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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The objective of the present work is to present the design optimization of composite cylindrical shell subjected to an axial compressive load and lateral pressure.

A novel optimization method is developed to predict the optimal fiber orientation in composite cylindrical shell. The optimization is carried out by coupling analytical and finite element (FE) results with a genetic algorithm (GA)-based optimization scheme developed in MATLAB. Linear eigenvalue were performed to evaluate the buckling behaviour of composite cylinders. In analytical part, besides the buckling analysis, Tsai-Wu failure criteria are employed to analyse the failure of the composite structure.

The optimal result obtained through this study is compared with traditionally used laminates with 0, 90, ±45 orientation. The results suggest that the application of this novel optimization algorithm leads to an increase of 94% in buckling strength.

The proposed optimal fiber orientation can provide a practical and efficient way for the designers to evaluate the buckling pressure of the composite shells in the design stage.

The main idea is the comparison between composites including natural fibres (such as the linoleum fibres) and typical composites including carbon fibres or glass fibres. The comparison is proposed for different structures (plates, cylinders, cylindrical and spherical shells), lamination sequences (cross-ply laminates and sandwiches with composite skins) and thickness ratios. The purpose of this paper is to understand if linoleum fibres could be useful for some specific aerospace applications.

A general exact three-dimensional shell model is used for the static analysis of the proposed structures to obtain displacements and stresses through the thickness. The shell model is based on a layer-wise approach and the differential equations of equilibrium are solved by means of the exponential matrix method.

In qualitative terms, composites including linoleum fibres have a mechanical behaviour similar to composites including glass or carbon fibres. In terms of stress and displacement values, composites including linoleum fibres can be used in aerospace applications with limited loads. They are comparable with composites including glass fibres. In general, they are not competitive with respect to composites including carbon fibres. Such conclusions have been verified for different structure geometries, lamination sequences and thickness ratios.

The proposed general exact 3D shell model allows the analysis of different geometries (plates and shells), materials and laminations in a unified manner using the differential equilibrium equations written in general orthogonal curvilinear coordinates. These equations written for spherical shells degenerate in those for cylinders, cylindrical shell panels and plates by means of opportune considerations about the radii of curvature. The proposed shell model allows an exhaustive comparison between different laminated and sandwich composite structures considering the typical zigzag form of displacements and the correct imposition of compatibility conditions for displacements and equilibrium conditions for transverse stresses.

The purpose of this study is to prepare ZnFe₂O₄ nanospheres, sheet MoS₂ and three ZnFe₂O₄@MoS₂ core-shell composites with various shell thicknesses, and add them to the base oil for friction and wear tests to simulate the wear conditions of hybrid bearings.

Through the characterization and analysis of the morphology of wear scars and the elemental composition of friction films, the tribological behavior and wear mechanism of sample materials as lubricant additives were investigated and the effects of shell thickness and sample concentration on the tribological properties of core–shell composite lubricant additives were discussed.

The findings demonstrate that each of the five sample materials can, to varying degrees, enhance the lubricating qualities of the base oil and that the core–shell nanocomposite sample lubricant additive has superior lubricating properties to those of ZnFe₂O₄ and MoS₂ alone, among them ZnFe₂O₄@MoS₂-2 core–shell composites with moderate shell thickness performed most ideally. In addition, the optimal concentration of the ZnFe₂O₄@MoS₂ lubricant additive was 0.5 Wt.%, and a concentration that was too high led to particle deposition and affected the friction effect.

In this work, ZnFe₂O₄@MoS₂ core–shell composites were synthesized for the first time using ZnFe₂O₄ as the carrier and the lubrication mechanism of core–shell composites and single materials were compared and studied, which illustrated the advantages of core–shell composite lubricant additives. At the same time, the influence of different shell thicknesses on the lubricant additives of core–shell composites was studied.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2022-0367/

To investigate the effects of delamination on free vibration characteristics of graphite‐epoxy composite pretwisted cylindrical shallow shells of various stacking sequences considering length of delamination as a parameter.

A multipoint constraint algorithm which leads to unsymmetric elastic stiffness matrix is incorporated into an eight noded isoparametric plate bending finite element to satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The study is focused upon long, intermediate and short cylindrical shells as defined by Aas‐Jakobsen's parameters and considers symmetric and unsymmetric composite laminates.

The non‐dimensional fundamental natural frequencies are obtained for angle ply (45/−45/45, 45/−45) and cross ply (0/90/0, 0/90) configurations corresponding to different crack lengths and twist angles. The study implies the importance of the symmetric laminate as well as the long shell.

The standard eigenvalue computations using QR iteration algorithm for the present analyses take enormous time and hence, an efficient eigen‐solver needs to be employed.

