Stresses In Shell Research Articles

Static analysis of foldable pressurized and thermally loaded cylindrical shell as an expander in sport equipment reinforced by G-Ori nanofillers

The present work investigates stress, strain and deformation analyses of a shear deformable cylindrical shell manufactures by a Copper (Cu) core reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads. The cylindrical models can be used in sport equipment especially in expander component. The effective material properties of the graphene origami auxetic reinforced Cu matrix are developed using micromechanical models cooperate both material properties of graphene and Cu in terms of local temperature, volume fraction and folding degree. The principle of virtual work is used to derive governing equations with accounting thermal loading.

Analysis of edge stress of combined shell under internal waves

Internal wave is essentially a gravity wave induced by the layered structure of water (e.g., density stable layering), with its maximum amplitude occurring within the ocean. Similar to surface waves, internal waves have significant influence on the strength and stability of a submerged body as an external factor. Meanwhile, combined shells are exposed to complicated loads under internal waves, and edge stress is dominant. In this study, the edge stresses of combined shell (typical hemisphere–cylinder combined shell and unfolded sphere–cylinder combined shell) under internal waves were analyzed. Indeed, a semi-empirical, semi-theoretical formula for the edge stress of combined shells (typical hemisphere–cylinder combined shell and unfolded sphere–cylinder combined shell) has been proposed. In this study, the semi-empirical, semi-theoretical formula was corrected by introducing internal wave loads, with the depth of the internal wave taken into consideration. In addition, the corrected formula was verified by finite element analysis, and a simplified equation for the calculation of edge stress of the combined shell under internal waves was developed, with errors in a rational range.

Stress-strain state of ceramic shell mold during formation of spherical steel casting in it. Part 2

The paper presents the results of numerical calculations of the solution to the problem of modeling the process of possible cracking in a spherical shell mold when pouring liquid steel into it and cooling the solidifying casting. The numerical scheme of the axisymmetric problem and the algorithm for its solution were given in Part 1. The crack resistance is estimated by magnitude of the normal stresses in the ceramic shell during its co-cooling with a solidifying casting. The results detailed analysis considered: fields of displacement, stresses, and temperatures both on spherical surface and in growing crust of solidified metal. The solution took into account the change in the shear modulus of the mold material from temperature, and an assessment of this refinement was given. The problem was solved in two ways. The first – with a constant shift modulus of the shell mold; the second – with its temperature-dependent shift modulus. There is a significant difference between these variants in terms of magnitude of the normal stresses arising in the shell mold. The authors analyzed resistance of the shell mold spherical geometry to external influences from its support filler and filling funnel. The problem of determining the contact and free surfaces at the boundary of the shell mold and support filler was solved. The results are presented graphically in the form of diagrams of stresses and temperatures over the studied area in its different sections and time intervals for cooling of the growing metal crust. The role of compressive normal stresses σ22 , σ33 on the surface of contact of the shell mold with liquid metal at the initial moment of cooling on probability of cracking in a spherical mold is shown. The level of strain-stress state in a spherical shell mold when cooling a steel casting in it is significantly determined by dependence of shift modulus of the shell mold on temperature.

Advanced Thick FGM Plates-Cylindrical Shells in Linear Unsteady Supersonic Flow

Introduction:: Thick functionally graded (FG) plates-cylindrical shells with third-order shear deformation theory (TSDT) of displacement models under thermal vibration in linear unsteady supersonic flow are investigated by using the generalized differential quadrature (GDQ) method. Method:: The nonlinear coefficient term of TSDT models and the advanced nonlinear shear correction coefficient expression are used to study the thermal vibration of thick FG plates and cylindrical shells in linear unsteady supersonic flow. At the intersection of FG plates-cylindrical shells, the displacements, stress resultants, and moment resultants could be reasonably assumed in the continuity condition for the differential volume in linear unsteady supersonic flow, respectively. Result:: The dynamic equilibrium differential equations of thick FG plates and cylindrical shells in linear unsteady supersonic flow, respectively in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads consist of the linear supersonic aerodynamic pressure and inertia terms can be presented. Two parametric effects including environment temperature and functionally graded material (FGM) power law index on the thermal stress and center displacement of thick FG plates-cylindrical shells in linear unsteady supersonic flow are investigated. Conclusion:: The linear unsteady supersonic flow over the outer surface of thick FG platescylindrical shells provides the additional aerodynamic effect on the values of displacements and stresses.

