• Steel and Composite Structures
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• v.16 no.4
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• pp.339-356
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• 2014

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

• Steel and Composite Structures
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• v.34 no.4
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• pp.615-623
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• 2020

In this paper, free vibration analysis of a functionally graded cylindrical nanoshell resting on Pasternak foundation is presented based on the nonlocal elasticity theory. A two-dimensional formulation along the axial and radial directions is presented based on the first-order shear deformation shell theory. Hamilton's principle is employed for derivation of the governing equations of motion. The solution to formulated boundary value problem is obtained based on a harmonic solution and trigonometric functions for various boundary conditions. The numerical results show influence of significant parameters such as small scale parameter, stiffness of Pasternak foundation, mode number, various boundary conditions, and selected dimensionless geometric parameters on natural frequencies of nanoshell.

• Steel and Composite Structures
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• v.14 no.5
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• pp.511-521
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• 2013

In this study we have considered the governing nonlinear equation of an eccentrically reinforced cylindrical shell. A new analytical method called He's Variational Approach (VA) is used to obtain the natural frequency of the nonlinear equation. This analytical representation gives excellent approximations to the numerical solution for the whole range of the oscillation amplitude, reducing the respective error of angular frequency in comparison with the variation approach method. It has been proved that the variational approach is very effective, convenient and does not require any linearization or small perturbation. Additionally it has been demonstrated that the variational approach is adequately accurate to nonlinear problems in physics and engineering.

• Steel and Composite Structures
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• v.46 no.5
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• pp.611-619
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• 2023

In the present work, the flutter characteristics of porous nanocomposite cylindrical shells, reinforced with graphene platelets (GPLs) in supersonic airflow, have been investigated. Different distributions for GPLs and porosities have been considered which are named uniform and non-uniform distributions thorough the shell's thickness. The effective material properties have been determined via Halpin-Tsai micromechanical model. The cylindrical shell formulation considering supersonic airflow has been developed in the context of first-order shell and first-order piston theories. The governing equations have been solved using Galerkin's method to find the frequency-pressure plots. It will be seen that the flutter points of the shell are dependent on the both amount and distribution of porosities and GPLs and also shell geometrical parameters.

• Geomechanics and Engineering
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• v.35 no.2
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• pp.181-194
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• 2023

The primary objective of this study is to examine the influence of geometry on the stability characteristics of cylindrical microstructures. This investigation entails a stability analysis of a bi-directional functionally graded (BD-FG) cylindrical imperfect concrete beam, focusing on the impact of geometry. Both the first-order shear deformation beam theory and the modified coupled stress theory are employed to explore the buckling and dynamic behaviors of the structure. The cylinder-shaped imperfect beam is constructed using a porosity-dependent functionally graded (FG) concrete material, wherein diverse porosity voids and material distributions are incorporated along the radial axis of the beam. The radius functions are considered in both uniform and nonuniform variations, reflecting their alterations along the length of the beam. The combination of these characteristics leads to the creation of BD-FG configurations. In order to enable the assessment of stability using energy principles, a numerical technique is utilized to formulate the equations for partial derivatives (PDEs).

• Steel and Composite Structures
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• v.51 no.2
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• pp.139-151
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• 2024

In this research, a semi-analytical solution is presented for computing mechanical displacements and thermal stresses in rotating thick cylindrical pressure vessels made of functionally graded material (FGM). The modulus of elasticity, linear thermal expansion coefficient, and density of the cylinder are assumed to change along the axial direction as a power-law function. It is also assumed that Poisson's ratio and thermal conductivity are constant. This cylinder was subjected to non-uniform internal pressure and thermal loading. Thermal loading varies in two directions. The governing equations are derived by the first-order shear deformation theory (FSDT). Using the multilayer method, a functionally graded (FG) cylinder with variable thickness is divided into n homogenous disks, and n sets of differential equations are obtained. Applying the boundary conditions and continuity conditions between the layers, the solution of this set of equations is obtained. To the best of the researchers' knowledge, in the literature, there is no study carried out bi-directional thermoelastic analysis of clamped-clamped rotating FGM thick-walled cylindrical pressure vessels under variable pressure in the longitudinal direction.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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• pp.51-71
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• 2018

This work proposes a theoretical and numerical study on the behavior of a tapered shaft rotor made of composite materials by the classical version h and the version p of the finite element method. Hierarchical form functions are used to define the model. The purpose of this paper is to determine the expressions of the kinetic and potential energies of the tree necessary for the results of the equations of motion. A comparison between the version h and the p version of the finite element method of the functions of polynomial and trigonometric hierarchical forms with six degrees of freedom per node, of a composite tapered and cylindrical shaft which rotates at a constant speed about its axis. It is found that when the number of functions of form (the version p) is increased, the solution converges. It is also observed that the conicity of the shaft increases the rigidity with respect to a uniform shaft having the same mechanical properties. The numerical simulation allowed us to determine the natural frequencies and the critical speeds of the composite shaft systems are compared with those available in the literature and the effectiveness of the methods used are discussed.

