Thermoelastic Vibration Analysis of Laminated Doubly Curved Shallow Panels Using Non-Linear FEM

Non-linear vibration behavior of the laminated composite curved panel of different geometries (cylindrical, elliptical, hyperboloid, paraboloid and flat panel) under thermal environment is investigated in this article. A non-linear mathematical model is developed based on higher-order shear deformation theory by taking Green–Lagrange type of non-linear kinematics. The governing equation of the vibrated panel is obtained through Hamilton's principle and discretized using the non-linear finite element steps. The responses are obtained through direct iterative method and compared with those available in published literature. The effect of different parameters on the non-linear vibration behavior of the curved panel has been discussed in detail.     

Thermoelastic Response of Cross-Ply Laminated Shells Based on a Rigorous Shell Theory

Thermal deformations in cross-ply laminated shells are investigated. The state space approach is used to generate exact solutions for the thermoelastic response of cross-ply spherical, cylindrical and doubly curved shells for various boundary conditions and subjected to general temperature field. The shells possess two parallel edges simply supported and the remaining ones having any possible combination of boundary conditions: free, clamped or simply supported. A rigorous thick deep first order shear deformation shell theory is used in the analysis. Deflections are computed for shells with various boundary conditions undergoing uniform and linearly varying temperature through the thickness. The exact solutions for thermal deflections can be used as benchmarks for approximate solutions such as Rayleigh-Ritz and finite element methods.     

Thermal Buckling Response of Functionally Graded Plates with Clamped Boundary Conditions

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are solved analytically for a plate with simply supported boundary conditions. Resulting equations are employed to obtain the closed-form solution for the thermal force resultant for each loading case. Numerical examples covering the effects of the plate aspect ratio, side-to-thickness ratio and gradient index on thermal force resultant are discussed.     

Nonlocal Flugge Shell Model for Thermal Buckling of Multi-Walled Carbon Nanotubes with Layerwise Boundary Conditions

Presented herein is the thermal buckling analysis of multi-walled carbon nanotubes on the basis of nonlocal Flugge shell model capturing small scale effects. Based upon the continuum mechanics, a multiple-shell model is adopted in which the nested tubes are coupled with each other through the van der Waals interlayer interaction. The utilized van der Waals model incorporating the interlayer interactions between any two layers, whether adjacent or non-adjacent is curvature dependent. To analytically solve the problem, the Rayleigh–Ritz method was implemented to the variational form equivalent to the Flugge type equations. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions. It is shown that the shell-like thermal buckling is significantly sensitive to the nonlocal parameter variation, whereas the column-like thermal buckling remains unaffected when the nonlocal parameter is varied.     

Thermal Stresses in a Hollow Cylinder with Convective Boundary Conditions on the Inside and Outside Surfaces

Analytical solutions for thermal stresses (radial, tangential, and axial) in a hollow cylinder with uniform internal heat generation for the thermal boundary condition of convective heating on the inside surface and convective cooling on the outside surface are derived. The analysis assumes the ends of the cylinder to be clamped, the axial strain to be negligible, and the radial stresses on the inside and the outside surfaces to be zero. Results are presented to illustrate the effects of internal heat generation parameter Q, convective environment temperatures ratio θ*, Biot number for convection on the inside surface Bi ₁, Biot number for convection on the outside surface Bi ₂, and the radii ratio ρ on thermal stresses distribution in the cylinder. The analytical solutions should serve as benchmarks for validating the numerical codes for dealing with more complicated cases.     

An Exact Solution for the Thermoelastic Deformations of Cross-Ply Laminated Arches with Arbitrary Boundary Conditions

Thermal deformations in symmetric and antisymmetric cross-ply laminated arches are investigated. The state-space approach has been used to generate exact solutions for the thermoelastic response of cross-ply arches for arbitrary boundary conditions and subjected to general temperature field. A rigorous first-order arch theory is used in the analysis. Deflections are computed for arches with various lamination schemes and boundary conditions undergoing uniform and linearly varying temperature through the thickness. The effect of shallowness of the arch on the maximum deflection is studied.     

