Spiral Stiffeners Research Articles

Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells

This study utilizes a semi-analytical approach to examine the nonlinear dynamic responses of multilayer functionally graded (MFG) cylindrical shells reinforced by FG spiral stiffeners (FGSSs), which may have symmetric or asymmetric angles, under a thermal condition. It is presumed that the temperature is distributed across the thickness direction. The shell includes three layers: an outer ceramic-rich layer, a middle FG layer, and an inner metal-rich layer. By applying classical shell theory (CST), the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the problem of nonlinear vibrations (NVs) has been addressed. Furthermore, the method of multiple scales (MMSs) is applied to investigate the nonlinear vibrational characteristics of the MFG cylindrical shells reinforced by FGSS, particularly focusing on the 1:2:4 internal resonance and the subharmonic resonance of order 1/2. This study finds that FG spiral stiffeners with symmetric or asymmetric angles and ambient temperature significantly affect the vibrational properties of the MFG cylindrical shells reinforced by spiral stiffeners.

Nonlinear torsional stability and buckling of spiral stiffened sigmoid FG thin circular cylindrical shells

This research employs an analytical approach to explore nonlinear torsional buckling behaviors of spiral-stiffened sigmoid FG (SSSFG) thin circular cylindrical shells. The research encompasses two variations of SSSFG cylindrical shells: those with internal and external spiral stiffeners. Furthermore, this study explores effects of two distinct material distributions for SSSFG cylindrical shells, specifically metal-ceramic-metal and ceramic-metal-ceramic layers, both following a sigmoid-law distribution. Theoretical formulations are obtained using the smeared stiffeners technique and classical shell theory, incorporating geometrical nonlinearity in the von-Kármán sense. The discretized nonlinear governing equations are obtained through Galerkin's method, and the approximate three-term solution for deflection is developed. Hence, explicit formulations are presented to ascertain the critical torsional load and depict the post-buckling torsional load–deflection curves. The outcomes of this study are validated by comparing them with the related research results existing in the literature. Significantly, the research highlights the influence of diverse parameters and the efficacy of stiffeners in enhancing the stability of SSSFG cylindrical shells. Researchers and engineers in this field may utilize the findings of this research as reference points for their design and research involving SSSFG cylindrical shells.

Sub-harmonic and super-harmonic resonances of spiral stiffened FG cylindrical panels of variable thickness embedded within a nonlinear elastic foundation

This research devotes to study the behaviors of sub- and super-harmonic resonances of spiral stiffened functionally graded (SSFG) variable thickness cylindrical panels (VTCP) exposed to external loading. The panel considered is rested on a nonlinear elastic foundation (NEF), which is composed of two linear foundations namely Pasternak and Winkler foundations, and a nonlinear foundation with cubic stiffness. The cylindrical panels of variable thickness are reinforced with internal spiral stiffeners. Both the cylindrical panels and spiral stiffeners are considered to be continuously graded along their thickness direction. To model the spiral stiffeners, the smeared stiffeners technique is utilized, and for deriving the discretized nonlinear governing equation of the SSFG-VTCP, the improved Donnell shell theory, von-Kármán equation, and Galerkin’s method are applied. In continuing, to examine the sub- and super-harmonic resonances, the method of multiple scales is implemented. Also, to validate the present results, in addition to comparing the present results with that of the previous research, the response of super-harmonic resonance, which is obtained theoretically, is compared with the 4th-order P-T method.

Nonlinear dynamic response and vibration of spiral stiffened FG toroidal shell segments with variable thickness

In this study, the nonlinear vibratory responses and primary resonance (PR) of the spiral stiffened functionally graded (SSFG)-toroidal shell segments (TSSs) are investigated. The shell segments considered are with variable thickness and subjected to external excitations. Both the concave and convex TSSs are investigated in this study. The TSSs considered are reinforced with internal spiral stiffeners and are assumed to be continuously graded along their thickness direction. To model the stiffeners, the smeared stiffeners technique is utilized. Also, the improved Donnell shell theory, von-Kármán nonlinear geometric assumptions, and Galerkin’s method are applied to derive the discretized nonlinear governing equation of SSFG-TSSs with variable thickness. To examine the PR responses, the multiple scales method is utilized. To investigate the nonlinear vibratory behaviors, the 4th order P-T method is used. Although the results of the present research are verified with previous research available in the literature, the response of nonlinear vibration is compared with the 4th order Runge–Kutta (R-K) method as well. The influences of geometrical and material parameters on the natural frequencies, nonlinear vibration, and PR responses of SSFG-TSSs are also studied.

