Non-homogeneous Shells Research Articles

Parameter optimization decomposition and synthesis algorithm for a bundle of rotation shells connected with a ring frame

The method of weight optimization of a shell structure consisting of a power ring frame connected to it on each side of non-homogeneous shells of rotation with variable wall thickness under the action of a spatially asymmetric load is presented. The construction decomposition algorithm is applied. The optimization of shells is carried out based on the necessary Pontryagin's optimality conditions with phase constraints. Finite-dimensional optimization methods are used to seek the optimal configuration of the ring frame. The synthesis of the construction is carried out by the method of successive approximations. Numerical optimization results are presented

Investigation of natural vibrations of thin-walled structures interacting with fluid

The problem of studying the dynamics of elements of hydro-technical structures interacting with fluid is considered in the article. On the basis of Lagrange’s variational principles, the basic equations are obtained that characterize the dynamics of complex, multiply connected structurally non-homogeneous shell systems interacting with flowing fluid. Dynamic equations of a cylindrical shell are obtained. To determine the fluid pressure on the shell surface, a boundary value problem based on the laws of hydroelasticity was used. A software package was developed for studying the dynamic characteristics of complex, multiply connected structurally non-homogeneous shell structures, as well as programs for studying the dynamic characteristics of a composite structure using the orthogonal sweep method. Dynamic characteristics are determined for different levels of water filling.

NUMERICAL SOLUTION OF THE DYNAMIC PROBLEM OF AXISYMMETRIC VIBRATIONS OF REINFORCED SHELLS

The reliability of the results obtained in the work is determined by the rigor and correctness of the statements of the initial problems; theoretical substantiation of the finite-difference schemes used; controlled accuracy of numerical calculations; conducting test calculations; compliance of the established regularities with the general properties of oscillations of thin-walled structural elements. The correctness of the formulation of the problems is achieved by using the well-known equations of the theory of shells and rods of the Tymoshenko type, which are approximations of the original equations of the three-dimensional theory of elasticity. When deriving the equations, the equations of oscillations of the multilayer shell in the smooth region and the equations of oscillations of reinforcing ribbed elements (transverse ribs) were obtained. It is not difficult to show that the indicated equations by the classification of equations in partial derivatives are equations of the hyperbolic type, which are an approximation of the oscillating equations of three-dimensional elastic bodies and sufficiently correctly reproduce wave processes in non-homogeneous shell structures, taking into account spatial gaps. Numerical algorithms for approximate solutions of the original equations are based on the use of the integro-interpolation method of constructing difference schemes. When constructing difference schemes, kinematic quantities refer to difference points with integer indices, and the values of deformations and moment forces refer to difference points with half-integer indices. This approximation of the initial kinematic and static values allows the fulfillment of the law of conservation of the total mechanical energy of the elastic structure at the difference level. The numerical algorithm is based on the use of separate finite-difference relations in the smooth domain and on the lines of spatial discontinuities with the second order of accuracy in spatial and temporal coordinates.

Biostratigraphical and palaeobiogeographical patterns of the larger porcelaneous foraminifer Austrotrillina Parr, 1942

Among the Tethyan larger porcelaneous foraminifera widespread from the middle–late Eocene to the middle Miocene, Austrotrillina Parr, 1942 is the only genus showing a non-homogeneous shell structure. This consists of a parakeriotheca, coated by a thin, dense tectum. Four Austrotrillina species (A. brunni, A. eocaenica, A. howchini, A. striata) have been often used as biostratigraphical markers in the Mediterranean and Indo-Pacific areas. New materials from southeastern Spain and Central Indo-Pacific (Indonesia, Kita-daito-jima, Kikai Seamount) were studied to assess their taxonomic status, species circumscription and palaeobiogeographical patterns. Based on re-assessed shell structures A. asmariensis Adams is considered a junior synonym of A. brunni Marie.Austrotrillina eocaenica first appears in the middle–late Eocene of Iran. Two Rupelian descendants, A. brunni and A. striata, migrated from the Western Tethys into the Indo-Pacific. Austrotrillina striata reached Indonesia and Western Australia in the Chattian, then disappeared in the Langhian of Kita-daito-jima. Austrotrillina brunni first occurred in the Burdigalian of Indonesia and Western Australia and disappeared in the early Serravallian of Western and South Australia. Austrotrillina brunni and A. striata disappeared in the Serravallian westernmost Mediterranean (southeastern Spain). From the Burdigalian the exclusive occurrence of A. howchini in the Indo-Pacific areas is a possible result of the closing Tethyan Seaway, which differentiated the Mediterranean and Indo-Pacific bioprovinces. This species disappears in the latemost Langhian–early Serravallian of South Australia and in the Kikai Seamount. The palaeobiogeographical distribution of these species suggests an early Miocene active connection of Eastern Africa with the Central Indo–West Pacific.