Exact Solution for Thermal Buckling of Functionally Graded Plates Resting on Elastic Foundations with Various Boundary Conditions

In this article, we investigate the buckling analysis of plates that are made of functionally graded materials (FGMs) resting on two-parameter Pasternak's foundations under thermal loads. Three different thermal loads were considered, i.e., uniform temperature rise (UTR), linear and non-linear temperature distributions (LTD and NTD) through the thickness. The mechanical and thermal properties of functionally graded material (FGM) vary continuously along the plate thickness according to a simple power law distribution. Employing an analytical approach, the five coupled governing stability equations, which are derived based on first-order shear deformation plate theory, are converted into two uncoupled partial differential equations (PDEs). Considering the Levy-type solution, these two PDEs are reduced to two ordinary differential equations (ODEs) with variable coefficients. Then, the ODEs are solved using an exact analytical solution, which is called the power series Frobenius method. The appropriate convergence study and comparison with previously published related articles was employed to verify the accuracy of the proposed method. After such verifications, the effects of parameters such as the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the critical buckling temperature difference are illustrated and explained. The critical buckling temperatures of functionally graded rectangular plates with six various boundary conditions are reported for the first time and can serve as benchmark results for researchers to validate their numerical and analytical methods in the future.     

汽轮机T型叶根有限元模态分析边界条件的研究

对汽轮机叶片有限元模态分析的边界条件处理方法进行了探讨，分析了各种边界条件对叶片自振频率的影响。通过大量的数值模拟，得出了各种边界条件与叶片固有频率变化关系，进而提出了弹性模拟叶片边界约束的计算模型，为叶片模态有限元数值计算及故障分析提供了理论基础。图6表3参5     

Easy Test for Stability of Laminated Beams with Structural Damping and Boundary Feedback Controls

In this paper, we consider the test problem of stability of the closed loop system composed of laminated beams with structural damping and boundary feedback controls. We give a simple test method of verifying the exponential stability of the closed loop system. The test system consists of the dominant parts of the closed loop system. Under certain condition, we show that if the test system is exponentially stable, then the closed loop system is also exponentially stable and the eigenvalues of the test system are asymptotic eigenvalues of the closed loop system. This research is supported by the Natural Science Foundation of China grant NSFC–60474017 and by the Liu Hui Center for Applied Mathematics, Nankai University & Tianjin University, P.R.China.     

Effects of Thermal Loading on the Buckling and Vibration of Ring-Stiffened Functionally Graded Shell

A theoretical method is developed to investigate the effects of thermal load and ring stiffeners on buckling and vibration characteristics of the functionally graded cylindrical shells, based on the first-order shear deformation theory (FSDT) considering rotary inertia. Heat conduction equation across the shell thickness is used to determine the temperature distribution. Material properties are assumed to be graded across the shell wall thickness of according to a power-law, in terms of the volume fractions of the constituents. The Rayleigh–Ritz procedure is applied to obtain the frequency equation. The effects of stiffener's number and size on natural frequency of functionally graded cylindrical shells are investigated. Moreover, the influences of material composition, thermal loading and shell geometry parameters on buckling and vibration are studied. The obtained results have been compared with the analytical results of other researchers, which showed good agreement. The new features of thermal vibration and buckling of ring-stiffened functionally graded cylindrical shells and some meaningful and interesting results obtained in this article are helpful for the application and the design of functionally graded structures under thermal and mechanical loads.     

Local Regularity of Optimal Trajectories for Control Problems with General Boundary Conditions

Let f and g be two smooth vector fields on a manifold M. Given a submanifold S of M, we study the local structure of time-optimal trajectories for the single-input control-affine system ̇q = f(q) + ug(q) with the initial condition q(0) S. When the codimension s of S in M is small (s 4) and the system has a small codimension singularity at a point q₀ S, we prove that all time-optimal trajectories contained in a sufficiently small neighborhood of q₀ are finite concatenations of bang and singular arcs. The proof is based on an extension of the index theory to the case of general boundary conditions.2000 Mathematics Subject Classification. 49K15, 49K30.     

