walled shell. Based on the solution of the obtained frequency equations, the frequencies of natural vibrations of the shell, including the thin-walled one, are determined. A comparative frequency analysis of longitudinal vibrations of a circular cylindrical elastic shell is carried out on the basis of the classical Kirchhoff-Love theory, refined theories of Hermann-Mirsky and Filippov-Khudoinazarov. On the basis of the results obtained, conclusions were drawn regarding the applicability of the studied oscillation equations, depending on the waveform and shell length. In particular, it was found that all the considered equations are unsuitable for describing wave processes in short shells, the lengths of which are commensurate with the transverse dimensions of the shells.

Nondestructive Prediction of the Buckling Load of Imperfect Shells

From soda cans to space rockets, thin-walled cylindrical shells are abundant, offering exceptional load carrying capacity at relatively low weight. However, the actual load at which any shell buckles and collapses is very sensitive to imperceptible defects and cannot be predicted, which challenges the of such structures. Consequently, probabilistic descriptions in terms of empirical design rules are used and designing reliable structures requires the use of conservative strength estimates. We introduce a nonlinear description where finite-amplitude perturbations trigger buckling. Drawing from the analogy between imperfect shells which buckle and imperfect pipe flow which becomes turbulent, we experimentally show that lateral probing of cylindrical shells reveals their strength nondestructively. A new ridge-tracking method is applied to commercial cylinders with a hole showing that when the location where buckling nucleates is known we can accurately predict the buckling load of each individual shell, within ±5%. Our study provides a new promising framework to understand shell buckling, and more generally, imperfection-sensitive instabilities.

Dynamic response and damage assessment of spherical robot GFRP spherical shell under low velocity impact

Abstract In the normal operation of a spherical robot, its spherical shell structure is often accompanied by low velocity impact. At the same time, the spherical shell structure should take into account its protective ability against high strength impact of small probability. Glass fiber reinforced polymer (GFRP), which has high specific strength, specific stiffness, corrosion resistance and an impact energy dissipation coefficient, can be used as the ideal spherical shell material for spherical robots. In this study, the low velocity impact damage of GFRP spherical shell is studied based on the background that a thin-walled shell structure of spherical robot may suffer from large deformation and dynamic load. This study is divided into three aspects: experiment, simulation and calculation. The dynamic response and residual bearing capacity of the GFRP spherical shell is obtained through experiments; the progressive damage model of the composite structure, which demonstrates expounded stress distribution, a structural deformation mode and an energy dissipation mechanism under impact, is established based on the Hashin criterion. Low velocity impact-penetrating failure of the elastic brittle thin-walled GFRP spherical shell is calculated according to the geometrical principle and energy method. In this paper, the material dynamic behavior and impact damage of a GFRP spherical shell are systematically studied. This is of great significance for the development of high-performance spherical robots and the realization of accurate control.

Reinforcing Inclusion Effect on the Stress Concentration within the Spherical Shell Having an Elliptical Opening Under Uniform Internal Pressure

The authors present the results of computer simulation of the stress-strain state of a thin-walled spherical shell with an elliptical opening and the surrounding reinforcing inclusion of another material. The effect of geometric and mechanical parameters of inclusions on the stress distribution around the opening and deformation of the shell under uniform internal pressure are investigated. The issue of stress concentration in modern leading fields of technology and industry, namely, in mechanical engineering, rocket, and space, is quite topical since it is associated with the reliability and durability of the designed structures or their elements. Stress concentrators can occur due to imperfections in the materials’ structure (cavities, cracks, foreign inclusions, etc.) or technological and structural necessity (openings, cutouts, leaks). Shell structures are used as load-carrying structures in many fields of engineering. They combine high strength with low weight, which contributes to their reliability and safety during operation. In most cases, shells in real structures have simple geometric surfaces (shells of rotation). Complex structures are usually a combination of such shells. It is important to investigate the effect of local stress concentrators as openings (considering inclusions) on the stress-strain state of shells. The methods of stress concentration reduction should be outlined. The authors performed a finite element analysis of the effect of reinforcements modeled by inclusions made of the different materials as compared with the shell material having an opening on the parameters of its stress-strain state. Such investigations are crucial for the design and optimization of the structures in many engineering fields.

