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.     

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.     

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.     

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.     

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.     

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.     

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.     

Multicriteria optimization of cylindrical sandwich shells under combined loads

The paper is about multicriteria optimization of thin-walled cylindrical shells subjected to simple loads, such as axial compression and external pressure, and combined loads (axial compression and pressure). The optimization problem is given as a bicriterial one, with the weight of the shell as the first objective, and the flexibility of the shell as the second. The set of constraints includes the stability condition, strength conditions for each layer, technological and constructional requirements, and so on. Numerical calculations were obtained with the help of the program MOST. MOST is designed to solve multicriteria optimization problems for nonlinear engineering models with discrete and continuous decision variables. In MOST a concept of Pareto optimum is introduced for generating a set of optimal compromise solutions. The best optimal solution must be chosen from the Pareto optimal set with the help of the preference functions. Results of numerical calculations are presented in the form of tables and diagrams.     

Failure of axially compressed frangible joints in cylindrical shells

A computer program for the analysis of stress, nonlinear collapse and bifurcation buckling of hybrid bodies of revolution (BOSOR6) is used for the prediction of failure of axially compressed cylinders containing frangible joints. Plasticity and moderately large deflections are included in the analytical models. The structure in the immediate neighborhoods of the frangible joint notches is modeled with use of eight-node solid isoparametric finite elements of revolution and the rest of the structure is modeled with use of computationally efficient thin shell elements.Theoretical predictions are compared to test results. Certain aspects of the test specimens and boundary conditions remain unknown, and parameters in the analytical models are established and varied in order to reveal what these test conditions must have been. For reasonable values of these parameters, theoretical and experimental joint failure loads agree to within 2%.     

Orthotropic cylindrical shells under line load along a generator

A technique for elastic analysis of an orthotropic cylindrical shell subjected to a uniform line load along a generator is developed. An accurate form of governing differential equations is derived and a mathematically discrete element method is used for its solution. The shell is divided into a finite number of longitudinal strips and the derivatives with respect to the circumferential coordinate in the governing equation are replaced by their finite difference relationships. The solution of the resulting equations is written in closed form. A computer program to implement this technique is developed and the computed results are compared with published experimental and analytical results. An excellent agreement is obtained. Some new results for a shell with fixed end boundary conditions are also presented.     

Geometrically nonlinear analysis of cylindrical shells using surface-parallel quadratic elements

A moderately thick cylindrical shell isoparametric element that is capable of accurately modeling cylindrically curved geometry, while also incorporating appropriate through-thickness kinematic relations is developed. The analysis accounts for fully nonlinear kinematic relations so that stable equilibrium paths in the advanced nonlinear regime can be accurately predicted. The present nonlinear finite element solution methodology is based on the hypothesis of linear displacement distribution through thickness (LDT) and the total Lagrangian formulation. A curvilinear side 16-node element with eight nodes on each of the top and bottom surfaces of a cylindrical shell has been implemented to model the transverse shear/normal deformation behavior represented by the LDT. The BFGS iterative scheme is used to solve the resulting nonlinear equations. A thin-shallow clamped cylindrical panel is investigated to test the convergence of the present element, and also to compare the special case of the present solution based on the KNSA (von Karman strain approximation) with those computed using the available faceted elements, discrete Kirchhoff constraint theory (DKT) and classical shallow shell finite elements, spanning the entire computed equilibrium path.     

Buckling and postbuckling of imperfect cylindrical shells under axial compression

A solution methodology is described for the complete analysis of a geometrically imperfect, thin, circular, cylindrical shell loaded by a uniform axial compression. The analysis includes pre-limit point behavior, the establishment of critical conditions (limit point) and post-limit point behavior. The solution scheme is then utilized to study the effects of various geometrical parameters (radius to thickness and length to radius ratios) on the response characteristics of an imperfect, unstiffened, thin, cylindrical shell. These effects are assessed for a virtually axisymmetric-type of geometric imperfection.