Analysis Of Shells Research Articles

Spectro-geometry dynamic analysis of FG-GPLRC cylindrical shell with periodically embedded dynamic vibration absorbers

This study presents a theoretical model of the functionally graded graphene platelet-reinforced composite (FG-GPLRC) cylindrical shell with periodically embedded dynamic vibration absorbers (DVAs) under different boundary constraints. The material parameters of the FG-GPLRC were first determined using the Halpin-Tsai micromechanical method and the general law of mixing. The energy expression for the system is developed based on the first-order shear deformation theory (FSDT). A simplified model of the DVA is carried out, which consists of a mass block, a linear damper and a linear spring after simplification. Displacement field vectors of the cylindrical shell are established based on the spectro-geometric method (SGM). The Rayleigh-Ritz method was used to determine the vibration response of the coupled model. The validity of the proposed method is confirmed through comparing with results from existing literature and finite element method (FEM) calculations. The effect of boundary conditions, FG-GPLRC material properties, geometrical parameters of cylindrical shells, distribution parameters of DVAs, and damping coefficient on the steady-state vibration of the coupled model is investigated on this basis.

Bending-based solution methodology using eigenvalue-eigenvector approach for analysis of foldable reinforced Golf Clubs cylindrical shell

This paper is organized to present eigenvalue-eigenvector based solution method for elastic bending analysis of foldable Golf Clubs cylindrical shell reinforced with graphene origami. The axisymmetric kinematic and constitutive relations are extended using the models with shear deformability and three-dimensional relations. The effective material properties are inserted into integration constants and constitutive relations in terms of angle and content of folded structure as well as thermal load. The virtual work principle is extended in order to derive governing equations and the eigenvalue-eigenvector method is applied for analytical solution. The results are presented along the longitudinal and radial coordinates with changes of angle and content of folded structure as well as thermal load. The results of this analysis may be used for optimized design and manufacturing of the golf clubs and other sport equipment.

Free and forced vibration analysis of uniform and stepped conical shell based on Jacobi-Ritz time domain semi-analytical method

Free and forced vibration analysis of uniform and stepped conical shell based on Jacobi-Ritz time domain semi-analytical method

A general element for shell analysis based on the scaled boundary finite element method

AbstractA novel technique, the scaling surface‐based Scaled Boundary Finite Element Method (SBFEM), is introduced as a method for formulating a general element for shell analysis. This displacement‐based element includes three translational degrees of freedom (DOFs) per node. Notably, only two‐dimensional discretization for one of the two parallel shell surfaces, referred to as the scaling surface, is necessary. The interpolation scheme for the scaling surface is postulated to be applicable to all surfaces parallel to it in the thickness. The derivation strictly adheres to the 3D theory of elasticity, without making additional kinematic assumptions. As a result, the displacement field along the thickness is analytically solved, and the element formulation is immune to transverse locking, membrane locking, and other issues, eliminating the need for additional remedies. Extensive investigations into the robustness and accuracy of the elements have been conducted using well‐known benchmark problems, along with additional challenging problems. Numerical examples confirm that the element formulation is free from transverse shear locking and membrane locking. Moreover, the proposed formulation is easily extendable to cases involving shell elements with varying thickness and holds the potential for extension to the nonlinear response analysis of shell structures.

Csr In Emerging Markets: Challenges And Opportunities For Shell Companies

This article explores the challenges and opportunities of Corporate Social Responsibility (CSR) in emerging markets, focusing on a case study of a Shell company. Emerging markets present unique dynamics that affect the implementation and effectiveness of CSR. Shell, as one of the world's largest energy companies, has operated in various emerging markets and sought to implement effective CSR practices. Through an in-depth analysis of Shell's operations in these markets, this article identifies key factors that influence CSR success and provides recommendations for best practices. It finds that while there are significant challenges related to local regulations, infrastructure and culture, there are great opportunities to increase CSR impact through collaboration with local stakeholders, technological innovation and local capacity building. The article concludes that adaptation and flexibility are key for multinational companies like Shell to face the challenges and capitalize on the opportunities of CSR in emerging markets.

Fast analysis approach for instability problems of thin shells utilizing ANNs and a Bayesian regularization back-propagation algorithm