Nonlinear Stability and Vibration Analyses of Functionally Graded Variable Thickness Toroidal Shell Segments Reinforced with Spiral Stiffeners

In this study, an analysis of nonlinear stability and vibration of functionally graded (FG) variable thickness toroidal shell segments (TSSs) reinforced with spiral stiffeners exposed to axial loading is presented using a combination of semi-analytical and analytical methods. Three types of variable thickness TSSs, including concave, convex, and cylindrical shells (CSs), are studied. Moreover, these structures are reinforced by external spiral stiffeners with various angles whose material properties are considered to be continuously graded along the thickness direction. In this regard, the smeared stiffeners technique is utilized to model the stiffeners, and the Donnell shell theory and the von Kármán equation are applied to derive the nonlinear governing equation for variable thickness TSSs reinforced with spiral stiffeners. Galerkin’s method is then used to obtain a discretized nonlinear governing equation to analyze the shells’ behavior. Also, the fourth-order P-T method is applied to analyze the nonlinear dynamic behaviors and the Budiansky–Roth criteria are used to examine the dynamic post-buckling (DPB) behavior. In this regard, it is noted that in terms of reliability and accuracy, the fourth-order P-T method has demonstrated advantages over the other numerical methods. Results are reported to evaluate the influences of stiffeners with different angles and input factors on the nonlinear vibration, dynamic and static post-buckling (SPB) behaviors of FG variable thickness TSSs reinforced with spiral stiffeners.

The axial compression mechanical properties and factors influencing spiral-ribbed thin-walled square concrete-filled steel tube composite members

Thin-walled concrete-filled steel tubular members have significant economic advantages, but are prone to local buckling, which has a great impact on structural safety. Therefore, this paper proposes a new spiral stiffened thin-walled CFST composite column to solve the above problems. The axial compression test found that spiral stiffeners can significantly improve the buckling resistance of thin-walled steel tubes, with the ultimate bearing capacity increased by 18 % and the ductility coefficient reaching about 2.0. Through the study of the mechanical mechanism, it is found that the spiral rib has little contribution to the vertical stiffness of the component, mainly by restricting the transverse deformation of the steel pipe to improve the mechanical performance of the component. At the same time, it is also found that the spiral rib can also play a strong constraint on the external concrete, and with a small amount of reinforcement, it can ensure the synergistic force of each part of the component. Based on the test, a parametric analysis was conducted on the pitch, the width-thickness ratio of the spiral rib and the influence law were quantified, and the design suggestions were provided. Finally, based on the fitting method, a formula for calculating the bearing capacity of this superimposed member was proposed. The new composite member has the advantages of less steel consumption, good mechanical properties, strong fire resistance, corrosion resistance, and good engineering application prospects.

Buckling behavior of spiral stiffened sandwich FGM cylindrical shells with porous core under axial compression using the FSDT

The linear buckling behavior of functionally graded cylindrical shells with porous core stiffened by spiral stiffeners under axial compression using the first-order shear deformation theory is presented in this paper. The improved Lekhnitskii’s smeared stiffeners technique is applied for shear deformable spiral FGM stiffeners. Approximate analytical solutions are assumed to satisfy the simply supported boundary conditions and the adjacent equilibrium criterion is applied to obtain closed-form relations of buckling loads. Effects of the number of FGM stiffeners, stiffener angle, volume fraction index and porosity coefficient on the buckling behavior of shells are numerically investigated.

Buckling behavior of spiral stiffened sandwich FGM cylindrical shells with porous core under axial compression using the FSDT

The linear buckling behavior of functionally graded cylindrical shells with porous core stiffened by spiral stiffeners under axial compression using the first-order shear deformation theory is presented in this paper. The improved Lekhnitskii’s smeared stiffeners technique is applied for shear deformable spiral FGM stiffeners. Approximate analytical solutions are assumed to satisfy the simply supported boundary conditions and the adjacent equilibrium criterion is applied to obtain closed-form relations of buckling loads. Effects of the number of FGM stiffeners, stiffener angle, volume fraction index and porosity coefficient on the buckling behavior of shells are numerically investigated.

Buckling behavior of spiral stiffened sandwich FGM cylindrical shells with porous core under axial compression using the FSDT

The linear buckling behavior of functionally graded cylindrical shells with porous core stiffened by spiral stiffeners under axial compression using the first-order shear deformation theory is presented in this paper. The improved Lekhnitskii’s smeared stiffeners technique is applied for shear deformable spiral FGM stiffeners. Approximate analytical solutions are assumed to satisfy the simply supported boundary conditions and the adjacent equilibrium criterion is applied to obtain closed-form relations of buckling loads. Effects of the number of FGM stiffeners, stiffener angle, volume fraction index and porosity coefficient on the buckling behavior of shells are numerically investigated.