Thermal Vibration of Thick FGM Conical Shells by Using Third-Order Shear Deformation Theory.

A time-dependent third-order shear deformation theory (TSDT) approach on the displacements of thick functionally graded material (FGM) conical shells under dynamic thermal vibration is studied. Dynamic equations of motion with TSDT for thick FGM conical shells are applied directly with the partial derivative of variable R*θ in the curve coordinates (x, θ, z) instead of y in the Cartesian coordinates (x, y, z) for thick FGM plates, where R* is the middle-surface radius at any point on conical shells. The generalized differential quadrature (GDQ) numerical method is used to solve the dynamic differential equations in equilibrium matrix forms under thermal loads. It is the novelty of the current study to identify the parametric effects of shear correction coefficient, environment temperature, TSDT model, and FGM power law index on the displacements and stresses in the thick conical shells only subjected to sinusoidal heating loads. The physical parts with values on the length-to-thickness ratio equals 5, and 10 FGMs can be used in an area of an airplane engine that usually operates near more than 1000 K of temperatures when the thermal stress is considered and affected. The important findings of the presented study are listed as follows. The values of normal stress are in decreasing tendencies with time in cases when the coefficient c1 equals 0.925925/mm2 in TSDT and length-to-thickness ratio equals 5. The shear stress values in x plane z direction on the minor middle-surface radius (r) equals the major middle-surface radius (R) over 8 and length-to-thickness ratio equals to 5 can withstand T = 1000 K of pressure.

Stress state of elastic shell of standard sample in process of cable tear out testing

Article purpose is establishment of a quantitative character for influence of structural parameters of a rubber-cable belt on tensile testing results of a standard belt sample and influence of structural parameters on distribution of stresses in a butt-joint connection. Article methodology is in model construction, stress state determination for elastic material of deformed shape located between cables of a sample by methods of linear theory of elasticity and in obtaining parameters of a stress-strain state of an elastic shell of a standard sample for cable tear out testing in a closed form. Influence character of geometric parameters of a rubber-cable belt on tensile testing results of a standard belt sample is established and it allows considering parameters during determining maximum stresses in elastic shell of a belt butt-joint connections. Influence character of a stress-strain state of a standard sample on geometric parameters of a belt is established. The results make it possible to determine a distribution of shear stresses in elastic shell of a belt in butt-joint connections considering the structure of connections based on testing the standard samples. This increases the safety of usage of butt-joint connections of rubber-cable belts and increases their lifecycle.

An analytical method for free vibration analysis of multi‐directional functionally graded porous doubly‐curved shells in thermal environment with various boundary conditions

This paper uses the analytical method with arbitrary boundary conditions to model and analyze the free vibrations of multi‐directionally functionally graded porous (MFGP) doubly‐curved shallow shells resting on the Pasternak foundation in a temperature environment. It is anticipated that all mechanical parameters, except Poisson's ratio, will change in the direction of length, width, and thickness. To comprehensively describe the shell's displacement, strain, and stress fields, a modified first‐order shear deformation theory (FSDT) with an assumption of cosine distribution shear stresses has been developed. The fact that the enhanced FSDT theory does not require the use of shear correction and that the shear stress at the two free faces of the shells is zero are two of the theory's most significant advantages. Using Hamilton's principle and improved FSDT, one may get the governing equation for free vibration analysis of MFGP doubly‐curved shallow shells. The Galerkin approach is proposed to solve the governing equation of MFGP doubly‐curved shallow shells with various boundary conditions. The trustworthiness of the article is evaluated via its publication in the article model's several special cases. From this point on, a collection of findings about the natural frequency of MFGP doubly‐curved shallow shells is identified and shown in the form of tables and graphs. The results provided in this manuscript can be used as a benchmark solution for further studies as far as the vibration behavior of the MFGP doubly‐curved shallow shells is concerned.

The lgi-miR-2d is Potentially Involved in Shell Melanin Synthesis by Targeting mitf in Manila Clam Ruditapes philippinarum.