Structural similitudes for the vibration characteristics of concave thin-walled conical shell

A structural similitude is proposed for the analysis of the vibration characteristics of concave thin-walled conical shell. The similitude laws are derived by invoking the least square method and transition models with different proportional input parameters. Analytical calculations show that satisfactory similitude in terms of natural frequency scaling can be achieved. Based on the analytical study, a series of modal tests is performed on the three-scaled thin-walled conical shell to verify the scaling laws. Emphasis is especially predicting and verifying the vibration characteristics of concave conical shell through the standard thin-walled conical shell to avoid manufacturing limitations.

Free vibration analysis of rotating thin-walled cylindrical shells with hard coating based on Rayleigh-Ritz method

This paper focuses on the free vibration analyses of the rotating hard-coating cylindrical shells with various boundary conditions and the effects of hard coating on the vibration behaviors of the rotating shells. To accurately predict more natural characteristics, the characteristic orthogonal polynomials are taken as the admissible displacement functions. Considering the influences of Coriolis force, centrifugal force and initial hoop tension caused by rotation, the equations of motion of the shells are established by the use of the Rayleigh-Ritz method. Based on the state vector method, an efficient method is developed to solve the equations. By comparing with the results of both the finite element analysis and published literatures, the high accuracy and good convergence of the proposed model are verified. In addition, the effects of the boundary conditions, parameters of hard coating, rotating speed and number of circumferential waves on the vibration behaviors of the hard-coating shells are evaluated. This study may provide a reference for the application of hard-coating damping treatment to the vibration suppression of rotating thin-walled structures.

Buckling Behavior of Sulfate-Corroded Thin-Walled Cylindrical Steel Shells Reinforced with CFRP

In this study, the buckling behavior of thin-walled cylindrical tanks exposed to sulfuric acid corrosion was investigated, and the buckling performance losses were recovered by reinforcing with Carbon fiber reinforced polymer (CFRP). Experiments were planned for three groups: Control samples without corrosion, full CFRP models and variable CFRP application group. The experiments were performed with 12 models of 800 × 400 × 0.45-mm dimensions. The prepared solutions were applied to the sealed test models as full and ½-filled and then exposed to sulfuric acid solution for 24 h, after which the experiments were performed. The mass losses were determined from the weights of the cylindrical samples, which were discharged after 24 h. After the corrosion, CFRP was applied to the cylinder, at ½ height of the cylinder and at 10 cm from its midpoint. The prepared model samples were placed in the test apparatus and sealed. In the experiments, vacuum was made using the vacuum pump, and data were recorded using the load cell. Deformations were measured by strain gauges and LVDT and transferred to the computer using a data collection device (datalogger). After data collection, vacuum-displacement plots were made. We aimed to recover a material that has undergone acid corrosion. The main goal of this work is to use the theoretical model, which is evaluated for limited geometrical ratios and for the perfect models, for the prediction of buckling behavior of sulfuric acid corroded thin-walled steel shells. We observed that the samples exposed to corrosion recovered 20–60% of their lost strength by CFRP application.

Elastic local buckling of periodic sinusoidal corrugated composite panels subjected to in-plane shear

The critical local buckling instability of simply supported sinusoidal panels subjected to in-plane shear loading is investigated semi-analytically using the Rayleigh-Ritz method. Due to significant weight-strength saving and increased out-of-plane rigidity, these thin corrugated structural elements have gained wide recognition as an alternative to flat plate structural elements. To utilize these structures effectively in applications, such as civil infrastructure, aircraft wings, among many others, it is important to attain a comprehensive understanding of the failure mechanisms of these structures. Such corrugated panels are easily analyzed by modeling as an equivalent flat plate; however, this approximate method cannot capture the local buckling effect due to the complicated geometries of sinusoidal panels. Hence, a more precise solution is developed to accurately predict the local buckling behavior based on classical shell theory using a representative periodic structural element which encapsulates the periodic buckling nature of the panel in shear. Excellent correlation is observed with the results based on the numerical finite element analysis. Parametric studies are conducted to explore the effects of the thickness, aspect ratio, corrugated amplitude and material properties of the panel on buckling. The derived semi-analytical solution can accurately capture the local buckling behavior at any thickness, any aspect ratios, and high corrugated amplitudes within the range of thin-walled shells. The proposed semi-analytical solution can be confidently used to aid in efficient and accurate design analysis and optimization of corrugated panels.