Determination of the excitation frequencies of laminated orthotropic non-homogeneous conical shells

Abstract The excitation frequencies of parametric vibration of laminated non-homogeneous orthotropic conical shells (LNHOCSs) under axial load periodically varying with time, are determined using the classical shell theory (CST). The basic equations are found using the Donnell-Mushtari shell theory and reduce to the Mathieu-Hill type differential equation, in which the instability is examined by the Bolotin method. To validate of current results was made a comparison with the previous studies. The effects of stacking sequences, axial load factors, non-homogeneity, as well as the variation of geometric characteristics on the backward and forward excitation frequencies (BFEFs) of conical shells are studied in detail.

Size-dependent nonlinear vibration of nonhomogeneous shell embedded with a piezoelectric layer based on surface/interface theory

Based on the Donnell’s nonlinear shallow-shell theory and electro-elastic surface/interface theory, the size-dependent nonlinear vibration of nonhomogeneous nano-shell covered with a piezoelectric nano-layer is addressed, and the surface energy effect on the vibration is analyzed. The Donnell’s nonlinear shallow-shell theory is introduced to derive the governing differential equations. The nonlinear mode shape functions for the longitudinal circumferential and radial variables are proposed to characterize the displacement fields and electric potential. In numerical examples, the amplitude frequency curves of the nano-shell are analyzed. The effects of the internal residual stress and the surface material properties on the nonlinear vibration of nano-shell are discussed. Comparison with the results without surface energy effect is presented to validate the results in this paper.

Free Vibration Response of Thin and Thick Nonhomogeneous Shells by Refined One-Dimensional Analysis

The free vibration analysis of thin- and thick-walled layered structures via a refined one-dimensional (1D) approach is addressed in this paper. Carrera unified formulation (CUF) is employed to introduce higher-order 1D models with a variable order of expansion for the displacement unknowns over the cross section. Classical Euler–Bernoulli (EBBM) and Timoshenko (TBM) beam theories are obtained as particular cases. Different kinds of vibrational modes with increasing half-wave numbers are investigated for short and relatively short cylindrical shells with different cross section geometries and laminations. Numerical results of natural frequencies and modal shapes are provided by using the finite element method (FEM), which permits various boundary conditions to be handled with ease. The analyses highlight that the refinement of the displacement field by means of higher-order terms is fundamental especially to capture vibrational modes that require warping and in-plane deformation to be detected. Classical beam models are not able to predict the realistic dynamic behavior of shells. Comparisons with three-dimensional elasticity solutions and solid finite element solutions prove that CUF provides accuracy in the free vibration analysis of even short, nonhomogeneous thin- and thick-walled shell structures, despite its 1D approach. The results clearly show that bending, radial, axial, and also shell lobe-type modes can be accurately evaluated by variable kinematic 1D CUF models with a remarkably lower computational effort compared to solid FE models.

Stability Analysis of Clamped Nonhomogeneous Shells on the Elastic Foundation

In the present study a theoretical analysis is presented for determining the stability characteristics of clamped non-homogeneous shells on the elastic foundation subjected to the lateral pressure. The basic equations have been derived for the shell, the Young modulus of which varies exponentially in the thickness direction and rests on the elastic foundation. By applying the Galerkin method to the basic equations, the expressions for the critical lateral pressure of the non-homogeneous shell with or without an elastic foundation are obtained. Finally, the e ects of the non-homogeneity, elastic foundation and shell characteristics on the critical lateral pressure have been studied.