Shell color as an important economic trait is also the crucial target trait for breeding and production. MicroRNA (miRNA) is an endogenous small non-coding RNA that can post-transcriptionally regulate the expression of target genes, it plays important roles in many life activities and physiological processes, such as shell color, stress response, and disease traits. In this study, we investigated the function of lgi-miR-2d in shell melanin formation and the expression patterns of lgi-miR-2d and target gene Rpmitf in Manila clam Ruditapes philippinarum. We further explored and verified the relationship between Rpmitf and lgi-miR-2d and identified the expression level of shell color-related gene changes by RNAi and injecting the antagomir of lgi-miR-2d, respectively. Our results indicated that lgi-miR-2d antagomir affected the expression of its target gene Rpmitf. In addition, the dual-luciferase reporter assay was conducted to confirm the direct interaction between lgi-miR-2d and Rpmitf. The results showed that the expression levels of melanin-related genes such as Rpmitf and tyr were significantly decreased in the positive treatment group compared with the blank control group after the Rpmitf dsRNA injection, indicating Rpmitf plays a crucial role in the melanin synthesis pathway. Taken together, we speculated that lgi-miR-2d might be negatively modulating Rpmitf, which might regulate other shell color-related genes, thereby affecting melanin synthesis in R. philippinarum.

PHÂN TÍCH TĨNH VỎ TRỤ FG-CNTRC CHỊU TẢI TRỌNG CƠ NHIỆT VỚI TÍNH CHẤT VẬT LIỆU PHỤ THUỘC VÀO NHIỆT ĐỘ

This article presents a thermo-elastic static analysis of the FG-CNTRC cylinderical shell subjected to a thermo-mechanical load. The temperature is assumed to vary through the thickness, and the temperature distribution is derived from the heat transfer formula. The gorvening equations of thermoelastic analysis are established by using the higher-order shear deformation theory, including the transverse normal stress effect. The material properties of FG-CNTRC are temperature-dependent. Using an analytical solution that used the single trigonometric series and the Laplace transformation to solve these equations of shell with the different boundary conditions. The present approach is validated by comparing the results with published results. The effects of different boundary conditions and temperatures on the displacement and stresses of the FG-CNTRC cylindrical shells are investigated. The results show the jumping variation of the stress components at the boundary position. Besides, when the temperature increases, the maximum absolute value of the axial stress increases while that of the circumferential stress decreases.

Thermomechanical problem of functionally graded spherical shells based on homogenization schemes: Data-driven volume fraction optimization with material uncertainties

Mechanical analysis and optimal design for functionally graded materials (FGMs) structures are significant. The present paper analyzes the parameter uncertainties problem for the thermomechanical response of the FGMs spherical shells with volume fraction power distribution. Here, the interval random uncertainty model is recommended to describe the uncertainties of each component of material parameters in FGMs, and a data-driven artificial neural network (ANN) fast calculation for FGMs spherical shells thermomechanical problems with uncertainties analysis is established and trained. The thermomechanical coupling response analysis and volume fraction optimization analysis of the FGMs spherical shell with material uncertainties are realized for zirconia-titanium FGMs, with the maximum normalized Von Mises stress as the structural safety index and the ANN as the fast calculation method. In addition, the Von Mises stress of the FGMs spherical shell and a ZrO2-Ti alloy double-layer spherical shell under different loads is compared. The results show that material parameter uncertainties, especially those in Young's modulus, thermal expansion coefficient, and uniaxial yield limit significantly affect structural safety. The structural safety index λ calculated based on the volume fraction optimization design of FGMs spherical shell is significantly lower than that of the ZrO2-Ti alloy double-layer. The ANN method greatly improves the computational efficiency for uncertain problems and maintains high accuracy, compared with the statistical analysis after many calculations by randomly selecting material parameters. This study provides a path for the safety design of FGMs structures with uncertain parameters.