Reusing & replacing performances of the AB-BRB with thin-walled concrete-infilled steel shells

In this paper, the assembled bolt-connected buckling-restrained brace (AB-BRB) with a pair of thin-walled concrete-infilled steel shells (CSS) is experimentally analyzed, centered on the reusing & replacing performance. A total of 8 specimens were well produced according to the proposed design method, and the hysteretic performances were examined under the quasi-static loading. During the process the replacing capacities were verified based on the indicator comparison. The nonlinear simulation method was also raised based on the Abaqus software and verified with the experimental data. After several replacement tests, the hysteresis indicators showed the retention of stiffness resulting from the consecutive out-of-plane support, as well as the smooth variation tendency resulting from the multiple-wave deformation pattern. The AB-BRB property after reusing illustrated the comparable performance to the primary one, and the reduction degree was mainly related to the bolt-slippage and local concrete crushing. The simulation showed ideal agreements with the experiment result, indicating the effectiveness of the model for performance predictions. The study verified the feasibility of reusing scenarios, recommended the design revisions and provided references for further parametric analysis.

Thermal-elastic buckling of the arch-shaped structures with FGP aluminum reinforced by composite graphene platelets

This paper presents the analytical process of the functionally graded porous (FGP) arch structure in an elevated thermal field. The FGP arch is reinforced by graphene platelets (GPLs). Analytical expressions are used to illustrate the distribution of the pores and GPLs in the cross profile. A small crown dent is considered by introducing a small point load on the crown portion. The nonlinear thin-walled shell theory is used to formulate the potential energy function of the deformed arch. Then, this energy function is expressed explicitly by assuming a cosine function to describe the radial displacement of the deformed arch. Two nonlinear formulae of equilibrium are obtained by differentiating the energy function, resulting in an implicit form of the critical temperature change, which reduces to an explicit form when the dent is negligible. Moreover, the derived analytical solutions are verified by an aluminum ring with homogeneity. Finally, an analysis is developed to estimate the effect of various geometric and material parameters on the critical temperature changes and the equilibrium plots.

Free flexural vibration of thin-walled honeycomb sandwich cylindrical shells

The free flexural vibration of thin-walled honeycomb sandwich cylindrical shell was investigated by experiments and Flügge's shell theory simulations. The natural frequencies were measured and compared with simulations three-dimensional model. In the simulation analysis, the porous honeycomb core is simplified as a homogeneous orthotropic material, and its equivalent material properties are determined by the corrected Gibson's formula. Flügge's shell theory is compared with experimental results and finite element method calculation results, and the maximum relative error is only 4.749%.The comparison results show that Flügge's shell theory can accurately calculate the natural frequency of the thin honeycomb sandwich cylindrical shell.

Polynomial Approximation-Based Optimal Design of Structures Interacting with an Aggressive Environment by the Random Search Method

The optimal design of structures that interact with an aggressive environment is considered on the example of a thin-walled shell exposed to the internal pressure of the aggressive gas. The simplicity of the above research object is related to quite simple equations describing the stress-strain state (SSS) of the structure. Any mathematical model simulating the corrosion damage process includes empirical coefficients characterizing the degree of influence of certain factors on the corrosion rate. Some coefficients (mainly those describe the corrosive environment behavior, which controls the temperature, concentration of certain substances, etc.) are constant, while others that describe the SSS effect on the corrosion damage rate of the structure, according to earlier findings of the author, vary during the optimal design procedure, significantly affecting the final design results. It should be noted that the proposed method should be applied not at the operation stage of the structure but at its design stage. To define the coefficients of the mathematical model of corrosion damage, a numerical method for multiple identifications of the mathematical model based on experimental data was proposed. This method gives satisfactory results but is quite cumbersome and time-consuming. The analytical method of polynomial approximation gives results comparable in efficiency but is more flexible and fast. Two modifications of the method of polynomial approximation to define the “optimal” set of coefficients of mathematical models of corrosion damage are developed. Numerical simulations are performed for the optimal design of a thin-walled cylindrical shell exposed to an aggressive environment.

