Optimal design of plastic cylindrical shells of von Mises material

Optimal design of plastic circular cylindrical shells of von Mises material is studied. The optimization problem is stated as the maximization problem of the load carrying capacity for given weight of the shell. Shells with constant and piecewise-constant thickness are considered. The maximization problem is performed under the requirement that the material volume of the stepped shell is equal to the case of the reference shell of constant thickness. The material of the shell is assumed to be an ideal rigid plastic obeying von Mises yield criterion. The considered nonlinear problems are solved by using the CASes method.     

Optimal design of underwater stiffened shells

The optimal design parameters of stiffened shells are determined using a rational multicriteria optimization approach. The adopted approach aims at simultaneously minimizing the shell vibration, associated sound radiation, weight of the stiffening rings as well as the cost of the stiffened shell. A finite element model is developed to determine the vibration and noise radiation from cylindrical shells into the surrounding fluid domain. The production cost as well as the life cycle and maintenance costs of the stiffened shells are computed using the Parametric Review of Information for Costing and Evaluation (PRICE) model. A Pareto/min-max multicriteria optimization approach is then utilized to select the optimal dimensions and spacing of the stiffeners. Numerical examples are presented to compare the vibration and noise radiation characteristics of optimally designed stiffened shells with the corresponding characteristics of plain un-stiffened shells. The obtained results emphasis the importance of the adopted multicriteria optimization approach in the design of quiet, low weight and low cost underwater shells which are suitable for various critical applications. Received September 14, 2000 Communicated by J. Sobieski     

Optimum design of stiffened cylindrical shells with natural frequency constraints

The design optimization of axially loaded, simply supported stiffened cylindrical shells for minimum mass is considered. The design variables are thickness of shell wall, thicknesses and depths of rings and stringers, number/spacing of rings and stringers. Natural frequency, local and overall buckling strengths and direct stress constraints are considered in the design problems. Three different combinations of stiffeners are considered. In each case, the independent effects of behaviour constraints are also studied. The optimum designs are achieved with one of the standard nonlinear constrained optimization techniques (Davidon-Fletcher-Powell method with interior penalty function formulation) and few optimal solutions are checked for the satisfaction of Kuhn-Tucker conditions.     

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.     

Optimal design of shells against buckling subjected to combined loadings

In this paper, the problem of optimal design of shells against instability is considered. A thin-walled shell is loaded, in general, by overall bending moment, constant or varying along an axis of a shell, by the appropriate shearing force and by an axial force and a constant torsional moment. We look for the shape of middle surface as well as the thickness of a shell, which ensures the maximum critical value of the loading parameter. The volume of material and the capacity of a shell are considered as equality constraints. The concept of a shell of uniform stability is applied.     

Optimal design of a cylindrical shell loaded by internal pressure

The problem of the optimal design of a noncircular cylindrical shell loaded by uniform internal pressure is presented. As an optimization criterion the minimal ratio of structure mass to medium mass is taken into account. Solution constraints are geometrical and strength conditions. Numerical analysis is realized using the finite element method. Optimal shapes of steel and aluminium shells are determined.     

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.     

Nonlinear analysis of reinforced concrete cylindrical shells

In this paper, analysis of reinforced concrete cylindrical shells is performed using a strain-based finite element. The shell element employed is bidimensional, cylindrical circular and has four-nodes and five nodal degrees of freedom. The nonlinearities due to concrete cracking and yielding of the steel are taken into account. The constitutive models for the materials employ the smeared cracking concept and a finite element layered approach. Concrete is modeled by a strain-induced orthotropic-elastic model under plane state of stress. A bilinear steel model is used and the stress/reversal with Baushinger effect is included. Examples show the good accuracy provided by this analysis.     

Free vibration analysis of circular cylindrical shells

Determination of the vibrational characteristics of circular cylindrical shells often requires significant computational effort. This paper presents the results of a comprehensive, computer based, numerical investigation of the free vibration of circular cylindrical shells. An analytical procedure which accurately predicts the natural frequencies and radial mode shapes (corresponding to axial wave number and circumferential wave number both equal to one) for a wide range of circular cylindrical shells is developed. The procedure is applicable to shells either with or without a top closure. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.     

Buckling analysis of ring-stiffened oval cylindrical shells

An energy principle is employed to derive the equations governing the stability of a simply-supported, eccentrically ring-stiffened, oval, orthotropic cylindrical shell. The kinematic relations used are those of Love-type shell theory and the effect of reinforcing rings is accounted for by a distributed stiffness approach. The cylinder is subjected to a combination of uniform axial and lateral pressures.

It is determined that the domain of stability of such a stiffened cylinder is bounded by two distinct solutions, herein denoted as corresponding to ‘long’ and ‘short’ axial wavelengths, with the extent of the short wavelength solution being dependent upon the degree of stiffening afforded by the rings.

The analysis of the effects of ring eccentricity shows that ovals are affected in a similar manner to circular cylinders in that outside rings provide the greatest capacity for sustaining axial compression, while inside rings are capable of supporting the greatest lateral pressure.

