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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.

The purpose of this paper is to investigate the linear and non-linear free vibration of a functionally graded material (FGM) rotating cantilever plate in the thermal environment. The study employs the development of a non-linear mathematical model using the higher order shear deformation theory in which the traction free condition is applied to derive the simplified displacement model with seven field variables instead of nine.

A mathematical model is developed based on the higher order shear deformation theory using von-Karman type non-linearity. The rotating plate domain has been discretized into C0 eight-noded quadratic serendipity elements with node wise 7 degrees of freedom. The material properties are considered temperature dependent and graded along the thickness direction obeying a simple power law distribution in terms of the volume fraction of constituents, based on Voigt’s micromechanical method. The governing equations are derived using Hamilton’s principle and are solved using the direct iterative method.

The importance of the present mathematical model developed for numerical analysis has been stated through the comparison studies. The results provide an insight into the vibration response of FGM rotating plate under thermal environment. The influence of various parameters like setting angle, volume fraction index, hub radius, rotation speed parameter, aspect ratio, side-thickness ratio and temperature gradient on linear and non-linear frequency parameters is discussed in detail.

A non-linear mathematical model is newly developed based on C0 continuity for the functionally graded rotating plate considering the 1D Fourier equation of heat conduction. The present findings can be utilized for the design of rotating plates made up of a FGM in the thermal environment under real-life situations.

Recently, a new formulation has been introduced for non-local mechanics in terms of fractional calculus. Fractional calculus is a branch of mathematical analysis that studies the differential operators of an arbitrary (real or complex) order and is used successfully in various fields such as mathematics, science and engineering. The purpose of this paper is to introduce a new fractional non-local theory which may be applicable in various simple or complex mechanical problems.

In this paper (by using fractional calculus), a fractional non-local theory based on the conformable fractional derivative (CFD) definition is presented, which is a generalized form of the Eringen non-local theory (ENT). The theory contains two free parameters: the fractional parameter which controls the stress gradient order in the constitutive relation and could be an integer and a non-integer and the non-local parameter to consider the small-scale effect in the micron and the sub-micron scales. The non-linear governing equation is solved by the Galerkin and the parameter expansion methods. The non-linearity of the governing equation is due to the presence of von-Kármán non-linearity and CFD definition.

The theory has been used to study linear and non-linear free vibration of the simply-supported (S-S) and the clamped-free (C-F) nano beams and then the influence of the fractional and the non-local parameters has been shown on the linear and non-linear frequency ratio.

A new parameter of the theory (the fractional parameter) makes the modeling more fixable – this model can conclude all of integer and non-integer operators and is not limited to special operators such as ENT. In other words, it allows us to use more sophisticated mathematics to model physical phenomena. On the other hand, in the comparison of classic fractional non-local theory, the theory applicable in various simple or complex mechanical problems may be used because of simpler forms of the governing equation owing to the use of CFD definition.

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.

In this paper, the problem of the elasto‐viscoplastic dynamic and thermal behaviour of geometrically non‐linear plates and shells is studied under the assumption of small strains and large rotations. The first‐order shear deformation shell theory and the Chaboche constitutive viscoplastic model taking the temperature fields into account are used for computations. An effective procedure using the central difference method of solving the equations of motion is applied. The trapezoidal method is used to integrate the constitutive viscoplastic law. A nine node isoparametric shell element has been utilised for the finite element algorithm. Finally, some examples are presented and compared with the results obtained by moderate rotation theory.

The paper reviews the application of the finite element method to the analysis of large‐deflection elasto‐plastic behaviour and traces the development of such a solution for plated structures. The accuracy of the approach is established by many comparisons with available solutions for isolated plates and conclusions are drawn on suitable idealizations for plated structures. The results of an analysis of a typical plate girder, allowing fully for the interaction between the component plates, are presented. Comparisons with experimentally measured values for the girder confirm the validity of the proposed approach for the study of the collapse modes of plated structures. The need for expensive experimentation is thereby reduced.

This paper deals with the well known degenerated shell element of Ahmad. The main concern focuses on the rank of the element stiffness matrix and the zero energy modes. Element formulation includes geometrical and material non‐linearities. The Lagrangian, heterosis and serendipity variants of displacement approximation are studied using full, selective or reduced in‐plane numerical integration. In the third direction the layered concept is adopted. The obtained results do not fully coincide with those published in References 2 and 3. The Figures presented in this paper, showing the displacement modes, clarify in a convenient form some of the element properties associated with particular element formulations. The work also shows the influence of the plastic and cracked material conditions on the stiffness matrix of the element.

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.

A unified approach is presented for the pseudo‐transient (static) linear and geometrically non‐linear analyses of composite laminates. A finite element idealization with a four‐noded linear and a nine‐noded quadrilateral isoparametric elements, both belonging to the Lagrangian family are used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. The accuracy of the formulation is then established by comparing the presnt pseudo‐transient analysis results with the present static Newton‐Raphson method results and other available analytical closed‐form two dimensional and finite element solutions. The usefulness and effectiveness of this approach is established by comparing computational time required by this approach and Newton‐Raphson's approach.

The aim of the present investigation was to study numerically the transient of thermal convection in a square cavity filled with low‐Prandtl‐number fluids. The flow is driven by the horizontal temperature gradient between the vertical walls maintained at different temperatures. Two‐dimensional equations of conservation and energy are solved using a finite element method and a fractional step time. The discrete equations systems are solved in the lap of each element‐mesh with the aim of verifying the Boussinesq hypothesis locally. To compare our results with the earlier predictions, we have chosen the fluids for Prandtl‐numbers 0.001, 0.005 and 0.01 and with Grashof numbers up to 1 × 10⁷. To predict the steady state solutions with an oscillary transient period, the results are reduced in terms of the time series average Nusselt‐number at the vertical walls, the velocity at the center of the cavity and near right boundary. In addition, the isotherms and the velocity field are produced with the aim of showing the main circulation and particularly the weak circulations at the corners of the cavity.