The strength tests of thin-walled composite shells under non-stationary loads of different physical nature

Mechanical action of energy fluxes of different physical nature is proposed to be simulated by one-side non-stationary loading. A set of gas-dynamic devices for generation of loads of the required space-time distribution is described. Two new explosive devices for formation of low-impulse loads of microsecond duration are proposed. The methods to measure the parameters of thin-walled composite constructions under dynamic and pulse loads are considered. Time deformation profiles of fiberglass cylindrical shell under low-impulse load of microsecond duration are given. The use of wire or foil sensors for the measurement of deformations gives close results when investigating the shell stage of deformation of fiberglass thin-walled constructions.

A design approach for the ring girder in elevated steel silos

Silos in the form of the thin-walled cylindrical steel shells are commonly supported on a ring girder, which rests on a limited number of columns to discharge the content by gravity flow into transportation systems. Local supports in the elevated steel silos produce a significant circumferential non-uniformity in the axial membrane stresses in the silo shell. One way of reducing the non-uniformity of these stresses is to use a very stiff ring girder which partially or fully redistributes the stresses from the local support into uniform stresses in the shell. Previous works that attempt to produce design expressions only address isolated ring girders and ignore the key role of the interaction between the cylindrical shell and the supporting ring girder. The aim of this study is to achieve a more efficient and realistic design of ring girders resting either on four supports, or on four supports with secondary beams, or on eight supports. Pursuant to this goal, variations of the stress resultants and displacements in the ring girder which rests on different support conditions are derived for the first time using Vlasov's curved beam theory. These expressions have been evaluated with finite element analyses for an isolated ring girder. Subsequently, a complementary finite element parametric study was conducted to investigate the variation of the stress resultants and displacements caused by the connection of the shell and ring girder resting on different supporting conditions. These variations were plotted as a function of the shell-ring girder stiffness ratio (ψ) for each support condition. Finally, considering lower bound limits for the stress resultants and displacements, design equations were proposed for ring girders which rest on different support conditions. These expressions may easily be placed in a practical spreadsheet, which could be used with different data to give realistic predictions.

Investigation on the vibration and interface state of a thin-walled cylindrical shell with bolted joints considering its bilinear stiffness

This paper innovatively proposed a semi-analytical modeling method for thin-walled cylindrical shells with bolted joints, and further analyzed its vibration response and the interface contact state. First, the bolted joint was investigated by quasi-static experiments. Then, based on the experimental phenomena, the constitutive model for bolted joints was established by simultaneously considering the different tensile and compressive stiffness (preloaded bilinear stiffness) and the friction behavior (including stick, slip, and separation) between the connection interfaces. This is rare in the previous modeling of bolted joints. Next, the established model of bolted joints was applied to a cylindrical shell. Based on Sanders shell theory, the Lagrange equation was used to derive the dynamic equation of the cylindrical shell with bolted joints. The model of the bolted joint and the cylindrical shell was verified by finite element method and natural frequency comparison respectively. Then, the effects of several parameters including the preload of bolts, excitation amplitude, coefficient of friction and number of bolts on the dynamic response and interface state of the cylindrical shell with bolted joints were analyzed, and several conclusions were obtained.