Finally, it is found that the buckling load of an oval cylinder under uniform lateral pressure slightly exceeds the corresponding value for an equivalent circular cylinder. As a further verification of this phenomenon, a Rayleigh-Ritz procedure is employed to determine the buckling load of an oval ring under uniform radial load. The results of this analysis corroborate those obtained for the cylinder.     

High-precision finite element analysis of cylindrical shells

This paper presents the finite element formulation to study the free vibration of cylindrical shells. The displacement function for the high-precision shell element with 16 degrees of freedom is approximated by a Hermitian polynomial of beam function type. The explicit formulation for the high-precision element is extremely efficient. For the purpose of comparison, the subject element is used to study the sample case of free vibration of a shell structure. The results are in good agreement with those published. The study shows that solution accuracy with fewer elements is assured and that accurate solutions are obtainable in the high-frequency range.     

Optimal design of shells against buckling by means of the simulated annealing method

In this paper, the problem of optimal design of shells against instability under combined state of loadings is considered. We look for the shape of a meridian as well as the thickness of a shell, which ensures the maximal critical value of the loading parameter. The equality constraining the volume of material and the capacity of a shell are considered. The concept of a shell of uniform stability is applied.     

功能梯度薄壁圆柱壳的自由振动

研究了由功能梯度材料制成的薄壁圆柱壳的自由振动.采用幂律分布规律描述功能梯度材料沿厚度的梯度性质,根据Donnell壳体理论,导出了功能梯度材料薄壁圆柱壳线性振动的简化控制方程.基于此理论分析了功能梯度圆柱壳的自由振动特性,给出了两端简支功能梯度材料薄壁圆柱壳小挠度固有振动的频率公式.以简支圆柱壳作为算例,与前人结果及有限元法对比验证了该简化功能梯度薄壁圆柱壳理论的正确性,同时讨论了周向波数及梯度指数对其频率的影响.     

Linear and nonlinear stability analysis of cylindrical shells

The paper describes the application of a curved isoparametric shell element to large displacement analyses including instability phenomena. A total Lagrangian formulation has been adopted using the standard incremental/iterative solution procedure. The linear stability analyses usually performed for the initial position were repeated at several advanced fundamental states on the nonlinear prebuckling path. Thus a current estimate of the final failure load is given. The method has been applied to several perfect and imperfect cylindrical shells under uniform pressure or wind load. Finally the example of a cylindrical panel under one concentrated transverse load is discussed.     

Analysis of stresses in internally loaded cylindrical shells

Simply supported cylindrical shells under internal fluid and granular loading are investigated. A Fourier series solution is presented and results are shown for various shell geometries. The accuracy of the results is discussed and a comparison is made with other approximate methods available in the materials handling industry.     

Shape optimization of dynamically loaded viscoelastic cylindrical shells

Axisymmetric deflections of cylindrical shells of variable thickness are examined. The shell material is linear viscoelastic. The loading is of the impulsive type—it induces inside the shell a radial velocity field. The amount of kinetic energy is prescribed. The thickness function includes some design parameters, which must be calculated so that deflections of the beam are minimal. Only designs with a given volume are considered.For solving this optimization problem the space variable and the time will be separated. For evaluating the minimum of the objective function the Nelder-Mead technique has been used. Computations show that the viscosity effect is essential only for very short shells. Some numerical examples are presented.     

Optimization of inelastic cylindrical shells with internal supports

A non-linear programming method is developed for optimization of inelastic cylindrical shells with internal ring supports. The shells under consideration are subjected to internal pressure loading and axial tension. The material of shells is a composite which is considered as an anisotropic inelastic material obeying the yield condition suggested by Lance and Robinson. Taking geometrical non/linearity of the structure into account optimal locations of internal ring supports are determined so that the cost function attains its minimum value. A particular problem of minimization of the mean deflection of the shell with weakened singular cross sections is treated in a greater detail.     

Optimal design of axially symmetrical shells under hydrostatic pressure with respect to their stability

In this paper, the problem of optimal design of axially symmetrical shells against instability is considered. We look for the shape of middle surface as well as the thickness (constant or variable) of a shell, which ensure maximal value of the critical hydrostatic pressure. As the equality constraints the volume of material and the capacity of a shell are considered. The concept of a shell of uniform stability is applied. Received November 23, 1998     

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.     

螺栓连接薄壁柱壳结构固有特性分析

本文以螺栓连接的薄壁柱壳结构为研究对象,基于ANSYS有限元分析软件,建立其精细有限元模型,并采用基于接触的预应力法分析系统的固有特性,通过与模态实验得到的系统振型和固有频率结果进行对比,验证所建模型的有效性和准确性,并在此基础上,分析系统转速和螺栓预紧力对系统固有特性的影响.研究结果表明：随着转速和预紧力的增加,结合面的连接刚度和系统刚度增加,系统的前6阶固有频率不断增加;转速较低时,预紧力对系统的固有特性的影响占主导;预紧力足够大时,转速对系统的固有频率的影响占主导.