Shells Of Constant Thickness Research Articles

Conical-Shaped Shells of Non-Uniform Thickness Vibration Analysis Using Higher-Order Shear Deformation Theory

Conical-Shaped Shells of Non-Uniform Thickness Vibration Analysis Using Higher-Order Shear Deformation Theory

Analytical Modeling for Photocurrent and Detectivity of TiO2/ZnS Core‐Shell Quantum Dot Photodetectors

AbstractIn this paper, a theoretical model has been presented to calculate the photocurrent and detectivity in a TiO2/ZnS core‐shell quantum dot (CSQD) photodetector. Analytical modeling permits to calculate the available photocurrent and corresponding detectivity from the CSQD structures. In this theoretical model, the subband energy levels of the CSQD are estimated using the 3D symmetric quantum box structures with a finite potential barrier. The finite band offset determines the number of available subband energy levels in the CSQD structures depending on the size of the core. Theoretical results show the variation of photocurrent and corresponding detectivity with different core sizes of the CSQD for a constant shell thickness. The calculations indicate that for electronic intersubband transitions detectivity is higher compared with the hole transitions.

Predicting the Geometry of Core-Shell Structures: How a Shape Changes with Constant Added Thickness.

The core-shell assembly motif is ubiquitous in chemistry. While the most obvious examples are core/shell-type nanoparticles, many other examples exist. The shape of the core/shell constructs is poorly understood, making it impossible to separate chemical effects from geometric effects. Here, we create a model for the core/shell construct and develop proof for how the eccentricity is expected to change as a function of the shell. We find that the addition of a constant thickness shell always creates a relatively more spherical shape for all shapes covered by our model unless the shape is already spherical or has some underlying radial symmetry. We apply this work to simulated AOT reverse micelles and demonstrate that it is remarkably successful at explaining the observed shapes of the chemical systems. We identify the three specific cases where the model breaks down and how this impacts eccentricity.

EQUATIONS OF MOTION OF AN ISOTROPIC SPHERICAL MOMENT ELASTIC SHELL*2

Using the previously obtained equations of motion of thin moment elastic shells of constant thickness with an arbitrary middle surface, the equations of motion of an isotropic moment spherical shell in terms of forces and “displacements” (kinematic parameters) are constructed. In this case, the metric of the middle spherical surface is taken into account, as the curvilinear coordinates of which two angular coordinates of the standard spherical coordinate system with the origin at the center of the middle surface are used. First, a closed system is written down, which includes the equations of motion in the physical components of the tensors of internal forces and moments, as well as additional similar characteristics corresponding to the moment properties of the model, and physical relationships. Then, by excluding physical relations, it is reduced to twelve equations of motion in kinematic parameters, written in operator form. In this case, the coefficients of partial derivative operators are simplified by neglecting terms that have a higher order of smallness relative to the thickness of the shell. Despite the bulkiness of the system, it is written in a compact form. Boundary conditions are not written, since the shell is considered closed. By introducing additional hypotheses similar to those used in the classical theory of shells (neglecting the compression of a normal fiber, the Kirchhoff – Love hypothesis about the connection between the tangential components of the rotation angle vector of a normal fiber and normal displacement, as well as the hypothesis about the connection between the normal to the middle surface part of the coordinate of the rotation angle vector and its tangential components) the number of equations and unknowns decreases. To carry out this procedure, a variational Hamilton equation is constructed, which takes into account the connections between kinematic parameters imposed by the hypotheses, and then the corresponding one is transformed using the generalized Ostrogradsky – Gauss theorem.

Transient Deformation of an Anisotropic Cylindrical Shell with Structural Features

In this work, a new transient function of normal displacements is obtained in a thin elastic anisotropic cylindrical shell of constant thickness with structural features. Structural features form of two sequences in angular direction of weld spots or rivets. Structural features are mathematically described by point boundary conditions of rigid pinching or point boundary conditions of hinge support, accordingly. A load with time variable amplitude and impact boundaries influences on the outer surface of the shell along the normal. Such movement of the shell is considered in the cylindrical coordinate system as connected with the shell axis. Kirchhoff–Love hypothesis are confirmed as a shell model. The solution of this problem can be formed with the help of Green function method and lift compensation method. The required function of transient normal displacements is represented as the sum of integral operators of Green convolution for an infinite shell with functions of current transient load and compensating loads out of point boundary conditions. Compensating loads satisfying to boundary conditions can be found based on the solution of Volterra integral equations of the first kind with the difference kernel. Green function is such kernel. The system solution can be executed including preliminary discretization of compensating time loads. The convolution integrals can be taken numerically with the help of quadrature formula by the method of rectangles. The verification of the method is represented by comparing the solution of specific case with the known solution for a hinged isotropic cylindrical shell.