Abstract This research develops a data-driven methodology for structural instability problems with highly nonlinear, difficult, noisy, and small data. A fast analysis and prediction (FAP) approach for instability problems of thin shells is first proposed. This approach contains two phases: the fast numerical analysis and the pure prediction utilizing artificial neural networks (ANNs) incorporated with the Bayesian regularization (B-R) algorithm as follows: (1) in Phase 1 (the fast numerical analysis), post-buckling analysis is conducted utilizing a minor amount of load steps. The load–displacement relation achieved from Phase 1 is not exact because of the small number of load steps utilized; (2) in Phase 2 (the prediction), the loads and deflections achieved from Phase 1 were employed as the data for training ANNs. The trained networks, including the load and displacement networks, were employed to fast predict loads and deflections at any step of the post-buckling analysis. After utilizing Phase 2, a smooth, complete and exact load–displacement curve was achieved. In Phase 1, the available formulation for post-buckling analysis of thin shells in the literature was utilized. Five popular types of instabilities chosen to confirm the effectiveness and exactness of the FAP were snap-through, snap-back, softening–hardening, kink instabilities, and delamination buckling and post-buckling of composites. The high exactness and effectiveness of the FAP were confirmed in the numerical verification section. The present approach saves a huge computation compared to the other ones. It was found that ANNs incorporated with the B-R algorithm have notable advantages compared to numerous neural networks. The proposed approach is applicable to simulations or experiments where data are “expensive”, highly nonlinear, difficult, and limited. Utilizing the proposed approach for these fields can dramatically save time and money.

Nonlinear static and dynamic analysis of corotational shell formulated on the special Euclidean group SE(3)

Nonlinear static and dynamic analysis of corotational shell formulated on the special Euclidean group SE(3)

Thermo-foldable bending analysis of tunable shells using a higher-order modeling

This article investigates effect of a higher order kinematic modeling on the elasto-static bending results of a shell in double curved form. The graphene origami is introduced in this article as a novel nanofiller with some chemical process to arrive at a controllable material. A copper matrix is used as main constituent reinforced with folded graphene origami. The virtual work principle is used to derive governing equations of the thickness-stretchable shell. After derivation of the governing equations and to arrive at the solution, a class of formulas is used from valid sources for effective material properties of the shell. A verification test is presented before exploring the effect of all main affecting parameters of the graphene origami and ambient on the bending results. The results of this work may be used in the analysis of structures with controllable responses.

Peculiarities of the Dynamical Hydration Shell of Native Conformation Protein Using a Bovine Serum Albumin Example.

This paper describes an approach based on the method of terahertz time-domain spectroscopy, which allows the analysis of dynamical hydration shells of proteins with a thickness of 1-2 nm. Using the example of bovine serum albumin in three conformations, it is shown that the hydration shells of the protein are characterized by increased binding of water molecules in the primary hydration layers, and in more distant areas of hydration, on the contrary, the water structure is somewhat destroyed. The fraction of free or weakly bound molecules, usually observed in the structure of liquid water in hydration shells, become more numerous but its average binding is greater than in undisturbed water. The energy distribution of hydrogen bonds in hydration shells is narrowed compared to undisturbed water. All these manifestations of hydration are most pronounced for the native conformation of the protein. Also, the hydration shells of the native protein are characterized by a smaller number of hydrogen bonds and a tendency to decrease their average energy compared to non-native conformations. The fact of a pronounced peculiarity of the hydration shells of the protein in the native conformation has been noted for different proteins before. However, the methodological approach used in this work for the first time allowed this peculiarity to be described by specific parameters of the intermolecular structure and dynamics of water.

Vibration and damping analyses of sandwich cylindrical and conical shells using meshfree method

Vibration and damping analyses of sandwich cylindrical and conical shells using meshfree method

Isogeometric method for buckling prediction and post-buckling analysis of variable stiffness composite underwater pressure shell

Composite cylindrical pressure hulls are thin-walled structures widely used for autonomous underwater vehicles. Buckling failure is one of the most important failure modes for these shells under external pressure. In existing buckling studies of cylindrical pressure hulls, FEM is the most popular analysis method but not efficient enough when dealing with structures with complex material distributions such as the variable stiffness composite shells. Motivated by this, an isogeometric method for buckling prediction and post-buckling analysis of variable stiffness composite underwater pressure shell is proposed in this article. In this method, based on Reissner–Mindlin shell formulas undergoing large deformation, a buckling analysis framework in IGA forms is established. Then a modified arc-length method is proposed based on kinematics used in the shell formulas, and is used to overcome the inaccuracy caused by the 2 degrees of freedom node rotation in the prediction step of arc-length method. In addition, the influence of bifurcation is considered, which may seriously affect the precision of buckling behavior simulation when the limit point is close to a bifurcation point. The computational accuracy of this framework has been validated in a series of constant stiffness composite shell cases involving buckling load prediction and post-buckling behavior simulation. For variable stiffness composite hull cases, this framework achieves the same precision as FEM with fewer elements. Therefore, the proposed framework provides an efficient way for the buckling design of underwater variable stiffness composite pressure hulls.

