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The purpose of this paper is to develop a general mathematical model for the evaluation of the theoretical flexural responses of the functionally graded carbon nanotube-reinforced composite doubly curved shell panel using higher-order shear deformation theory with thermal load. It is well-known that functionally graded materials are a multidimensional problem, and the present numerical model is also capable of solving the flexural behaviour of different shell panel made up of carbon nanotube-reinforced composite with adequate accuracy in the absence of experimentation.

In this current paper, the responses of the single-walled carbon nanotube-reinforced composite panel is computed numerically using the proposed generalised higher-order mathematical model through a homemade computer code developed in MATLAB. The desired flexural responses are computed numerically using the variational method.

The validity and the convergence behaviour of the present higher-order model indicate the necessity for the analysis of multidimensional structure under the combined loading condition. The effect of various design parameters on the flexural behaviour of functionally graded carbon nanotube doubly curved shell panel are examined to highlight the applicability of the presently proposed higher-order model under thermal environment.

In this paper, for the first time, the static behaviour of functionally graded carbon nanotube-reinforced composite doubly curved shell panel is analysed using higher-order shear deformation theory. The properties of carbon nanotube and the matrix material are considered to be temperature dependent. The present model is so general that it is capable of solving various geometries from single curve to doubly curved panel, including the flat panel.

The purpose of this paper is to analyse the nonlinear flexural behaviour of laminated curved panel under uniformly distributed load. The study has been extended to analyse different types of shell panels by employing the newly developed nonlinear mathematical model.

The authors have developed a novel nonlinear mathematical model based on the higher order shear deformation theory for laminated curved panel by taking the geometric nonlinearity in Green-Lagrange sense. In addition to that all the nonlinear higher order terms are considered in the present formulation for more accurate prediction of the flexural behaviour of laminated panels. The sets of nonlinear governing equations are obtained using variational principle and discretised using nonlinear finite element steps. Finally, the nonlinear responses are computed through the direct iterative method for shell panels of various geometries (spherical/cylindrical/hyperboloid/elliptical).

The importance of the present numerical model for small strain large deformation problems has been demonstrated through the convergence and the comparison studies. The results give insight into the laminated composite panel behaviour under mechanical loading and their deformation behaviour. The effects of different design parameters and the shell geometries on the flexural responses of the laminated curved structures are analysed in detailed. It is also observed that the present numerical model are realistic in nature as compared to other available mathematical model for the nonlinear analysis of the laminated structure.

A novel nonlinear mathematical model is developed first time to address the severe geometrical nonlinearity for curved laminated structures. The outcome from this paper can be utilized for the design of the laminated structures under real life circumstances.

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.

The purpose of this paper is to develop a general mathematical model for the evaluation of the bending and vibration responses of the skew sandwich composite plate using higher-order shear deformation theory. The sandwich structural components are highly preferable in modern engineering application because of their desirable structural advantages despite the manufacturing and analysis complexities. The present model is developed to solve the bending and vibration problem of the skew sandwich composite plate with adequate accuracy numerically in the absence of the experimental analysis.

The skew sandwich composite plate structure is modelled in the present analysis by considering laminated face sheet in conjunction with isotropic and/or orthotropic core numerically with the help of the higher-order mathematical model. Further, the responses are computed numerically with the help of in-house computer code developed in matrix laboratory (MATLAB) environment in conjunction with finite element (FE) steps. The system governing equations are derived via variational technique for the computation of the static and the frequency responses.

The skew sandwich composite plate is investigated using the higher-order kinematic model where the transverse displacement through the thickness is considered to be linear. The convergence and the validation study of the bending and the frequency values of the sandwich structure indicate the necessary accuracy. Further, the current model has been used to highlight the applicability of the higher-order kinematics for the evaluation of the sandwich structural responses (frequency and static deflections) for different design parameters.

In the present paper, the bending and the vibration responses of the skew sandwich composite plate are analysed numerically using the equivalent single-layer higher-order kinematic theory for the isotropic and the orthotropic core numerically with the help of isoparametric FE steps. Finally, it is understood that the present model is capable of solving the sandwich structural responses with less computation cost and adequate accuracy.