The effect of infill density on the fire properties of polylactic acid 3D printed parts: A short communication

The use of 3D printing technology for manufacturing construction materials is gaining popularity, however, only a few studies have reported the fire behavior of such parts. In this research, the fire properties of 3D printed polylactide acid (PLA) parts with varying infill densities along with the tensile properties were analysed. The results from the fire tests showed that increasing the infill density increased the fuel load, which sustained combustion. Hence, the peak heat release rate and total heat release increased with an increment in infill density percentage. It was also observed that the increasing infill density had no effect on the flammability rating of the parts due to the constant shell thickness used for all the parts. In addition, the tensile strength and ductility of the parts increased with density as a porous part is more susceptible to failure than a solid homogeneous part.

3D topology optimization of sandwich structures with anisotropic shells

The development of a density-based 3D minimum compliance topology optimization approach for sandwich structures with anisotropic shells is presented. A constant thickness shell is enforced at the interface of a base structure through a two-step filtering approach. Homogenous effective properties of a cellular material are assigned to the base structure while the shell is treated as a constant stiffness laminate with anisotropic properties. Local shell normal vectors are obtained from the density gradient introduced in the second filtering step and local material orientations in the shell’s tangent plane are approximated based on the fabrication process of the structure. Simple approximating strategies using the Gauss map are presented for a fabric draping process and the fused filament fabrication additive manufacturing process. The effect of material anisotropy on the optimal topology is studied on the Messerschmitt Bölkow Blohm beam benchmark problem. An application to composite structures is then presented where a square, simply supported laminate is reinforced on one face by a topology optimized sandwich structure. Though manufacturability cannot be ensured in the current implementation, careful consideration of the optimization parameters allow to constrain the problem towards manufacturable solutions using additively manufactured cores.

Effect of core-diameters and shell-thicknesses of Fe3O4/SiO2 composite abrasives on the performance of ultrasound-assisted magnetorheological polishing for sapphire

In this paper, the Fe 3 O 4 /SiO 2 (core/shell) composite abrasives with different core-diameters and shell-thicknesses were prepared successfully by adjusting the TEOS dosages in the hydrolysis reaction, and characterized on the aspects of surface morphology, internal structures, phase components and magnetic properties. Then, targeted experiments were conducted to explore the effects of core-diameters and shell-thicknesses of the composite abrasives on the performance of ultrasound assisted magnetorheological polishing (UAMP) for sapphire wafer. The experimental results show that when the shell-thickness of the composite abrasives is reduced from 30 nm to 10 nm, the surface roughness Ra of thus polished sapphire wafers decreases firstly and then increases afterward, which is opposite to the trend of material removal rate (MRR). And Ra and MRR reach the optimal values of 0.276 nm and 2.068 µm/h, respectively, when using the magnetorheological slurry of composite abrasive with 15 nm shell-thickness. It is believed that the formation rate of the softer chemical products on sapphire surface and their mechanical removal rate almost attain a balance in this case. For abrasives with constant shell-thickness of 10 nm, a lower Ra is achieved when using the composite abrasive with a core-diameter of 100 nm, compared to those abrasives with the core diameter of 200 nm or 20 nm. Although the utilization of composite abrasive with larger core-diameter achieves a higher MRR in UAMP, the surface quality of sapphire wafer deteriorates significantly, with many scratches existing on the wafer surface.

Static Buckling of a Pre-loaded Complex Nano-composite Shell

This paper describes a technique for analyzing the phenomenon of static buckling of a pre-loaded complex nano-composite shell. Most of the works devoted to the analysis of complex structures consider vibration processes, while the phenomenon of buckling can be an important factor that limits the use of new materials in space-rocket hardware. A nano-composite constant-thickness shell consisting of two spherical covers and a cylindrical body is considered. It is acted upon by internal pressure and an axial compressive force. This shell simulates the fuel tank of a launch vehicle. Conditions under which the shell is deformed non-axisymmetrically, buckling statically, are investigated. A technique is proposed that allows the problem to be divided into the analysis of the pre-loaded state of the shell and the analysis of buckling. Further analysis is performed using a technique based on the high-order shear deformation theory and the Ritz method. The problem is discretized by representing the variables that determine the state of the shell in the form of expansions in basis functions with unknown coefficients. Thus, it is the expansion coefficients that become unknown in the problem. The problem of analyzing the pre-stressed state of a structure is reduced to solving a system of linear algebraic equations with respect to the expansion coefficients. The problem of buckling analysis can be reduced to the problem of eigenvalues. The solution to this problem makes it possible to find the minimum value of the compressive load at which the shell buckles, as well as the forms of buckling. The results of applying the developed technique were compared with those of finite element modeling of a structure made of the simplest nano-composite material. The comparison results indicate a high accuracy of the technique described. At the same time, the use of the finite element method for the analysis of large-scale thin-walled structures made of functionally gradient materials is extremely difficult, in contrast to the methodology proposed in the paper. Comparison of various types of nano-reinforcement showed that a rational choice of the type of reinforcement can significantly increase the critical load. In this case, the internal pressure on the shell also significantly affects the critical load.