Nonlinear buckling and postbuckling of spiral stiffened FG-GPLRC cylindrical shells subjected to torsional loads

The nonlinear buckling behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical shells reinforced by ring, stringer and/or spiral FG-GPLRC stiffeners under torsional loads is studied by an analytical approach. The governing equations are based on the Donnell shell theory with geometrical nonlinearity of von Kármán-Donnell-type, combining the improvability of Lekhnitskii’s smeared stiffeners technique for spiral FG-GPLRC stiffeners. The effects of mechanical and thermal loads are considered in this paper. The number of spiral stiffeners, stiffener angle, and graphene volume fraction, are numerically investigated. A very large effect of spiral FG-GPLRC stiffeners on the nonlinear buckling behavior of shells in comparison with orthogonal FG-GPLRC stiffeners is approved in numerical results.

Nonlinear buckling and postbuckling of spiral stiffened FG-GPLRC cylindrical shells subjected to torsional loads

The nonlinear buckling behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical shells reinforced by ring, stringer and/or spiral FG-GPLRC stiffeners under torsional loads is studied by an analytical approach. The governing equations are based on the Donnell shell theory with geometrical nonlinearity of von Kármán-Donnell-type, combining the improvability of Lekhnitskii’s smeared stiffeners technique for spiral FG-GPLRC stiffeners. The effects of mechanical and thermal loads are considered in this paper. The number of spiral stiffeners, stiffener angle, and graphene volume fraction, are numerically investigated. A very large effect of spiral FG-GPLRC stiffeners on the nonlinear buckling behavior of shells in comparison with orthogonal FG-GPLRC stiffeners is approved in numerical results.

Nonlinear buckling and postbuckling of spiral stiffened FG-GPLRC cylindrical shells subjected to torsional loads

The nonlinear buckling behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical shells reinforced by ring, stringer and/or spiral FG-GPLRC stiffeners under torsional loads is studied by an analytical approach. The governing equations are based on the Donnell shell theory with geometrical nonlinearity of von Kármán-Donnell-type, combining the improvability of Lekhnitskii’s smeared stiffeners technique for spiral FG-GPLRC stiffeners. The effects of mechanical and thermal loads are considered in this paper. The number of spiral stiffeners, stiffener angle, and graphene volume fraction, are numerically investigated. A very large effect of spiral FG-GPLRC stiffeners on the nonlinear buckling behavior of shells in comparison with orthogonal FG-GPLRC stiffeners is approved in numerical results.

Nonlinear behavior of FG porous cylindrical sandwich shells reinforced by spiral stiffeners under torsional load including thermal effect

This work deals with the nonlinear behavior of sandwich cylindrical shells reinforced by spiral stiffener subjected to torsional load in the thermal environment. The sandwich cylindrical shells composed of functionally graded porous core and two functionally graded (FG) face sheets is considered for the first time. Based on the Donnell shell theory with von Karman geometrical nonlinearity in conjunction with Lekhnitskii's smeared stiffeners technique for spiral stiffeners, the governing equations are obtained. The comparisons are made with available results to show the validation of the proposed analytic approach. The effects of various shell geometrical characteristics, angle stiffeners, number of spiral stiffeners, material parameters, and temperature change are investigated.

Analytical modeling for offshore composite rubber hose with spiral stiffeners under internal pressure

Internal pressure is the most important functional load for the offshore composite rubber hose. In this paper, the stress and radial displacement of the hose under internal pressure are investigated. The hose dimensions are length of 10.7 m and nominal bore diameter of 500 mm. The composite structure is mainly composed of cord-rubber reinforcement layers and a spiral steel stiffener. To calculate the stress and deformation of the hose, the stiffener and composite cord-rubber layers are theoretically analyzed based on the Euler–Bernoulli beam theory and the Donnell shell theory, respectively. The stiffener distinguishes the hose from common filament wound un-stiffened composite pipes in regard to the stress distribution and radial deformation. It is found that the stiffener plays an important role in affecting the mechanical behavior of composite reinforcement. Influences of the cord-winding angle, the stiffener spacing, and the stiffener’s tensile stiffness on the axial, hoop and shear stresses, and the radial displacement are investigated. The analytical model shows a good agreement with the finite element model. It is supposed to be of significant reference for practical engineering.