On the vibration of laminated nonhomogeneous orthotropic shells

In this paper, an analytical procedure is given to study the free vibration of the laminated homogeneous and non-homogeneous orthotropic conical shells with freely supported edges. The basic relations, the modified Donnell type motion and compatibility equations have been derived for laminated orthotropic truncated conical shells with variable Young’s moduli and densities in the thickness direction of the layers. By applying the Galerkin method, to the basic equations, the expressions for the dimensionless frequency parameter of the laminated homogeneous and non-homogeneous orthotropic truncated conical shells are obtained. The appropriate formulas for the single-layer and laminated complete conical and cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, the influences of the non-homogeneity, the number and ordering of layers and the variations of the conical shell characteristics on the dimensionless frequency parameter are investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature.

EFFECT OF THE TWO-PARAMETER ELASTIC FOUNDATION ON THE CRITICAL PARAMETERS OF NONHOMOGENEOUS ORTHOTROPIC SHELLS

A theoretical analysis is presented for determining the free vibrational and buckling characteristics of the nonhomogeneous, orthotropic, thin-walled, circular cylindrical and conical shells under a hydrostatic pressure and resting on a two-parameter elastic foundation. The basic relations have been obtained for the orthotropic truncated conical shell, the Young's moduli and density of which vary continuously in the thickness direction. By applying the Galerkin method, the buckling hydrostatic pressure and dimensionless frequency parameter of the homogeneous and nonhomogeneous orthotropic truncated conical shells with or without elastic foundations are obtained. Finally, the effects of the Winkler and Pasternak-type elastic foundations, the variations of shell characteristics, the effects of the nonhomogeneity and orthotropy on the critical parameters have been studied. The results are presented in tables, figures and compared with other works.

Optical Properties of Metallic Nanotubes with Broken Symmetry: Detection of Eccentricity

The optical properties of dielectric core-metallic concentric shell nanoparticles show a highly sensitive dependence on geometrical parameters of the system. It is due to the strong interaction between plasmon modes excited on the surfaces of the metallic shell. Perturbations in the symmetries of the system modify these interactions and enable new ones, giving rise to dramatic variations in the far field spectrum. In this paper, we examine the electromagnetic response (far and near fields) of hollow metallic nanotubes (nts) with empty or dielectric core as a function of the offset parameter between the core and the shell. The evolution of extinction spectra shows a strong redshift for the dipolar resonance when the offset parameter is increasing, whereas new multipole interactions can be observed at high energy. As dimers, the extinction cross section for nts with nonhomogeneous shell thickness depends on incidence angle with respect to offset axis. We show that for a given offset, the lowest energy peak in extinction curves experiences both, a blueshift and increase of intensity when the angle of incidence is varied with respect to the axis of eccentricity. Maxima of both intensity and blueshift are achieved for an incidence perpendicular to the axis of eccentricity. We show that the optical properties provide sufficient information to unambiguously characterize the system. To compute the electromagnetic field at any point in space, we implemented a rigorous integral formalism (2D geometry) for the two fundamental modes of polarization (s and p modes).

110 粘性流体を含む不均質多孔質弾性殻の動的応答(材料力学II)

110 粘性流体を含む不均質多孔質弾性殻の動的応答(材料力学II)

Large Nonlinear Responses of Spatially Nonhomogeneous Stochastic Shell Structures Under Nonstationary Random Excitations

A novel approach for determining large nonlinear responses of spatially homogeneous and nonhomogeneous stochastic shell structures under intensive transient excitations is presented. The intensive transient excitations are modeled as combinations of deterministic and nonstationary random excitations. The emphases are on (i) spatially nonhomogeneous and homogeneous stochastic shell structures with large spatial variations, (ii) large nonlinear responses with finite strains and finite rotations, (iii) intensive deterministic and nonstationary random disturbances, and (iv) the large responses of a specific spherical cap under intensive apex nonstationary random disturbance. The shell structures are approximated by the lower order mixed or hybrid strain based triangular shell finite elements developed earlier by the author and his associate. The novel approach consists of the stochastic central difference method, time coordinate transformation, and modified adaptive time schemes. Computed results of a temporally and spatially stochastic shell structure are presented. Computationally, the procedure is very efficient compared with those entirely or partially based on the Monte Carlo simulation, and it is free from the limitations associated with those employing the perturbation approximation techniques, such as the so-called stochastic finite element or probabilistic finite element method. The computed results obtained and those presented demonstrate that the approach is simple and easy to apply.