New vibration modes are exhibited by the delaminated composite structures. The existence of invisible interlaminar cracking can be identified with the help of prior knowledge of natural frequencies for a delaminated composite pretwisted shell which can be idealized as a turbine blade with low aspect ratio.

This paper presents a numerical approach for natural frequency determination of composite pretwisted shallow shells having delamination without taking care of the effect of dynamic contact between delaminated layers. The non‐dimensional frequencies obtained could serve as reference solutions for future investigators.

In this paper we derive a simple finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurrence of finite rotations which are described by two independent angles. A layerwise linear elastic material model for composites has been chosen. A consistent linearization of all equations has been derived for the application of a pure Newton method in the nonlinear solution process. Thus a quadratic convergence behaviour can be achieved in the vicinity of the solution point. Examples show the applicability and effectivity of the developed element.

The aim of this paper is to investigate the initiation and progress of damage in laminated composite shells at elevated moisture concentration and temperature due to low‐velocity impacts.

A finite element analysis procedure is developed to investigate the initiation and propagation of damage in laminated composite shells in hygrothermal environments.

It was found inter alia, that in the case of rise of temperature present FEM results match well with closed form solutions and that stress results at different levels of moisture concentration agree with the results published in the open literature.

The paper provides in‐depth insight into the progress of damage in laminated shell structures.

The paper investigates initiation and progress of damage in laminated composite shell structures due to low‐velocity impacts.

The purpose of this paper is to propose a comparative study between different structures composed of fiber-reinforced composite materials. Plates, cylinders and cylindrical and spherical shell panels in symmetric 0°/90°/0° and antisymmetric 0°/90°/0°/90° configurations are analyzed considering carbon fiber, glass fiber and linoleum fiber reinforcements.

A free vibration analysis is proposed for different materials, lamination sequences, vibration modes, half-wave numbers and thickness ratios. Such an analysis is conducted by means of an exact three-dimensional shell model which is valid for simply supported structures and cross-ply laminations. The employed model is based on a layer-wise approach and on three-dimensional shell equilibrium equations written in general orthogonal curvilinear coordinates.

The proposed study confirms the well-known superiority of the carbon fiber-reinforced composites. Linoleum fiber-reinforced composites prove to be comparable to glass fiber-reinforced composites in the case of free vibration analysis. Therefore, similar frequencies are obtained for all the geometries, thickness ratios, laminations sequences, vibration modes and a large spectrum of half-wave numbers. This partial conclusion needs further confirmations via static, buckling and fatigue analyses.

An exact three-dimensional shell model has been used to compare several geometries embedding carbon fiber composites and natural fiber composites.

This paper aims to analyze the stability of laminated shells subjected to axial loads or external pressure with considering various geometries and boundary conditions. The main aim of the present study is developing an efficient combined method which uses the advantages of different methods, such as finite element method (FEM) and isogeometric analysis (IGA), to achieve multipurpose targets. Two types of material including laminated composite and sandwich functionally graded material are considered.

A novel type of finite strip method called isogeometric B3-spline finite strip method (IG-SFSM) is used to solve the eigenvalue buckling problem. IG-SFSM uses B3-spline basis functions to interpolate the buckling displacements and mapping operations in the longitudinal direction of the strips, whereas the Lagrangian functions are used in transverse direction. The current presented IG-SFSM is formulated based on the degenerated shell method.

The buckling behavior of laminated shells is discussed by solving several examples corresponding to shells with various geometries, boundary conditions and material properties. The effects of mechanical and geometrical properties on critical loads of shells are investigated using the related results obtained by IG-SFSM.

This paper shows that the proposed IG-SFSM leads to the critical loads with an approved accuracy comparing with the same examples extracted from the literature. Moreover, it leads to a high level of convergence rate and low cost of solving the stability problems in comparison to the FEM.

A linear and geometrically non‐linear computation of a laminated composite torispherical shell subjected to internal pressure was performed by using the layered finite element whose formulation is based on degeneration principle. Geometric non‐linearity in terms of large deformations with total Lagrangian formulation was taken into account. The effect of the lamination schemes on geometric non‐linear behaviour and stress resultant distributions was analysed. The fibre directions have not a great influence on the shape of the load‐displacement curves. In contrast to the hoop stress resultant distribution, the moment distribution is significantly influenced by the lamination schemes. The influence of the lamination schemes on bending moments is greater in non‐linear than in linear computations. Likewise, the effect of the fibre orientation is greater on the hoop than on the meridional moment distribution. In unsymmetric laminated shells the values of the hoop moments exceed those of the meridional moments which is a considerable difference from metallic isotropic shells.