• Structural Engineering and Mechanics
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• v.25 no.2
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• pp.239-268
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• 2007

This paper deals with optimal stacking sequence design of laminate composite structures. The stacking sequence optimisation of laminate composites is formulated as a combinatorial problem and is solved using Simulated Annealing (SA), an algorithm devised based on inspiration of physical process of annealing of solids. The combinatorial constraints are handled using a correction strategy. The SA algorithm is strengthened by embedding Tabu search in order to prevent recycling of recently visited solutions and the resulting algorithm is referred to as tabu embedded simulated Annealing (TSA) algorithm. Computational performance of the proposed TSA algorithm is enhanced through cache-fetch implementation. Numerical experiments have been conducted by considering rectangular composite panels and composite cylindrical shell with different ply numbers and orientations. Numerical studies indicate that the TSA algorithm is quite effective in providing practical designs for lay-up sequence optimisation of laminate composites. The effect of various neighbourhood search algorithms on the convergence characteristics of TSA algorithm is investigated. The sensitiveness of the proposed optimisation algorithm for various parameter settings in simulated annealing is explored through parametric studies. Later, the TSA algorithm is employed for multi-criteria optimisation of hybrid composite cylinders for simultaneously optimising cost as well as weight with constraint on buckling load. The two objectives are initially considered individually and later collectively to solve as a multi-criteria optimisation problem. Finally, the computational efficiency of the TSA based stacking sequence optimisation algorithm has been compared with the genetic algorithm and found to be superior in performance.

• Steel and Composite Structures
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• v.21 no.1
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• pp.217-247
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• 2016

Five extended cylindrical reticulated shells are proposed by changing distribution rule of diagonal rods based on three fundamental types. Modeling programs for fundamental types and extended types of cylindrical reticulated shell are compiled by using the ANSYS Parametric Design Language (APDL). On this basis, conditional formulas are derived when the grid shape of cylindrical reticulated shells is equilateral triangle. Internal force analysis of cylindrical reticulated shells is carried out. The variation and distribution regularities of maximum displacement and stress are studied. A shape optimization program is proposed by adopting the sequence two-stage algorithm (RDQA) in FORTRAN environment based on the characteristics of cylindrical reticulated shells and the ideas of discrete variable optimization design. Shape optimization is achieved by considering the objective function of the minimum total steel consumption, global and locality constraints. The shape optimization for three fundamental types and five extended types is calculated with the span of 30 m~80 m and rise-span ratio of 1/7~1/3. The variations of the total steel consumption along with the span and rise-span ratio are analyzed with contrast to the results of shape optimization. The optimal combination of main design parameters for five extended cylindrical reticulated shells is investigated. The total steel consumption affected by distribution rule of diagonal rods is discussed. The results show that: (1) Parametric modeling method is simple, efficient and practical, which can quickly generate different types of cylindrical reticulated shells. (2) The mechanical properties of five extended cylindrical reticulated shells are better than their fundamental types. (3) The total steel consumption of cylindrical reticulated shells is optimized to be the least when rise-span ratio is 1/6. (4) The extended type of three-way grid cylindrical reticulated shell should be preferentially adopted in practical engineering. (5) The grid shape of reticulated shells should be designed to equilateral triangle as much as possible because of its reasonable stress and the lowest total steel consumption.

• Steel and Composite Structures
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• v.52 no.1
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• pp.15-29
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• 2024

This research investigates the application of novel functionally graded small-scale materials (FGSMs) in sport and sports structures through an engineering design lens. Functionally graded materials (FGMs) offer tailored material properties, promising enhanced performance and durability. Utilizing an interdisciplinary approach, this study explores the integration of FGSMs in sports equipment and infrastructure. Design considerations specific to sports engineering are emphasized, including lightweight, high-strength materials capable of withstanding dynamic loads. Advanced manufacturing techniques, such as additive manufacturing and nanotechnology, enable precise control over material composition and microstructure. Computational modeling is employed to evaluate the mechanical behavior and performance characteristics of FGSM-based components. Through case studies and comparative analyses, the study showcases the potential of FGSMs to revolutionize sports equipment and structures, offering improved performance, safety, and sustainability. This research contributes to the advancement of sports engineering by exploring the design and application of FGSMs in sport and sports structures.