Asymmetric Large Deformation Superharmonic and Subharmonic Resonances of Spiral Stiffened Imperfect FG Cylindrical Shells Resting on Generalized Nonlinear Viscoelastic Foundations

This paper is devoted to superharmonic and subharmonic behavior investigation of imperfect functionally graded (FG) cylindrical shells with external FG spiral stiffeners under large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler–Pasternak foundation augmented by a Kelvin–Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. The von Kármán strain-displacement kinematic nonlinearity is employed in the constitutive laws of the shell and stiffeners. The external spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. The coupled governing equations are solved by using Galerkin’s method in conjunction with the stress function concept. The multiple scales method is utilized to detect the subharmonic and superharmonic resonances and the frequency–amplitude relations of the 1/3 and 1/2 subharmonic and 3/1 and 2/1 superharmonic resonances of the system. Finally, the influences of the stiffeners helical angles, foundation type, coefficient of the nonlinear elastic foundation, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

Combination resonances of imperfect SSFG cylindrical shells rested on viscoelastic foundations

The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, von-Karman equation and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

Nonlinear vibration of stiffened multilayer FG cylindrical shells with spiral stiffeners rested on damping and elastic foundation in thermal environment

Abstract This paper presents the nonlinear vibration of multilayer FG cylindrical shells reinforced by spiral FG stiffeners surrounded by damping and elastic foundation in thermal environment. The primary, superharmonic and subharmonic resonances of spiral stiffened multilayer FG cylindrical shell are analyzed. It is assumed that the material properties are dependent to temperature. The linear elastic foundation is based on the Winkler and Pasternak model. In order to model the stiffeners, the technique of smeared stiffener is utilized. With regard to classical plate theory of shells, von Karman equation and Hook law, the relations of stress-strain is derived for shell and stiffeners. According to the Galerkin method, the discretized motion equation is obtained. The primary, superharmonic and subharmonic resonances in presence of thermal environment are analyzed by using the method of multiple scales. The influence of the material parameters, temperature, elastic foundation and various geometrical characteristics on the primary, superharmonic and subharmonic resonances is investigated.

Nonlinear buckling and postbuckling of sandwich FGM cylindrical shells reinforced by spiral stiffeners under torsion loads in thermal environment

The main purpose of this paper is the investigation of the nonlinear torsional buckling and postbuckling of sandwich functionally graded cylindrical shells with the von Karman large deflection nonlinearities under thermal effect by an analytical method. The shell skin is reinforced by stringer, circular ring and spiral stiffeners, the material properties of shell skin and stiffeners are assumed to vary continuously through the thickness. The very large effect of spiral stiffeners on the buckling load-carrying capacity of a cylindrical shell in comparison with orthogonal stiffeners is clearly proved in numerical investigations. Based on the Donnell shell theory and the improved smeared stiffener technique for both thermal and mechanical terms of spiral stiffeners, the equilibrium equations of the shell are established in this paper. By using the Galerkin method, the postbuckling curves and critical buckling loads are obtained. The effects of temperature change, stiffeners, material and dimensional parameters on the nonlinear torsional buckling and postbuckling of shell are numerically analyzed.

Nonlinear Stability of Sandwich Functionally Graded Cylindrical Shells with Stiffeners Under Axial Compression in Thermal Environment

The geometrically nonlinear response of sandwich functionally graded cylindrical shells reinforced by orthogonal and/or spiral stiffeners and subjected to axial compressive loads is investigated in this paper. Two types of sandwich functionally graded material models are considered. The formulations are based on the Donnell shell theory considering geometrical nonlinearity and Pasternak’s elastic foundation. The improved Lekhnitskii’s smeared stiffener technique is used to account for the stiffener effects with both mechanical and thermal stresses. The results obtained indicate that the spiral stiffeners have significantly beneficial influences in comparison with orthogonal stiffeners on the nonlinear buckling behavior of shells. The relatively large effects of temperature change, geometrical and material parameters are also demonstrated in the numerical investigations.

Nonlinear Thermo-Mechanical Stability Analysis of Eccentrically Spiral Stiffened Sandwich Functionally Graded Cylindrical Shells Subjected to External Pressure

A new analytical approach to investigate the nonlinear buckling and postbuckling of the sandwich functionally graded circular cylindrical shells reinforced by ring and stringer or spiral stiffeners subjected to external pressure is presented in this paper. By employing the Donnell shell theory, the geometrical nonlinearity in Von Kármán sense and developed Lekhnitskii’s smeared stiffener technique, the governing equations of sandwich functionally graded circular cylindrical shells are derived. Resulting equations are solved by applying the Galerkin method to obtain the explicit expression of critical buckling external pressure load and postbuckling load–deflection curve. Effects of spiral stiffeners, thermal environment, external pressure, and geometrical parameters on nonlinear buckling behavior of sandwich functionally graded circular cylindrical shells are shown in numerical results.