The usefulness of static condensation in the finite element analysis of stiffened submersible cylindrical hulls

The usefulness of the static condensation technique in the finite element analysis of stiffened submersible. cylindrical hulls is examined in this paper. The finite element formulation used herein is essentially the same as outlined by the authors in an earlier paper wherein the stiffener is modeled rigorously using axisymmetric thin annular plate elements for the web and axisymmetric thin shell elements for the flange. The static condensation technique has been applied in this paper to reduce these stiffener finite elements so that their effect can be transferred to the shell node at the point of attachment of the stiffener with the shell. The advantage of such condensation of the stiffener elements is the smaller number of equations to be solved without the rigor of the stiffener modeling being lost in any way. The manner of incorporating the condensation in the computer program has been described. Examples of several stiffened submersible cylindrical hulls have been considered as an illustration of the use of the program.     

Edge reinforced circular elastic inclusions in cylindrical shells

The effect of having an edge reinforcement around a circular elastic inclusion in a cylindrical shell is studied. The influence of various parameters of the reinforcement such as area of cross section and moment of inertia on the stress concentrations around the inclusion is investigated. It is found that for certain inclusion parameters it is possible to get an optimum reinforcement, which gives minimum stress concentration around the inclusion. The effect of moment of inertia of the reinforcement of SCF is found to be negligible. The results are plotted in a non-dimensional form and a comparison with flat plate results is made which show the curvature effect. In the limiting case of a rigid reinforcement the results tend to those of a rigid circular inclusion. Results are also presented for different values of μ_e the ratio of extensional rigidity of shell to that of the inclusion.     

Design and analysis of small submersible pressure hulls

Small submersibles, which permit man to observe and work as part of the three-dimensional undersea environment, are among the most promising tools for achieving effective exploitation of the oceans. An important element of any submersible is the pressure hull, frequently contributing one-fourth to one-half and more of the total vehicle weight. The Naval Ship Research and Development Center has played a major role in developing pressure hull structures for undersea vehicles. This paper describes some of the principal structural features of existing and envisioned small submersibles and summarizes recent advances in design and analysis methods. Particular emphasis is given to computer programs developed and/or used at the Center. Specifically, it describes advances in stress, stability, and vibration analyses as well as early stage developments in structural fatigue and reliability analyses. It also discusses computer programs and automated procedures designed for rapid response in feasibility studies and preliminary and final design cycles; these provide for both the generation of input data and the graphical display of computed results.     

Extended capability for automated design of frame-stiffened,submersible, cylindrical shells

This paper presents a procedure and computer program for the minimum weight design of circular, cylindrical, ‘T’ frame (ring) reinforced, submersible shells where all metal thicknesses may be confined to specified gage thickness values. Using the designer specified parameters defining shell radius shell length, eccentricity, operating depth, design factors of safety, construction materials properties and when used, the specified gage thickness values, the program will generate those values of skin thickness stifiener web and flange thicknesses, stiffener web depth and flange width, and if desired, stiffener spacing that will produce the smallest shell weight to liquid weight displaced ratio.Experience with the program has demonstrated that there is usually little weight penalty associated with the use of discrete metal thickness values when the stiffener spacing can be optimized. This weight penalty can, however, be significant where the number of stiffeners is held fixed.     

Bending versus membrane theory in the design of fluid filled, circular cylindrical shells

The note discusses the solutions which result from using Flügge's simpler membrane equations in the analysis of thin walled, fluid filled beam-type, circular cylindrical shells, simply supported over large spans. Comparisons are made with the more comprehensive bending equations in terms of the normal (longitudinal) stresses occurring at the center of the beam.A simple error analysis applied to each stress profile indicates that the variations are not merely a function of sectional slenderness, h²/12a², where h and a are thickness and radius of shell respectively. It is shown that length is also important in weighing the relative merits of the two systems of equations. Instead of referring to longitudinal and circumferential half waves, as is done by Flügge, a simpler parameter, K, incorporating longitudinal and sectional slenderness, is seen to be significant.     