Natural vibrations of truncated conical shells of variable thickness

The paper presents the results of studying the natural frequencies of circular truncated conical shells, the thickness of which varies along the length according to different laws. The behavior of elastic structure is described in the framework of the classical theory of shells based on the Kirchhoff-Love hypotheses. The corresponding geometric and physical relations together with the equations of motion are reduced to a system of ordinary differential equations for new unknowns. The solution to the formulated boundary value problem is found using Godunov's orthogonal sweep method involving the numerical integration of differential equations by the fourth order Runge-Kutta method. The natural frequencies of vibrations are evaluated using a combination of a step-wise procedure and subsequent refinement by the interval bisection method. The reliability of the obtained results is verified by making a comparison with the known numerical-analytical solutions. The dependences of the minimum vibration frequencies obtained at shell thicknesses subject to a power-law variation (linear and quadratic, having symmetric and asymmetric shapes) and harmonic variation (with positive and negative curvature) are investigated for shells with different combinations of boundary conditions (free support, rigid and cantilever fastening), cone angles and linear dimensions. The results of the study confirm the existence of configurations, which provide a significant increase in the frequency spectrum in comparison with shells of constant thickness under the same limitations on the weight of the structure.

Thin Spherical Elastic-Plastic Shells under the Action of Concentrated Loads

Thin isotropic rotation shells of constant thickness taking into account the appearance of plastic deformations under the local loads are considered. The method of running with discrete orthogonalization is used for the numerical realisation of the present problem. Thin spherical shells with the angle 90 degrees and the relation of the radius to the thickness 100 under local load are considered.

Vibration analysis of a fluid conveying sandwich cylindrical shell with a soft core

The free vibrations of a circular cylindrical sandwich shell with a flexible core containing a flowing fluid are investigated. Within the framework of the higher-order sandwich panel theory which assumes a variable displacement through the thickness, the core flexibility is taken into account. Using Hamilton’s extended principle, for an inviscid, non-rotational, laminar and incompressible flow, via the potential flow theory, the governing equations of the coupled structure and fluid system are derived. The eigenvalue problem’s equations are found by implementing a modal expansion method which has been validated by the existing results and is found to be accurate. The effect of the axial flow velocity, circumferential wave number, core to total thickness ratio and total thickness to mean radius ratio on the natural frequencies are investigated. It is found that taking into account the core's flexibility results in lower frequency values. The study shows that, unlike in dry shells, increasing the ratio of core thickness to total thickness reduces the natural frequencies monotonically in wet shells. For a constant total shell thickness, the critical velocity of the fluid decreases with increases in core thickness.

Stress-constrained shell-lattice infill structural optimisation for additive manufacturing

ABSTRACT This paper presents a numerical study on stress-constrained shell-lattice infill structural optimisation. This problem is inherently challenging for several reasons: (i) different stress measures have to be used for the solid shell and the porous lattice infill, and the two types of stress constraints make the problem extremely complex to solve and (ii) involvement of the shell layer further complicates the optimisation problem modelling and its solution. To address these challenges, two stress constraints were formulated, i.e. a von Mises stress-based constraint for the solid shell layer and a Tsai-Hill yield criteria-based constraint for the porous lattice. Then, level set function is adopted to represent the shape of the shell layer and the constant-thickness shell layer is modelled based on the signed distance feature. Then, a comprehensive and accurate sensitivity result is derived to guide the concurrent structural shape and lattice density optimisation. A few numerical examples will be studied to prove the effectiveness of the developed algorithm. Some interesting phenomena have been observed, such as the soft narrow band at the shell-lattice interface to mitigate stress concentration.