Dynamic Stress and Deformation of Non-Homogeneous Poroelastic Shells of Revolution Saturated in Viscous Fluid

This paper describes an analytical formulation and a numerical solution of the elastic dynamic problems of non-homogeneous poroelastic shells of revolution saturated in viscous fluid. The porosity and porous diameter of the material are assumed to be continuously varied along the shell thickness. The equations of motion and the relations between strains and displacements are derived by extending the Sanders shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The flow of viscous fluid through a porous elastic solid is governed by Darcy's law. In the numerical analysis of the fundamental equations an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula proposed by Houbolt. As a numerical example, the simply supported cylindrical shell under a semi-sinusoidal internal load with respect to time is analyzed. Numerical computations are carried out by changing porosity and mean void radius along the shell thickness, and the variations of pore pressure, displacements and internal forces with time are analyzed.

Dynamic Stress and Deformation of Non-Homogeneous Poroelastic Shells of Revolution Saturated in Viscous Fluid

This paper describes an analytical formulation and a numerical solution of the elastic dynamic problems of non-homogeneous poroelastic shells of revolution saturated in viscous fluid. The porosity and porous diameter of the material are assumed to be continuously varied along the shell thickness. The equations of motion and the relations between strains and displacements are derived by extending the Sanders shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The flow of viscous fluid through a porous elastic solid is governed by Darcy's law. In the numerical analysis of the fundamental equations an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula proposed by Houbolt. As a numerical example, the simply supported cylindrical shell under a semi-sinusoidal internal load with respect to time is analyzed. Numerical computations are carried out by changing porosity and mean void radius along the shell thickness, and the variations of pore pressure, displacements and internal forces with time are analyzed.

On the solution of a coupled thermo-mechanical problem for non-homogeneous Timoshenko-type shells

In this work a coupled thermo-mechanical problem of non-homogeneous shells with variable thickness and variable Young modulus (a so-called Timoshenko type model) is considered. The problem is reduced to uniformly correct problem in the form of a first order difference operator equation. In addition, a similar approach can easily be applied to the Kirchhoff–Love model.

FREE VIBRATIONS OF DOUBLY CURVED IN-PLANE NON-HOMOGENEOUS SHELLS

A method for investigating free vibrations rectangular non-homogeneous shells is proposed. By non-homogeneity, we define a chage of stiffness of shell bending caused by an introduction of another material or change of a shell thickness is defined. It is assumed that a shell possesses an arbitrary value of rectangular parts with different bending stiffness.

Численный алгоритм определения спектральных характеристик неоднородных оболочечных конструкций

Численный алгоритм определения спектральных характеристик неоднородных оболочечных конструкций

Ellipticity of koiter's and naghdi's models for nonhomogeneous anisotropic shells

We show that the bilinear forms associated to the linear thin shell models of Koiter and Naghdi, for a nonhomogeneous and anisotropic material are elliptic. Essentially we use the fact that these bilinear forms are deduced from the three dimensional elasticity tensor, which is positive defined and also the techniques introduced by M. Bernadou, P.G. Ciarlet and B. Miara for homogeneous and isotropic shells (cf. [1], [2], [3], [4]). The ellipticity assures the existence and uniqueness of solution for these models. For Koiter's model, a similar problem was considered by D. Caillerie and E. Sanchez-Palencia [5]

Metal powder granulation in a plasma-spouted/fluidized bed

D.c. plasma-spouted/fluidized bed was applied to the granulation of spherical alloy grains from metal powder mixtures. From a mixture of iron powder ( d p = 149−210 μm) and aluminum powder ( d p = 74−88 μm and 125−149 μm) alloy grains of 1–5 mm in diameter were obtained. The grains exhibited a dense homogeneous core and a porous nonhomogeneous shell structure. The grains were quite spherical; the average aspect ratio of the grains was larger than 0.85. The mass fraction of iron in the core section of product grains depended on the Al Fe ratio of initial powder mixtures but was insensitive to the size of product grains and to the size of initial aluminum particles. The growth mechanism was discussed based on the growth rate measurement. Selective growth of seed grains was observed when sufficient seed grains were added to the starting powder mixture.