Eccentric electrophoretic motion of a sphere in circular cylindrical microchannels

The eccentric electrophoretic motion of a spherical particle in an aqueous electrolyte solution in circular cylindrical microchannels is studied in this paper. The objective is to investigate the influences of separation distance and channel size on particle motion. A theoretical model is developed to describe the electric field, the flow field and the particle motion. A finite element based direct numerical simulation method is employed to solve the model. Numerical results show that, when the particle is eccentrically positioned in the channel, the electric field and the flow field are not symmetric, and the strongest electric field and the highest flow velocity occur in the small gap region. It is shown that the rotational velocity of the particle increases with the decrease of the separation distance. With the decrease of the separation distance, the translational velocity increases in a smaller channel; while it decreases first and then increases in a relatively large channel. When a particle moves eccentrically at a smaller separation distance from the channel wall, both the translational velocity and the rotational velocity increase with the decrease of the channel size.     

Parametric instability of a circular cylindrical shell with geometric imperfections

The static and dynamic behavior of a compressed circular cylindrical shell having geometric imperfections is analyzed. The analysis is mainly performed by means of the Donnell’s nonlinear shallow-shell theory. However, the refined Sanders shell theory is also used for comparison. A suitable expansion of the radial displacement, able to describe both buckling and dynamic behaviors is developed; the effect of geometric imperfections is accounted for by means of a modal representation. The response of the shell subjected to a sinusoidal axial excitation at its ends, giving rise to a parametric excitation, is considered. The effect of imperfections on the critical value of the dynamic load, that causes the loss of stability of the system, is analyzed. Interesting nonlinear dynamic phenomena are observed: direct resonance with softening behavior and parametric instability with period doubling response.     

Structural, morphological and micromechanical studies on fly ash reinforced PMMA composites

This paper is focused on the study of the structural, morphological, mechanical and microhardness studies on Fly ash reinforced PMMA composites. Fly ash reinforced PMMA composites have been prepared with the sol–gel method. Fourier transformed infrared (FT-IR) spectroscopy, X-ray diffraction, microhardness and atomic force microscopy (AFM) studies have been done on prepared composite. The AFM images confirm the presence of fly ash particles in nanophase within the PMMA matrix. The crystalline size of the in situ generated nanoparticles was investigated with X-ray diffraction technique and it is found that the crystallinity index increases with increasing the concentration of the fly ash. The structural characterization has been done with FT-IR spectroscopy. The FT-IR spectra of pure PMMA and fly ash based composites has been observed and analyzed. The Vickers microhardness indentation technique has been employed to detect the effect of reinforcement of fly ash in the PMMA matrix. Significant changes were observed in the various properties of the fly ash reinforced PMMA composites.     

Asymmetric vibration analysis of thick composite circular cylindrical shells with variable thickness

Thick isotropic and composite shells of revolution are analyzed for vibration characteristics. The theory used is that proposed by Naghdi, which includes the thickness normal strain and shear deformation. A curved-semianalytical finite element is used to solve the problem. Parametric studies are conducted to study the effect of various parameters on the vibration behavior of shells. The effect of thickness variation along the axial direction with a constraint on mass is also studied.     

Boundary stabilization of a thin circular cylindrical shell subject to axisymmetric deformation

In this paper, stabilization of a thin circular cylindrical shell with one edge clamped and the other edge acted by boundary control is studied. It is shown that uniform stability can be achieved.     

Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell

In this research, thermal buckling and forced vibration characteristics of the imperfect composite cylindrical nanoshell reinforced with graphene nanoplatelets (GNP) in thermal environments are presented. Halpin–Tsai nanomechanical model is used to determine the material properties of each layer. The size-dependent effects of GNPRC nanoshell is analyzed using modified couple stress theory. For the first time, in the present study, porous functionally graded multilayer couple stress (FMCS) parameter which changes along the thickness is considered. The novelty of the current study is to consider the effects of porosity, GNPRC, FMCS and thermal environment on the resonance frequencies, thermal buckling and dynamic deflections of a nanoshell using FMCS parameter. The governing equations and boundary conditions are developed using Hamilton’s principle and solved by an analytical method. The results show that, porosity, GNP distribution pattern, modified couple stress parameter, length to radius ratio, mode number and the effect of thermal environment have an important role on the resonance frequencies, relative frequency change, thermal buckling, and dynamic deflections of the porous GNPRC cylindrical nanoshell using FMCS parameter. The results of current study can be useful in the field of materials science, micro-electro-mechanical systems and nano electromechanical systems such as microactuators and microsensors.

     

Combined stiffening and in-plane boundary conditions effects on the buckling of circular cylindrical stiffened-shells

The influence of in-plane boundary conditions on the critical loads of axially compressed simply supported stiffened cylindrical shells, stiffened by stringers and by combinations of rings and stringers is studied. It is observed that the axial restraint, u = 0, at the edges and the dimensions of either the stringers or the rings characterize the type of influence experienced. In shells stiffened by “medium” and “heavy” stringers the axial restraint is a predominant factor and the “weak in shear”, N_xφ = 0, B.Cs. have only a slight secondary effect. For such shells a “stiffening” effect is observed for SS2 and SS4 B.Cs. As the stringers become “weaker” the influence of the axial restraint diminishes and the isotropic or ring-stiffened like type of behavior, “sensitivity” to the vanishing of the circumferential restraint, overcomes the “stiffening” effect due to u = 0.In shells stiffened by combinations of rings and stringers the influence of the in-plane boundary conditions is governed by the relative magnitudes of the rings and stringers under consideration. Combinations of “heavy” stringers and “weak” rings behave like stringer-stiffened shells, exhibiting the “stiffening” effect due to u = 0 whereas shells stiffened by “heavy” rings and “light” stringers tend to behave like ring-stiffened shells, revealing their “sensitivity” to the “weak in shear” boundary conditions, N_xφ = 0.     

Structural synthesis of fast two-layer neural networks

Methods of construction of structural models of fast two-layer neural networks are considered. The methods are based on the criteria of minimum computing operations and maximum degrees of freedom. Optimal structural models of two-layer neural networks are constructed. Illustrative examples are given. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 47–56, July–August, 2000.     

A numerical study of capillary stability in a circular cylindrical container with a concave spheroidal bottom

We study computationally the stability under gravitational and surface forces of a liquid in a circular cylindrical container with a concave spheroidal bottom for the case in which the volume of liquid is sufficiently small so that the bottom is not covered entirely. We assume the gravitational field to be directed along the axis of symmetry of the container, and for a specific container shape we compute the critical Bond number as a function of liquid volume for contact angles γ = 0°, 1°, 2°, and 4°. For the case γ = 0° we present graphically several critical equilibrium configurations and corresponding perturbation modes.     

Natural vibrations and stability of a stationary or rotating circular cylindrical shell containing a rotating fluid

The finite element method is applied to analyze a stationary or rotating cylindrical shell containing a co-rotating compressible fluid. The motion of the rotating fluid is described in the framework of the potential theory. The behavior of shells is analyzed using the classical shell theory. It has been found that the loss of stability in the stationary shells occurs in the form of a flutter. It has been shown that in the case of rotating shells the loss of stability is prevented by taking into account the initial circumferential tension caused by the centrifugal forces.     

Structural optimization of modular product families with application to car space frame structures

This paper extends classical structural optimization from single-product optimization to optimization of a whole family of products that have common modules. It integrates the family commonality problem with the finite element models of the structures. A general mathematical frame where optimization is seen as a balance between cost and performance is given. The most obvious cost function is mass, while performance is taken to be a weighted sum of compliances. As a case study, a car product family consisting of three products is presented. These three products are a base model, a seven-seat version, and a pickup version. The study shows how optimal results are effected by requiring modules to be shared between products. Loads emanating from prescribed acceleration fields that simulate crash situations are used. This is a proof-of-concept paper which is a first step toward including more general manufacturing costs than mass and performance measures other than compliance.     