Calculation of stress concentrations in orthotropic cylindrical shells with holes on the basis of a variational method

A variational numerical-analytical method (called the RVR method) is suggested for calculating the strength and stiffness of statically loaded non-thin orthotropic shell structures weakened by holes (stress concentrators) of arbitrary shapes and sizes. The theoretically substantiated new method is based on the Reissner variational principle and the method of I. N. Vekua (the method of decomposing the desired functions into the Fourier series of the orthogonal Legendre polynomials with respect to the coordinate along the constant shell thickness). In this case, the use in the proposed RVR method of the general equations of three-dimensional problems of the linear theory of elasticity makes it possible to determine the total stress-strained state of an elastic shell (in particular, a plate) with holes. At the same time, using the R-functions, at the analytical level, the geometric information of boundary-value problems for multiply connected domains is taken into account and solutions structures are constructed that exactly satisfy different variants of boundary conditions. The use of a software-implemented algorithm for the two-sided integral assessment of the accuracy of approximate solutions in the study of mixed variational problems helps automate the search for such a number of approximations in which the process of convergence of solutions becomes stable. For orthotropic and isotropic materials, the possibilities of the RVR method are shown in numerical examples of solving the corresponding boundary value problems of calculating the stress concentration in a cylindrical shell with an elliptical or rectangular hole under axial load. The results of the performed tests are discussed, and the features characteristic of the new method prove that it can be effectively used in the design of critical lamellar and shell elements of structures in various fields of modern technology.

Numerical use of {[formula omitted]}-approximation method thermoelastic anisotropic thin shell theory equations represented in a special form

A linear uncoupled quasi-static theory of thermoelastic anisotropic thin shells of constant thickness is formulated. In the derivation of equations and boundary conditions, a variant of the {m,n}-approximation method, which is based on the variational principle of the thermoelasticity theory, is used. According to this method, the unknown functions are represented in the form of a series of Legendre polynomials in the transverse coordinate that agree with the force boundary conditions on the facial surfaces. From the system of equations of the constructed theory for generalised displacements, strains, and stresses, a system of equations for generalised displacements is obtained; this system is solved for the second derivatives of generalised displacements with respect to one of the Gaussian parameters of the middle surface. For a system of partial differential equations represented in such a form, the known techniques for the reduction of systems of two-dimensional equations to normal systems of ordinary differential equations, which can be solved by standard numerical methods, can be applied. The system of equations for generalised displacements is reduced to a normal system of ordinary differential equations in the case of a plane deformation of a cylindrical panel. Through the use of these equations and the S. K. Godunov method of orthogonal successive substitutions, the bending problems of a planar beam subjected to a mechanical load or a thermal load and a circular cylindrical panel exposed to a thermal load are numerically solved. It is demonstrated that the proposed equations are particularly suitable for the analysis of boundary effects in planar beams and circular cylindrical panels.

Finite Element Modelling and Free Vibration Analysis of RC Shell & Spatial Structures for Seismic Evaluation

In this study, the finite element modeling of Shell and spatial structures has been done to understand its performance during earthquake using SAP 2000 (version 14). The structure is idealized as an assemblage of thin constant thickness shell element with each element subdivided into 3 numbers of layers. This study deals with free vibration analysis of shell and spatial structures to get a first important insight into structural dynamic properties. The free vibration analysis of Cylindrical Shell structure, V-type folded plate structure and Spherical Dome structure is done using the finite element model in software SAP 2000. It is relatively a simpler way to explore the seismic behavior of structures and an attempt has been made here for shell and spatial structures. A three-dimensional finite element analysis is performed to assess the seismic performance of the structure subjected to earthquake actions.

Smart damping of large amplitude vibrations of variable thickness laminated composite shells

This paper is concerned with the smart constrained layer damping (SCLD) treatment of laminated composite shells with variable thickness undergoing geometrically nonlinear vibrations. Three dimensional fractional derivative model (FDM) has been implemented for modelling the constrained viscoelastic layer of the SCLD treatment. The constraining layer of the SCLD treatment is made of vertically/obliquely reinforced 1–3 piezoelectric composites (PZCs) and acts as the distributed actuator. The strain-displacement relations are based on the simplified Novozhilov nonlinear shell theory to introduce the geometric nonlinearity in the large amplitude vibrations of the variable thickness shells. A three dimensional smart nonlinear finite element (FE) model has been developed for carrying out this analysis. Several numerical results are presented to check the accuracy of the present three-dimensional FDM for analyzing the passive and active control authority of the SCLD patch. Also the efficacy of the activated SCLD patch in controlling geometrically nonlinear vibration is computed for variable thickness shells and compared with shells of constant thickness.