Quantifying tidal versus non-tidal stresses in driving time-varying fluxes of Enceladus' plume eruptions

In this study we investigate the relative importance of endogenic vs. exogenic stresses in controlling the location and timing of active ice-shell deformation on Enceladus, which is expressed by cyclic plume eruptive flux along active fault zones (i.e., the tiger stripes). Although the variation of the eruption flux on Enceladus follows the periodicity of the diurnal tide, it remains unclear why there is a consistent phase delay of the observed peak eruption when compared to the predicted peak tidal stress. Here, we explore whether endogenic stresses in the ice shell are capable of explaining this observed phase delay. To achieve this goal, we performed geologic mapping along the tiger-stripe faults that host the erupting plumes. Using the fault kinematics established from our mapping, we determine the general stress state (i.e., the principal-stress directions) along the tiger-stripe faults. This knowledge in turn forms the basis for inferring the most likely plume-eruption mechanism. Our mapping shows that the tiger-stripe fractures are not tensile cracks but are instead left-slip fault zones locally displaying extensional fissures. This insight leads to a hypothesis that strike-slip faults and their local tensile cracks experience simultaneous shear and tensile failure, and that the tensional opening reaches maximum at the time of the peak plume flux. We quantified this hypothesis using a stress decomposition model that assesses (1) the relative importance in magnitude between the tectonic stress and tidal stress exerted on the tiger-stripe faults and (2) the role of ice shell properties such as the shear strengths, tensile strengths, and ice shell thickness in controlling the eruption phase delay. Using laboratory-determined ice strengths and the best estimate of the ice shell thickness at the South Polar Terrain of Enceladus, which hosts the tiger-stripe faults, our model results indicate that the endogenic tectonic stress is comparable in magnitude to the tidal stress. Although we cannot rule out warm-ice convection, true polar wander, and non-synchronous rotation as causes of endogenic stresses, the large variation in ice shell thickness makes the lateral gravitational-potential gradient the most plausible source of the endogenic stress required by our model results.

Viscoelasticity of hydrating shotcrete as key to realistic tunnel shell stress assessment with the New Austrian Tunneling Method

The New Austrian Tunneling Method (NATM) essentially rests on observational information concerning displacements measured in selected positions at the inner surface of shotcrete tunnel shells. The combination of these measurements with advanced material and structural mechanics, in the course of so-called hybrid methods, have successfully delivered, for more than 20 years, practically relevant estimations of internal and external forces and corresponding degrees of utilization. The reliability of the latter, however, may crucially depend on the used material model. Based on a recently proposed analytical structural mechanics model [Acta Mech 233, 2989–3019 (2022)], and focusing on the benchmark example of measurement cross section MC1452 of the Sieberg tunnel, driven in the 1990s in Miocene clay marl, the present paper compares the estimations of forces and degrees of utilization arising from differently refined constitutive concepts, namely (i) aging elasticity, (ii) aging linear viscoelasticity, and (iii) aging nonlinear viscoelasticity. It turns out that only the consideration of aging nonlinear viscoelastic material behavior provides access to realistic values for the degree of utilization, being lower than one. Simpler material models would indicate local material failure, which was not observed in situ.

On mechanics of piezocomposite shell structures

This study presents an original and novel investigation into the mechanics of piezo-flexo-magneto-elastic nanocomposite doubly-curved shells (PFMDCSs) and the ability to detect the lower and higher levels of electro-magnetic fields. In this context, by utilizing the first-order shear deformation shell model, stresses and strains are acquired. By imposing Hamilton's principle and the von Kármán approach, the governing equations have been obtained. The intelligent shell model consists of size-dependent influences, viz., strain gradients. This will take place via Mindlin's strain gradient elasticity theory and the subsequent re-establishing of the mathematical framework by incorporating this concept. The strain gradient results in a flexoelectric/flexomagnetic effect. The converse effect of the magnetic field on the basis of a close circuit has been assumed. The developed bending equations have been transferred into the algebraic ones by substituting an analytical technique based on homogeneous immovable simple support for the four edges. The problem has been solved according to the Newton-Raphson iteration scheme, and transverse deflections have been computed. For researching the rightness and precision of the shell models together with the solution process, a comparison is prepared by the finite element method (FEM) results for simplified shells, and a good correlation has been observed. At last, by examining several factors governing the problem, the conditions under which the magnetic effects can be noticeable and dominant in doubly-curved shells have been sought. This study could serve as a benchmark reference for piezoceramic-DCSs, as the presented governing equations are original. The most interesting outcome of this research is that the electro-magnetic response of intelligent structures can be entirely geometry-dependent.