Computer simulation of an ideal fluid,constant depth,fluidic controlled submersible vehicle

This study was carried out to find a mathematical model that represents uniform potential incompressible steady flow over a two-dimensional blunt body that has mass flow injected into the main flow at a predetermined location on the body geometry. It has application as a towed submersible vehicle.A change in depth of the vehicle is sensed by a depth valve which introduces a pitch command to the fluidic device. The control activates a thruster, thereby restoring the vehicle to its desired depth. The fluidic control part of the vehicle, however, is not investigated in the study.The shape of the vehicle (a streamline) is obtained by a combination of the elemenatry flow patterns, namely, uniform flow and a distribution of sources and sinks. The computer is used to determine the best combination possible by adjusting the elementary flow patterns and the positions of the control jet on the vehicle. Some numerical examples have been made. It is seen that a suitable mathematical model of a towed vehicle to operate automatically at constant depth can be designed.     

Predictive modeling of the lateral drift capacity of circular reinforced concrete columns using an evolutionary algorithm

The drift capacity of reinforced concrete (RC) columns is a crucial factor in displacement and seismic based design procedure of RC structures, since they might be able to withstand the loads or dissipate the energy applied through deformation and ductility. Considering the high costs of testing methods for observing the drift capacity and ductility of RC structural members in addition to the impact of numerous parameters, numerical analyses and predictive modeling techniques have very much been appreciated by researchers and engineers in this field. This study is concerned with providing an alternative approach, termed as linear genetic programming (LGP), for predictive modeling of the lateral drift capacity (Δ_max) of circular RC columns. A new model is developed by LGP incorporating various key variables existing in the experimental database employed and those well-known models presented by various researchers. The LGP model is examined from various perspectives. The comparison analysis of the results with those obtained by previously proposed models confirm the precision of the LGP model in estimation of the Δ_max factor. The results reveal the fact that the LGP model impressively outperforms the existing models in terms of predictability and performance and can be definitely used for further engineering purposes. These approve the applicability of LGP technique for numerical analysis and modeling of complicated engineering problems.

     

Structural parametric synthesis of automatic control systems with distributed parameters

The problem of synthesizing automatic controllers for one class of linear plants with distributed parameters is considered from the general point of structural theory of distributed systems. On this basis, methods to construct control algorithms for various modifications of control actions are proposed. The results obtained are illustrated by examples of synthesizing automatic control systems of nonstationary heat conduction processes.     

Collapse of long, noncircular, cylindrical shells under pure bending

This paper describes an extension of a method developed in a previous paper to determine the moment carrying capacity of elastoplastic noncircular cylindrical shells with infinite length by the finite element method. As a result of the shape change in the cross section of a shell during deformation, the bending moment reaches a global maximum value and then decreases as the bending curvature further increases. The shell would consequently collapse at the maximum moment. However, a bifurcation buckling may occur before the maximum moment can be developed. This bifurcation buckling could induce collapse of the shell under a moment less than the maximum. Determination of the likelihood that the bifurcation buckling would generate shell collapse may be made from the initial post-buckling behavior. An initial post-buckling analysis based on the J₂ deformation theory of plasticity has been developed in this paper. The finite element method with one spatial variable is used to locate the bifurcation point as well as to analyze the initial post-buckling behavior. Numerical examples of cylindrical shells with various cross-sectional shapes are shown. In particular, for a shell of square cross section, the moment at the bifurcation is much lower than the maximum value; however, the initial post-buckling analysis reveals that the state of equilibrium is still stable. Deep post-buckling analysis is required to determine the moment carrying capacity of a shell with such cross section.