A Refined Sine Finite Element with Transverse Normal Stress for Thermoelastic Analysis of Laminated Composite in Cylindrical Bending

An unidimensional three-node composite finite element including the transverse normal effect is presented in the framework of the thermoelastic coupling. The kinematics is based on a sinus distribution with layer refinement and a second-order expansion for the deflection. The calculation of the transverse normal stress comes from a weak formulation and takes into account the physical considerations. Numerical results for displacements and stresses are provided for very thick and thin structures in cylindrical bending. They are compared with exact elasticity solution and the results are promising.     

Thermal Post-Buckling and Vibration Analysis of Composite Conical Shell Structures Using Layerwise Theory

The thermal post-buckling and vibration characteristics of composite conical shells are investigated using a finite element method. Based on the layerwise theory and the von Karman displacement strain relationships, the nonlinear finite element equations of motion are derived for the thermoelastic response of the composite conical shell structure. The cylindrical arc-length method is used to account for the snapping phenomenon. The influence of the structural parameters, such as the semi-cone angle, thickness ratio, and shallowness angle (curvature), on the structural stability of the composite conical shell subjected to the thermal load is also observed.     

Thermal Buckling Analysis of Embedded Single-Walled Carbon Nanotubes with Arbitrary Boundary Conditions Using the Nonlocal Timoshenko Beam Theory

In this paper, the thermal buckling behavior of single-walled carbon nanotubes (SWCNTs) embedded in an elastic medium is studied. To this end, the SWCNTs are modeled based on the nonlocal Timoshenko beam theory into which the effect of the elastic medium is incorporated The generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations and to consider different commonly used boundary conditions (BCs). For simply supported BCs, the results obtained from the present analysis are compared with the ones from the exact solution and an excellent agreement has been achieved. The effects of the aspect ratio, nonlocal parameter and the Winkler parameter on the dimensionless critical buckling temperature are carefully investigated.     

Thermal and economical analysis of a central solar heating system with underground seasonal storage in Turkey

Thermal performance and economic feasibility of two types of central solar heating system with seasonal storage under four climatically different Turkey locations are investigated. The effects of storage volume and collector area on the thermal performance and cost are studied for three load sizes. The simulation model of the system consisting of flat plate solar collectors, a heat pump, under ground storage tank and heating load based on a finite element analysis and finite element code ANSYS™ is chosen as a convenient tool. In this study, the lowest solar fraction value for Trabzon (41°N) and the highest solar fraction value for Adana (37°N) are obtained. Based on the economic analysis, the payback period of system is found to be about 25–35 years for Turkey.     

Heat and Mass Transfer Flow of a Nanofluid over an Inclined Plate under Enhanced Boundary Conditions with Magnetic Field and Thermal Radiation

This article presents the magnetohydrodynamic boundary layer flow, heat and mass transfer characteristics of a nanofluid over an inclined porous vertical plate with thermal radiation and chemical reaction. The new enhanced concentration boundary condition on the surface of the wall is considered in this analysis. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using the similarity variables and are solved numerically using the finite element method. The effect of key parameters such as magnetic parameter (M), buoyancy ratio (Nr), Prandtl number (Pr), thermal radiation (R), Brownian motion (Nb), thermophoresis (Nt), Lewis number (Le), and chemical reaction parameter (Cr) on velocity, temperature, and concentration distributions is discussed in detail and the results are shown graphically. Furthermore, the impact of these parameters on skin‐friction coefficient, Nusselt number, and Sherwood number is also investigated and the results are shown in tabular form. The developed algorithm is validated with works published previously and was found to be in good agreement. The thermal boundary layer thickness is elevated, whereas the solutal boundary layer thickness retards with the improving values of the Brownian motion parameter (Nb). The rates of nondimensional temperature and concentration both decelerate with higher values of the thermophoresis parameter (Nt).