A reliability-based design against post-buckling load drop in spherical shell cap with stochastic imperfections

Elastic buckling is a critical design consideration for deep spherical shell caps. Significant reduction is observed in the experimental critical load from the linearized eigen-buckling analysis, for reasons extensively discussed in the past and relooked recently through the energy barrier concepts. The Knock Down Factors (KDFs) were proposed to account for such a reduction. The highly conservative KDFs constitute the lower bound of a large experimental dataset; that can be reconciled by nonlinear stability analysis of the imperfect shell. This study models the KDFs as Uncertain-but-Bounded (UBB) variables to present a Reliability-Based Design (RBD) for spherical shell caps having random geometric imperfections in radius (R) and thickness (t). The RBD furnishes the pertinent design variables ((R/t) ratio and the dome height-to-base radius (H/r0) ratio) for a target reliability index (β) and the respective KDFs. A metamodelling approach is employed to reduce the computational burden of the proposed RBD for a thin spherical shell cap having zero-mean, stationary, homogeneous, gaussian stochastic geometric imperfections. The Riks algorithm is employed in the commercial code ABAQUS for the finite element-based nonlinear stability analysis of shells. The KDFs and the reliability bounds are presented for varying degrees of imperfections. Remarkably, the margin of conservatism in the KDFs is shown to be narrowed down by incorporating the dependency on (H/r0).

Seismic vulnerability analysis of single-layer lattice shells with different rise-to-span ratios: Focusing on the selection of Sa(T1)-based intensity measures

This study conducted a detailed examination of seismic vulnerability across different limit states for Schwedler single-layer lattice shells with differing rise-to-span ratios. A comparative analysis of seismic intensity measures, particularly those centered around Sa(T1), was performed to evaluate their effectiveness in vulnerability analysis. To comprehensively address the inherent uncertainties in seismic actions, the study selected a dual set of ground motion scenarios, encompassing both far-field and pulse-type near-field events. A novel approach was employed, integrating a multi-indicator seismic performance assessment model based on the residual seismic safety framework, aiming to thoroughly quantify the cumulative seismic damage to lattice structures. Utilizing the multiple stripes analysis technique enabled the efficient generation of analytical results for vulnerability assessments at various damage thresholds. The findings revealed that lattice shells with larger rise-to-span ratios exhibit increased seismic robustness, notably with far-field seismic events causing more significant damage than their pulse-type near-field counterparts. Furthermore, the study determined that employing seismic intensity measures which consider the effects of higher modes significantly reduces variability in the vulnerability analysis when dealing with pulse-type near-field seismic activity. As a result, the use of the seismic intensity measure IM123 is recommended for assessing the vulnerability of lattice shells with varying rise-to-span ratios, under both far-field and near-field seismic conditions.

Buckling analysis of FGM shells of revolution in thermal environment

This work presents an analytical investigation for analyzing the mechanical buckling of shells of revolution made of functionally graded materials, subjected to external uniform pressure taking into account the effects of uniform temperature rise. The material compositions only vary smoothly along its thickness direction with the power law distribution. Using the adjacent equilibrium criterion and classical shell theory, the linearization stability equations have been established. The resulting equations which they are the system of three variable coefficient partial differential equations in terms of displacement components are investigated by Galerkin method. The closed-form expression for determining the critical buckling load is obtained. In numerical results, the effects of material properties, dimensional parameters, and temperature on the buckling of shells of revolution are discussed in details.

Vibration analysis of an open cylindrical thin shell under random excitation

This paper introduces an analytical approach to the random vibration of a cylindrical thin shell structure with an opening angle of 180°. The approach involves employing the exact analytical solution for the natural vibration of a thin shell structure with an opening, grounded in a continuum model, and a pseudo-excitation method to derive the exact analytical solution of the random response power spectral density for the open cylindrical thin shell structure. Simultaneously, a comparison is made between the results obtained through the analytical method and those obtained by using the finite element program, confirming the effectiveness of the analytical model constructed in this study. Finally, an analysis is conducted on the impact of thickness on the characteristics of the vibration response of the open cylindrical thin shell.

Integrated Crashworthiness Analysis of Electric Vehicle Battery Shells and Chassis: A Finite Element Study with Abaqus

This paper aims to comprehend and predict the mechanical behavior of the genuine Tesla Model-S chassis and the battery module during a crash in Abaqus/Explicit. The parametric method was incorporated with varying impact velocities from 27.7, 55.5, and 100m/s and battery shell thickness from 1mm to 3mm. The asymmetry model was considered for both the chassis and battery pack. Aluminum 6061 and ASI430 SS are assigned to the chassis profile and the battery shells (cells). A Johnson-Cook (JC) plastic and damage failure model has been implemented to simulate realistic crash behavior. Displacement, energy, and force results were captured during the simulation. A battery shell thickness of 3mm showed higher resistance than a 1mm thick shell at 55.5 m/s. The numerical findings reveal the dynamic response in displacement and compression under various loading conditions for both individual profiles. Additionally, the study presents a detailed inspection of each cell module, graphically demonstrating how the individual cells respond to initial positions, crashes, and external deformation (shear) caused by collision energy. The finite element model is validated against previous experimental and numerical studies, successfully simulating crashworthiness. The present study provides significant insights that have the potential to improve the safety and efficiency of battery-operated vehicles through the design and optimization of their structures.

