Sandwich Conical Shells Research Articles

Vibration and buckling analysis of laminated sandwich conical shells using higher order shear deformation theory and differential quadrature method

Vibration and buckling analysis of laminated sandwich truncated conical shells with compressible or incompressible core are presented in this work considering curvature effects. The formulation uses the quadratic and cubic functions for transverse and in-plane displacements of the core and the first-order shear deformation theory for the face sheets. The motion equations of each individual layer are derived according to the principle of minimum total potential energy considering the continuity of the displacements and the internal stress fields at the interfaces. Differential quadrature method is applied in order to obtain the frequency and buckling load of the sandwich structure. The effects of different parameters such as core to face sheet stiffness ratio, number of layers of the face sheets, boundary condition, geometrical parameters of the core and the face sheets, semi vertex angle of the cone, trapezoidal shape, and in-plane stresses of the core are examined on the vibration and buckling response of sandwich truncated conical shells. Comparison of the present results with those reported in the literature confirms the accuracy of the proposed theory. Numerical results indicate that the effects of in-plane stresses of the core significantly affect the frequency with increasing the core to face sheet stiffness ratio.

Low-velocity impact response of sandwich conical shell with agglomerated single-walled carbon nanotubes-reinforced face sheets considering structural damping

In the present article, dynamic response of a thick sandwich truncated conical shells with a transversely flexible/inflexible core and nanocomposite face sheets subjected to low-velocity impact was studied. The face sheets are reinforced with single-walled carbon nanotubes where the agglomeration effects are considered based on Mori–Tanaka model. A new equivalent three-degree-of-freedom spring-mass-damper model is utilized to describe the contact force between impactor and sandwich truncated conical shells. Based on an improved higher order sandwich panel theory, the equations of motion are derived by Hamilton’s principal incorporating the curvature, in-plane stress of the core and the structural damping effects. Differential quadrature method is applied for obtaining the contact force and displacement histories. After validity of the present study, the effects of the single-walled carbon nanotubes volume fraction, single-walled carbon nanotubes agglomeration, number of the layers of the face sheets, boundary conditions, semi-vertex angle of the cone, impact velocity, and mass of impactor on the low-velocity impact response of the nanocomposite structure are studied in details. Numerical results show that increasing the volume fraction of single-walled carbon nanotubes can reduce the amplitude of the dynamic response of the nanocomposite structure.

The stability analysis of shear deformable FGM sandwich conical shells under the axial load

The purpose of this study is to investigate the stability of freely supported FGM sandwich conical shells subjected to the axial load within the first order shear deformation theory (FOSDT). The basic equations of FGM sandwich conical shells are displayed based on the Donnell shell theory. Galerkin’s method is utilized to convert the partial differential equations to algebraically equations. The novelty of this study is to achieve closed-form solution for the critical axial load of FGM sandwich conical shells within the FOSDT. The parameter which is included in the obtained expressions is get from the minimum conditions of the critical axial load. The results obtained in this study compared with other studies and get good agreement. Emphasis is placed on studying the influences of FGM layers and transverse shear stresses on the magnitudes of the critical axial load for FGM sandwich conical shells with different geometrical dimensions.

The stability of the sandwich conical shell panel - the stress state analysis

The stability of the sandwich conical shell panel - the stress state analysis

Low Velocity Impact Response of Laminated Composite Truncated Sandwich Conical Shells with Various Boundary Conditions Using Complete Model and GDQ Method

In this paper, the dynamic analysis of the composite sandwich truncated conical shells (STCS) with various boundary conditions subjected to the low velocity impact was studied analytically, based on the higher order sandwich panel theory. The impact was assumed to occur normally over the top face-sheet, and the contact force history was predicted using two solution models of the motion which were derived based on Hamilton’s principle by considering the displacement continuity conditions between the layers⸳ In order to obtain the contact force and the displacement histories, the differential quadrature method (DQM) was used. In this investigation, the effects of different parameters such as the number of layers of the face sheets, the boundary conditions, the semi vertex angle of the cone, and the impact velocity of the impactor on the impact response of the complete model were studied.

A Modified Fourier Solution for Free Damped Vibration Analysis of Sandwich Viscoelastic-Core Conical Shells and Annular Plates with Arbitrary Restraints

In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.

Analytical and finite-element solutions for the buckling of composite sandwich conical shell with clamped ends under external pressure

This paper focuses on the buckling analysis of composite sandwich conical shells subjected to a uniform external lateral pressure based on the first-order shear deformation theory. Approximate analytical solutions are assumed to satisfy fully clamped boundary conditions and then Fourier decomposition and Galerkin method is applied to achieve closed-form relations of buckling loads. The closed analytical formula for the critical pressure has been verified by comparison with the finite-element solutions and a special case where the angle of the conical shell approaches zero, that is, a cylindrical shell. Based on this formula buckling analyses of sandwich conical shells with different types of core materials have been accomplished. The outcomes are achieved considering the effects of half-vertex cone angle, core thickness and indicating applicability, accuracy, and stability of the present method.