A FE2 shell model with periodic boundary conditions for thin and thick shells

AbstractIn this article a FE2 shell model for thin and thick shells within a first order homogenization scheme is presented. A variational formulation for the two‐scale boundary value problem and the associated finite element formulation is developed. Constraints with 5 or 9 Lagrange parameters are derived which eliminate both rigid body movements and dependencies of the shear stiffness on the size of the representative volume elements (RVEs). At the bottom and top surface of the RVEs which extend through the total thickness of the shell stress boundary conditions are present. The periodic boundary conditions at the lateral surfaces are applied in such a way that particular membrane, bending and shear modes are not restrained. This is shown by means of a homogeneous RVE. The first of all linear formulation is extended to finite strain problems introducing transformation relations for the stress resultants and the material matrix. The transformations are performed at the Gauss points on macro level. Several boundary value problems including large deformations, stability and inelasticity are computed and compared with 3D reference solutions.

Unconventional cyclic plasticity model implementation for shell and plane stress elements in UMAT/Abaqus

Finite element simulations are widely used in several industrial sectors (civil, aerospace, mechanical, naval, biomedical, etc.) to design components or structures. Often, the resolution of highly non-linear problems requires the recurse to dense meshes with the consequent increase in computation time. This aspect becomes particularly relevant for cyclic mobility problems where repeated loading might affect the computational cost. Therefore, the efficiency of finite elements represents a crucial aspect of speeding up the design process. Past works of the authors focused on developing the additive hypoelastic-based and multiplicative hyperelastic-based constitutive equations of the Extended Subloading Surface model for three-dimensional finite elements adopting fully implicit integration schemes. In this paper, the constitutive equations of the Extended Subloading Surface theory are reformulated for shell and plane stress elements, aiming to obtain an efficient computational tool suitable for cyclic mobility problems. The numerical implementation considers isotropic hardening, kinematic hardening, and material anisotropy. Numerical solutions obtained utilising shell/plane stress and solids elements are also discussed.

Study on the Ultimate Load Failure Mechanism and Structural Optimization Design of Insulators.

This study aims to enhance the productivity of high-voltage transmission line insulators and their operational safety by investigating their failure mechanisms under ultimate load conditions. Destructive tests were conducted on a specific type of insulator under ultimate load conditions. A high-speed camera was used to document the insulator's failure process and collect strain data from designated points. A simulation model of the insulator was established to predict the effects of ultimate loads. The simulation results identified a maximum first principal stress of 94.549 MPa in the porcelain shell, with stress distribution characteristics resembling a cantilever beam subjected to bending. This implied that the insulator failure occurred when the stress reached the bending strength of the porcelain shell. To validate the simulation's accuracy, bending and tensile strength tests were conducted on the ceramic materials constituting the insulator. The bending strength of the porcelain shell was 100.52 MPa, showing a 5.6% variation from the simulation results, which indicated the reliability of the simulation model. Finally, optimization designs on the design parameters P1 and P2 of the insulator were conducted. The results indicated that setting P1 to 8° and P2 to 90.062 mm decreased the first principal stress of the porcelain shell by 47.6% and Von Mises stress by 31.6% under ultimate load conditions, significantly enhancing the load-bearing capacity. This research contributed to improving the production yield and safety performance of insulators.

Design method of variable slippage coefficient non‐geodesic filament‐wound composite pressure vessels