Force control-based vibration suppression in robotic grinding of large thin-wall shells

Vibration suppression is a major difficulty in the grinding of low-stiffness large thin-wall shells. The paper proposes that effective workpiece vibration control can be performed by a novel force-controlled end-effector integrated into a robotic grinding workcell. First, a dynamics model is built to capture the characteristics and vibration suppression mechanism of force control-based robotic grinding, then a novel force control-based vibration suppression method is designed for grinding large thin-wall shells, and three robotic grinding tests are conducted to validate the effects of the new method and the grinding performance of the force control-based robotic grinding workcell. The results are: 75% reduction in the amplitude of workpiece vibration; effective suppression of non-tool passing frequency; stable grinding of large thin-wall shells remarkably enhancing grinding depth up to 0.3 mm per pass, grinding depth error less than ±0.1 mm, and significant improvement of the workpiece surface quality up to Ra=0.762 μm.

Compactness variability of metal deployable load-carrying shell structures

The paper considers the basic conditions that allow changing the compactness of metal deployable structures while maintaining their rigidity, sustainability and uniformity of deployment. The comparison of the finite-element models of the deployment of thin-walled metal shells having equal initial geometry and thickness at a different number of folds and compactness has been performed. The full-scale experiment to deploy similar shells and compare the kinetics of the deploying process with the results of the numerical experiment was conducted. The interconnection of the geometric accuracy of the unfolding of multisectional deployable structures of the conical type with their compactness, and elastoplastic properties of the material of the metal shell has been investigated. The paper presents the results of the performed experimental studies of tightness conditions of the metal shell related to the quality, plasticity and strength of its welded joints.

Accelerated Koiter method for post-buckling analysis of thin-walled shells under axial compression

Due to the high specific strength and stiffness, thin-walled shells are widely used in aerospace engineering structures. However, along with the increase of the structure size or the structure hierarchy, the computational cost of the post-buckling analysis of thin-walled shells would increase sharply and then the imperfection sensitivity analysis would become time-consuming. In this study, an accelerated Koiter method is proposed to improve the efficiency of post-buckling analysis and imperfection sensitivity analysis of thin-walled shells under axial compression. In the framework of the accelerated Koiter method, a single mode Koiter method considering pre-buckling nonlinear behavior is used to reduce the computational time of repeated imperfection analysis, which can accurately predict the effect of the small amplitude imperfection. Furthermore, in order to obtain the expanded point of Koiter method, a Combined Approximation (CA)-based iterative eigenvalue algorithm is constructed to obtain the pre-buckling state in the neighborhood of the bifurcation point and reduce computational cost by the reasonable step length prediction. Finally, the efficiency and accuracy of the proposed method are demonstrated by means of four illustrative examples, including the composite cylindrical shell, the isotropic cylindrical shell, the isotropic conical shell and the hierarchical stiffened cylindrical shell under axial compression.

Investigation of the contact zone of a cylindrical shell located between two parallel rigid plates with a gap

The article presents the results of a study of the contact zone of a thin-walled cylindrical shell located between two parallel rigid plates. The shell under consideration was located with various gaps from the rigid plate and was subsequently subjected to internal pressure. In the course of such a study, experimental, numerical and analytical estimates of the contact zone width were obtained depending on the discharge pressure. The obtained numerical and analytical estimates are tested with experiment. To study the width of the contact zone, depending on the gap, a testing workbench was used. The problem of numerical and analytical modelling was solved by the finite element analysis in the Ansys Workbench system. The solution to transcendental equation was found numerically using the Newton-Raphson method. As a result of experimental, numerical and analytical studies, results were obtained for a plane-oval shell with gaps of 0.5 mm, 1 mm and 2 mm, depending on the applied pressure.

A Tunable Variable-Torque Compliant Hinge Using Open-Section Shells

Abstract This paper is concerned with a compliant-hinge mechanism that can provide a wide range of torque-angle profiles. The mechanism consists of thin-walled open-section shells that are subjected to combined twisting and bending. A pair of open-section shells is so arranged as to get a large rotation about a virtual axis with high stiffness along other axes. A replaceable cam-like guideway regulates the bending of the open-section shells as they twist, thereby generating the desired torque profile. An energy-based, graphical, and computational design method is formulated to obtain the guideway profile for a specified torque profile. A physical prototype is constructed for an assistive chair for the elderly to demonstrate the variable-torque output and the efficacy of the hinge.