Design, fabrication and testing of composite sandwich integral structure of spacecraft antenna

An innovative design of the space offset mirror antenna made of composite material is presented in the paper. The antenna body is designed in the form of a composite sandwich conical shell with a cutout made on the side surface. The body geometry is selected to conform to and accommodate the signal transmitting zone. The antenna reflector is located at the bottom part of the sandwich cone and the feed is placed at the top creating a compact antenna configuration. A full-size prototype of the antenna has been designed, built and tested. Design parameters of the sandwich structure have been determined based on the results of finite-element modal analysis. The experimental results of vibration and thermal cycling testing of the prototype provide a proof of concept and evidence of the design feasibility. It is shown that the stiffness characteristics of the proposed integral sandwich antenna ensure efficient applications of such composite structures in the space antennas designed for various ranges of radio wave transmission.

New enhanced higher order free vibration analysis of thick truncated conical sandwich shells with flexible cores

This paper dealt the free vibration analysis of thick truncated conical composite sandwich shells with transversely flexible cores and simply supported boundary conditions based on a new improved and enhanced higher order sandwich shell theory. Geometries were used in the present work for the consideration of different radii curvatures of the face sheets and the core was unique. The coupled governing partial differential equations were derived by the Hamilton's principle. The in-plane circumferential and axial stresses of the core were considered in the new enhanced model. The first order shear deformation theory was used for the inner and outer composite face sheets and for the core, a polynomial description of the displacement fields was assumed based on the second Frostig's model. The effects of types of boundary conditions, conical angles, length to radius ratio, core to shell thickness ratio and core radius to shell thickness ratio on the free vibration analysis of truncated conical composite sandwich shells were also studied. Numerical results are presented and compared with the latest results found in literature. Also, the results were validated with those derived by ABAQUS FE code.

Temperature-dependent buckling analysis of sandwich truncated conical shells with FG facesheets

In this study, an improved high-order theory is presented for temperature-dependent buckling analysis of sandwich conical shell with thin functionally graded (FG) facesheets and homogenous soft core. First shear deformation theory (FSDT) is used for the facesheets and cubic functions are assumed for the transverse and in-plane displacements of the core. The nonlinear Von-Karman type relations are used to obtain the strain components. The equilibrium equations are derived via principle of minimum potential energy. Analytical solution for static analysis of simply supported sandwich conical shells under axial in-plane compressive load and in the temperature environments is performed using Galerkin’s solution. Numerical modeling is made by ABAQUS finite element (FE) code. The comparison shows that the present results are in good agreement with the results in the literature and the present FE results.

The Distribution of Stress in a Sandwich Conical Shell Panel Under Combined Load

The paper presents an analysis of the stress distribution in the open, cone-shaped, sandwich shell panel. The shell under consideration consists of two load-carrying facings and a core layer of the soft type. The facings are made of an isotropic, compressible, work-hardening material and they are geometrically and physically symmetrical, so they are of equal thicknesses and the same material properties. The core layer resists transverse shear only. The shell under consideration is under combined external load in the form of lateral pressure and a longitudinal force. Different ratios of the longitudinal force to the lateral pressure are taken into account. In each case, the components of the effective stress as well as the effective stress values corresponding to the shell deformation were determined. To determine the stress state which occurs during the shell deformation, the stability equations have to be derived. The effective stress corresponding to the deformations in the shell under consideration can occur within the elastic, elastic-plastic or plastic range. In order to determine the stress distribution in the shell under consideration which corresponds to the on- and post-critical state, the constitutive relations of the Nadai-Hencky deformation theory, alongside the Huber-Mises-Hencky yield condition, are accepted. Analyses show that, in certain cases, there are very large differences between the values of the components of the stress state. In such cases, it seems to be possible to omit the components with small values.

Nonlinear Dynamic Buckling for Truncated Sandwich Shallow Conical Shell Structure Subjected to Pulse Impact

Nonlinear dynamic buckling for sandwich shallow conical shell structure under uniform triangular pulse is investigated. Based on the Reissner’s assumption and Hamiton’s principle, the nonlinear dynamic governing equation of sandwich shallow spherical shells is derived. The corresponding nonlinear dynamic response equations are obtained by Galerkin method and solved by Runge-Kutta method. Budiansky-Roth criterion expressed by displacements of rigid center is employed to determine the critical impact bucking load. The effects of geometric parameters and physical parameters on impact buckling are discussed.

Buckling and stability of elastic-plastic sandwich conical shells

Shell structures are very interesting from the design point of view and these are well recognized in the scientific literature. In this paper the analysis of the buckling loads and stability paths of a sandwich conical shell with unsymmetrical faces under combined load based on the assumptions of moderately large deflections (geometrically nonlinear theory) is considered and elastic-plastic properties of the material of the faces are taken into considerations. External load is assumed to be two-parametrical one and it is assumed that the shell deforms into the plastic range before buckling. Constitutive relations in the analysis are those of the Nadai-Hencky deformation theory of plasticity and Prandtl-Reuss plastic flow theory with the H-M-H (Huber-Mises-Hencky) yield condition. The governing stability equations are obtained by strain energy approach and Ritz method is used to solve the equations with the help of analytical-numerical methods using computer.