AbstractPrevious studies on the design methods of filament winding paths for composite pressure vessels have mainly focused on geodesic and constant slippage coefficient non‐geodesic patterns, neglecting the design of variable slippage coefficients along the fiber path. In this paper, a design method of variable slippage coefficient non‐geodesic filament wound composite pressure vessels is proposed. The study begins by establishing a meridian rotation mapping model and deriving fiber path equations on the shell surface. Subsequently, the fiber paths, curvature characteristics, slippage coefficients, and shell stress responses of the shell under variable geometrical parameters are simulated and analyzed. Next, the winding parameters are optimized while considering bandwidth and stable winding constraints. The optimal winding parameters are determined, and filament winding simulations are conducted on composite pressure vessels. Results demonstrate the feasibility of the proposed method for variable slippage coefficient fiber path winding mode, providing a new and effective filament winding path design approach for composite pressure vessels.Highlights Establishment of meridian rotation mapping model and simulation of shell fiber paths under variable geometric parameters. The fiber paths, curvature characteristics, slippage coefficients, and winding angles of the shell under variable geometrical parameters are simulated and analyzed. Stress response analysis of shells based on Tsai‐Wu failure criterion and classical lamination theory stress field dimensionless modeling. Construction of winding parameter optimization strategies and bandwidth error evaluation based on stable winding and fiber bandwidth constraints. Simulation of variable slippage coefficient non‐geodesic filament winding for composite pressure vessels with different parameters.

On issue of stress and curvature of shell of continuous cast billet

On issue of stress and curvature of shell of continuous cast billet

Impact Responses and Wave Dissipation Investigation of a Composite Sandwich Shell Reinforced by Multilayer Negative Poisson's Ratio Viscoelastic Polymer Material Honeycomb.

This analysis investigated the impact wave response and propagation on a composite sandwich shell when subjected to a low-velocity external shock, considering hygrothermal effects. The sandwich shell was crafted using face layers composed of functional gradient metal-ceramic matrix material and a core layer reinforced with negative Poisson's honeycomb. The honeycomb layer consisted of a combination of viscoelastic polymer material and elastic material. The equivalent parameters for the functional gradient material in the face layers were determined using the Mori-Tanaka and Voigt models, and the parameters for the negative Poisson's ratio honeycomb reinforcement core layer were obtained through Gibson's unit cell model. Parameters relevant to a low-velocity impact were derived using a modified Hertz contact law. The internal deformations, strains, and stress of the composite sandwich shell were described based on the higher-order shear deformation theory. The dynamic equilibrium equations were established using Hamilton's principle, and the Galerkin method along with the Newmark direct integration scheme was employed to calculate the shell's response to impact. The validity of the analysis was confirmed through a comparison with published literature. This investigation showed that a multilayer negative Poisson's ratio viscoelastic polymer material honeycomb-cored structure can dissipate impact wave energy swiftly and suppress shock effectively.

Influence of slab structure on the behavioral analysis of hybrid outrigger system

SummaryOutriggers are internal structural systems used to enhance the stiffness and strength of high‐rise structures. This research investigates the efficacy of a hybrid outrigger system (HOS) which consists of one conventional and one virtual outrigger at two distinct floor levels in high‐rise RCC buildings. A non‐dimensional quantity, ϒ, defined as the relative stiffness ratio between the core and the diaphragm is used to describe variations in the stiffness of the building's core, stiffness of floor diaphragm, breadth, and height of the structure, in the behavioral analysis of the HOS. To investigate the efficacy and optimum locations of the hybrid outriggers, static and dynamic analysis are carried out on models with four‐story heights of 140, 210, 280, and 350 m under static wind loading, uniform wind loading, equivalent static earthquake loading, and dynamic earthquake loading. Results are assessed based on the responses from roof displacement (Disptop), base bending moment, roof acceleration (Acctop), fundamental period, and absolute maximum inter‐story drift ratio (ISDabs.max). Based on the minimum responses of the aforementioned dependent parameters under wind and earthquake excitations, the corresponding optimum locations of hybrid outriggers are investigated. To investigate the impact of the slab on the functionality of the HOS, the behavior of shell stress variation in the tension and compression side of the slab at the outrigger floor level and the force transmission through the column at the outrigger level is analyzed. Also, the optimum location of the hybrid outriggers based on the ideal performance index (IdealPI) is investigated. IdealPI is defined as a parameter that considers the combined response of Disptop, Acctop, and ISDabs.max and the criteria required for the structure under wind and seismic loads. From the behavioral analysis results, it is found that an increase in the stiffness of the slab showed an improved performance of the HOS compared to an increase in the stiffness of the core, and HOS performance can be maximized by increasing both thickness of the slab and outrigger arm length. The findings of the optimum location analysis could serve as a guide for structural engineers when selecting suitable positions for hybrid outriggers in high‐rise structures.