Static and dynamic buckling analysis of two-layer shells include auxetic honeycomb core combined with laminated three-phase polymer/GNP/fiber surface resting on Kerr elastic medium in hygro-thermal environments

This article investigates the static and dynamic buckling behavior of a double-curved sandwich shell composed of two layers via improved first-order shear deformation theory without using the shear correction is utilized to model the sandwich shell. The sandwich two-layer shell are held together by elastic pins, each layer made from an ultra-light auxetic honeycomb core layer (negative Poisson’s ratio) and is reinforced by a layer of tri-phase polymer, graphene nanoplatelets (GNP), and fiber. The double-curved sandwich shell is supported by a Kerr elastic medium in hygro-thermal environment assuming that temperature and humidity only cause forces to be applied tangentially to the shell and do not change the mechanical properties of the shell material. The motion equations of sandwich two-layer shell are derived by Hamilton’s principle, then the finite element method and Bolotin method are used to derive the dynamic instability region of sandwich two-layer shell. The accuracy of these results is confirmed by a comparison with established statements within the specific conditions of the problem model. The influence of inputs on the static and dynamic stability of sandwich two-layer shell is fully explored and discussed. Additionally, this serves as a crucial foundation for the calculation and design of structures that can integrate a variety of materials with different properties with low cost and simplification.

Free vibration analysis of a sandwich conical shell with a magnetorheological elastomer core, enriched with carbone nanotubes and functionally graded porous face layers

In this paper, the free vibration behaviors of a sandwich conical shell with a magnetorheological elastomer (MRE) core enriched with carbon nanotubes (CNTs) and two functionally graded (FG) porous face layers are investigated. The mathematical modeling of the shell is performed via the first-order shear deformation theory (FSDT) incorporating the continuity conditions between the face layers and the core. The porosity parameters are adjusted to provide the same mass for all porosity dispersion patterns. The governing equations and boundary conditions are derived via Hamilton’s principle and are solved through a semi-analytical solution to attain the natural frequencies and the loss factors for various boundary conditions. First, appropriate triangular functions are utilized to provide an exact solution in the circumferential direction. Then, a numerical solution is presented in the meridional direction utilizing the differential quadrature method (DQM). The influences of various factors on the natural frequencies and loss factors are investigated including intensity of the applied magnetic field, mass fraction of the CNTs subjoined to the core, thickness of the CNT-reinforced MRE core, thickness of the FG porous face layers, porosity parameter and dispersion pattern of the pores in the FG porous face layers, and the boundary conditions. Numerical results show that although subjoining CNTs to the MRE core and applying magnetic field have weak effects on the natural frequencies of the shell, increases in the mass fraction of the CNTs and intensity of the applied magnetic field result in remarkable increases in the loss factors, and provide stronger vibration suppression.

Amplified seasonality in western Europe in a warmer world.

Documenting the seasonal temperature cycle constitutes an essential step toward mitigating risks associated with extreme weather events in a future warmer world. The mid-Piacenzian Warm Period (mPWP), 3.3 to 3.0 million years ago, featured global temperatures approximately 3°C above preindustrial levels. It represents an ideal period for directed paleoclimate reconstructions equivalent to model projections for 2100 under moderate Shared Socioeconomic Pathway SSP2-4.5. Here, seasonal clumped isotope analyses of fossil mollusk shells from the North Sea are presented to test Pliocene Model Intercomparison Project 2 outcomes. Joint data and model evidence reveals enhanced summer warming (+4.3° ± 1.0°C) compared to winter (+2.5° ± 1.5°C) during the mPWP, equivalent to SSP2-4.5 outcomes for future climate. We show that Arctic amplification of global warming weakens mid-latitude summer circulation while intensifying seasonal contrast in temperature and precipitation, leading to an increased risk of summer heat waves and other extreme weather events in Europe's future.

Geometric Characteristics of Surfaces with Curved Trapezoidal Plan

A method of forming a curved orthogonal coordinate system on a plane and a technique of constructing new surface shapes with curved trapezoidal plans are presented. Multiple examples of curved trapezoidal plans based on different directrix curves and surfaces with the given plans, including combinations of surfaces with different conjugate directrix curves, are illustrated. The proposed technique of surface forming may be used in architecture and construction for development of thin-walled space structures in both urban and industrial buildings. But for the analysis of thin shells, geometric characteristics of the middle surface of the shell are usually used. Vector equation of surfaces with curved trapezoidal plan was used to obtain the formulas for the fundamental form coefficients and surface curvatures. Examples of calculation of the fundamental form coefficients and curvatures of surfaces with particular directrix curves and vertical coordinate functions are presented.