Stability Behavior of Cylindrical and Conical Sandwich Shells with Flexible Core

A higher-order theory for the analysis of cylindrical and conical sandwich shells with flexible core is presented. The formulation is based on a three-layer sandwich model. The governing equations and the boundary conditions of each individual layer are derived according to the principle of minimum total potential energy. With the consideration of the continuity of the displacements and the internal stress fields at the interfaces, the governing partial differential equations for the sandwich shell are achieved. They are reduced into ordinary differential equations using Fourier decomposition and then solved through a numerical integration procedure. The theory is verified by comparison of achieved results to those published in the literature and to finite element computations.

A generalized layerwise finite element for multi-layer damping treatments

This paper presents a 4-node facet type quadrangular shell finite element, based on a layerwise theory, developed for dynamic modelling of laminated structures with viscoelastic damping layers. The bending stiffness of the facet shell element is based on the Reissner–Mindlin assumptions and the plate theory is enriched with a shear locking protection adopting the MITC approach. The membrane component is corrected by using incompatible quadratic modes and the drilling degrees of freedom are introduced through a fictitious stiffness stabilization matrix. Linear static tests, using several pathological tests, showed good and convergent results. Dynamic analysis evaluation is provided by using two eigenproblems with exact analytical solution, as well as a conical sandwich shell with a closed-form analytical solution and a semi-analytical ring finite element solution. The applicability of the proposed finite element to viscoelastic core sandwich plates is assessed through experimental validation.

Nonlinear stability of truncated shallow conical sandwich shell with variable thickness

The theory of nonlinear stability for a truncated shallow conical shell with variable thickness under the action of uniform pressure was presented. The fundamental equations and boundary conditions were derived by means of calculus of variations. An analytic solution for the critical buckling pressure of the shell with a hyperbolically varying thickness is obtained by use of modified iteration method. The results of numerical calculations are presented in diagrams, which show the influence of geometrical and physical parameters on the buckling behavior.

AN h–p FINITE ELEMENT VIBRATION ANALYSIS OF OPEN CONICAL SANDWICH PANELS AND CONICAL SANDWICH FRUSTA

The vibration study of a general three-layer conical sandwich panel based on theh –p version of the finite element method is presented in this paper. No restriction is placed on the degree of curvature of the shell, thereby relaxing the strictures associated with shallow shell theory. The methodology incorporates a new set of trigonometric functions to provide the element p -enrichment, and elements may be joined together to model either open conical panels, or complete conical frusta (circumferentially connected, but open at each end). The full range of classical boundary conditions, which includes free, clamped, simply supported and shear diaphragm edges, may be applied in any combination to open and closed panels, thereby facilitating the study of a wide range of conical sandwich shells. The convergence properties of this element have been established for different combinations of the h - and p -parameters, thereby assuring its integrity for more general use. Since very little work has been reported on the vibration characteristic of either circumferentially closed or open conical sandwich panels, the main thrust of this work has been to present and validate an efficient modelling technique, rather than to perform numerous parameter and/or sensitivity studies. To this end, some new results are presented and subsequently validated using a commercially available finite element package. It is shown that for results of comparable accuracy, models constructed using the h–p formulation require significantly fewer degrees of freedom than those assembled using the commercial package. Some preliminary experimental results are also included for completeness.

VIBRATION AND DAMPING ANALYSIS OF LAMINATED COMPOSITE AND SANDWICH SHELLS

Damping analysis under harmonic oscillations of a laminated composite and sandwich shells is performed. Finite-element modeling is based on the first-order shear deformation theory including rotation around the normal. The second-order isoparametric triangular finite-element nodal variables are three displacements and three rotations. A shear correction factor is introduced to account for the fact that the transverse shear distribution is not uniform through the shell thickness. A model of hysteretic damping is used to evaluate damping properties of the structure in harmonic oscillations. Damped frequencies of the shell are calculated by using the Lanczos method. Modal damping of the structure is calculated by using the energy method. Numerical examples of damping and vibration analysis of laminated composite and sandwich cylindrical and conical shells are presented. The numerical results are in good agreement with the reference solutions and experimental data.

Non-linear vibration of shallow conical sandwich shells

This paper derives fundamental equations and boundary conditions of the non-linear free vibration theory for shallow conical sandwich shells by means of Hamilton's principle. Analytic solutions of the ratio of non-linear period to linear period vs the non-dimensional amplitude for the shells with two types of boundary conditions are obtained by Galerkin's method. Finally, effects of the geometrical parameter, physical parameter and boundary conditions on non-linear vibration are discussed.

Optimization of the thickness of layers of sandwich conical shells

We deal with an optimal control problem for variational inequalities, where the linear operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for optimal control is applied to optimal design problems for sandwich conical shells where a variable thickness of given layers appears as a control variable.