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 purpose of this paper is to develop a general mathematical model for laminated curved structure of different geometries using higher-order shear deformation theory to evaluate in-plane and out of plane shear stress and strains correctly. Subsequently, the model has to be validated by comparing the responses with developed simulation model (ANSYS) as well as available published literature. It is also proposed to analyse thermal buckling load parameter of laminated structures using Green–Lagrange type non-linear strains for excess thermal distortion under uniform temperature loading.

Laminated structures known for their flexibility as compared to conventional material and the deformation behaviour are greatly affected due to combined thermal/aerodynamic environment. The vibration/buckling behaviour of shell structures are very different than that of the plate structures due to their curvature effect. To model the exact behaviour of laminated structures mathematically, a general mathematical model is developed for laminated shell geometries. The responses are evaluated numerically using a finite element model-based computer code developed in MATLAB environment. Subsequently, a simulation model has been developed in ANSYS using ANSYS parametric design language code to evaluate the responses.

Vibration and thermal buckling responses of laminated composite curved panels have been obtained based on proposed model through a customised computer code in MATLAB environment and ANSYS simulation model using ANSYS parametric design language code. The convergence behaviour are tested and compared with those available in published literature and ANSYS results. Finally, the investigation has been extended to examine the effect of different parameters (thickness ratios, curvature ratios, modular ratios, number of layers and support conditions) on the free vibration and thermal buckling responses of laminated curved structures.

The present paper intends to give sufficient amount of numerical experimentation, which may lead to help in designing of finished product made up of laminated composites. Most of the aerospace, space research and defence organisation intend to develop low cost and high durable products for real hazard conditions by taking combined loading and environmental conditions. Further, case studies might lead to a lighter design of the laminated composite panels used in high-performance systems, where the weight reduction is the major parameter, such as aerospace, space craft and missile structures.

In this analysis, the geometrical distortion due to temperature is being introduced through Green–Lagrange sense in the framework of higher-order shear deformation theory for different types of laminated shells (cylindrical/spherical/hyperboloid/elliptical). A simulation-based model is developed using ANSYS parametric design language in ANSYS environment for different geometries and loading condition and compared with the numerical model.

To predict the critical flutter load and frequencies of doubly curved panels using first‐order shear deformation theory considering the effects of shear deformation and rotary inertia.Design/methodology/approach – A finite element analysis procedure is based on the extension of dynamic, shear deformable theory initially according to Sanders' theory, which can be reduced to Love's and Donnell's theories by means of tracers.Findings – Flutter is observed to be more common than divergence under follower loading; the magnitude of the flutter load is gradually decreasing with the increasing cut‐out size; load bandwidth and type of load conditions have significant influence on flutter and divergence characteristics of both isotropic and laminated curved panels; damping is perceived to have significant effect on flutter behaviour; the effect of direction control parameter with damping significantly affects the critical load.Practical implications – The practical behaviour of follower forces involving: aerodynamic drag; engine thrust; cantilever pipe conveying fluid; gas turbine rotor; automatic control system application; and automobile disk brakes can be monitored more successfully.Originality/value – Will assist students of elastic systems, both conservative and non‐conservative.

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.

Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.

Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.

A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.

FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.

The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.

Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

To investigate the large amplitude free flexural vibration of doubly curved shallow shells in the presence of cutouts.

Finite element model using an eight‐noded C⁰ continuity, isoparametric quadrilateral element is employed. Nonlinear strains of von Karman type are incorporated into the first‐order shear deformation theory.

Cylindrical shell shows mostly hard spring behavior whereas spherical shell shows both hard spring and soft spring behavior with the increase of amplitude ratios for different cutout sizes, radii of curvature and thickness parameters. At a particular value of the amplitude ratio, the frequency ratio of shells is governed by the interactive effects of stiffness and mass.

Aircraft, spacecraft and many other structures where shell panels are used, undergo large amplitude nonlinear vibrations.

The paper will assist researchers of vibration behavior of elastic systems.

A simple triangular shell element which incorporates the effects of coupling between membrane and flexural behaviour and avoids membrane locking is described. The element uses a discrete Kirchhoff bending formulation and a constant strain membrane element. For the purpose of permitting inextensional modes and thus avoiding membrane locking, a decomposition technique, which can also be viewed as a strain projection method, is used. The method is illustrated first for a beam element and then for a triangular shell element. Results are presented for a variety of linear static problems to illustrate its accuracy and some highly non‐linear problems to indicate its applicability to collapse analysis.