Optimal design of a cylindrical composite panel of piecewise constant thickness

PurposeThe purpose of this paper is to investigate the problem of optimizing geometrical and physical parameters of a stepped shell that maximize its rigidity and strength for given overall shell dimensions and fixed weight equal to the weight of a shell of constant thickness.Design/methodology/approachA mathematical model of the construction’s stress-strain state is described by solving a system of differential equations for each of the constituent parts of the shell, conjugation conditions on the division lines and boundary conditions. The stated optimization problem is reduced to a nonlinear programming problem, which is solved by the deformable polyhedron method in combination with the method of direct search and using the parallel computing package in the Wolfram Mathematica software application.FindingsAs follows from the results of the calculation, optimizing the shell parameters allows for a substantial increase in rigidity (decrease of the greatest deflection) and strength (increase of the load-carrying capacity) of the shell of constant stepwise thickness, as opposed to a shell of constant thickness, with constant weight and dimensions.Originality/valueA problem of optimal design of a cylindrical composite panel of piecewise constant thickness is solved in the presented work. Numerical examples demonstrate that a substantial increase in rigidity and strength of a stepped composite shell can be achieved by the optimal choice of its geometrical and physical parameters.

05.16: Stability behavior of graded dented cylindrical steel shells under the action of combined external and axial pressure

ABSTRACTThin‐walled cylindrical steel shells such as silos, tanks and other containers are used in various applications of engineering. For economic reasons, large fluid storage steel tanks are made with varying thickness in height. Cylindrical steel shells with stepwise variable wall thickness are the most prevalent structural components in petrochemical and oil industry. However, during the construction procedure and service life, these reservoirs may be exposed to some geometrical imperfections in the form of dents. These shells are subjected to peripheral pressure loading and when a large liquid storage is discharged, an internal suction will be applied to its wall and head, causing external pressure on the wall and axial compression on the head. These structures are prone to fail by buckling under external pressure and axial compression. Previous studies show that the stability behavior of cylindrical shells under pressure load is strongly dependent on the nature and magnitude of the imperfections. Despite many studies on the buckling behavior of thin‐walled cylindrical steel shells of constant thickness, so far only a few investigations have been undertaken to examine instability behavior of these structures with thickness variation under the action of combined external pressure and axial compression, considering the dent imperfections. In this study, the effects of vertical and horizontal dents on the buckling and post‐buckling behavior of dented graded cylindrical steel shells with two and three layers under the action of a combination of peripheral and axial pressure are investigated. The models are designed in practical dimensions, with some horizontal and vertical dents in different positions. In the present study, non‐linear buckling and post‐buckling solutions of thin‐walled cylindrical steel shell with varying thickness are obtained by using ABAQUS, which is a general‐purpose finite element program designed specifically for advanced structural analysis.

THEORETICAL INVESTIGATION OF STRESSES DISTRIBUTIONS IN HOLLOW SANDCRETE BLOCKS DUE TO VARIATION OF CAVITY SIZES AND NUMBER WEB THICKNESS

The relationship between cavity size and number on one hand and combinations of web thicknesses were investigated theoretically. The least number of cavities was 4 for end-web to centre web ratio of 1:2 at constant shell thickness with the least web thickness equal to 12.5mm. The effects of the number of cavities and web thickness on strength were also investigated. The test thin plate distributes the load on the block and the hollow block is regarded as a two way slab. One of the principal findings is that the variation of maximum stresses with the number of cavity is Gaussian for end-web to centre-web ratio of 1:1 but polynomial for 1:2. In addition, the lowest stress is induced when the end to centre ratio is one. The maximum stress, (21.5N/mm 2 ) occurred at the cavity length (a * ) of 125mm for 3 cavities while the end (end centre) web thickness (t) was 25mm respectively. In order words, this combination should be avoided as it will lead to creation of highest stress in the hollow sandcrete blocks. The configuration which will result in least stress (0.5N/mm 2 ) is ( a * , N, t) = (50mm, 4mm, 50mm). However, this combination also gave a high maximum stress (6.9N/mm 2 ) in a web, implying that the right choice of configuration should be rather the one that creates the smallest set of maximum stresses in all members. Overall, the best configuration is 2 cavities with web thickness 50mm for an end web to centre web ratio of 1:1 (3.3N/mm 2 ). The corresponding values for 1: 2 ratios are 3 cavities with 50mm shell thickness (4.8N/mm 2 ). The method presented showed meaningful insight could be investigating theoretically. http://dx.doi.org/10.4314/njt.v35i2.4