scholarly journals Optimal Design of Single-Layered Reinforced Cylindrical Shells

2021 ◽  
Vol 24 (1) ◽  
pp. 58-64
Author(s):  
Heorhii V. Filatov ◽  
Keyword(s):  
Optimal Design ◽  
Numerical Experiment ◽  
Wall Thickness ◽  
Random Search ◽  
Cylindrical Shells ◽  
Compressive Load ◽  
Mathematical Programming Problem ◽  
Feasible Region ◽  
Shell Weight ◽  
Longitudinal Stiffeners

This paper discusses the application of the random search method for the optimal design of single-layered reinforced cylindrical shells operating in a neutral environment. When setting a mathematical programming problem, the minimum shell weight is considered as an objective function. The critical stresses are determined according to the linear theory in the elastic region of the material. As the constraints imposed on the feasible region, the constraints on the strength, general buckling and partial buckling of a shell are accepted. The aim of this paper is to study the weight efficiency of various types of shell reinforcements and the influence of an optimum-weight shell on the parameters of an axially-compressed one. A numerical experiment was carried out. Dependencies of shell weight, wall thickness, and reinforcement parameters on the magnitude of a compressive load were investigated for shells with different types of reinforcement. As a result of the numerical experiment performed, it was found that with an increase in compressive load magnitude, there is a tendency to an increase in the wall thickness of an optimal shell, with an increase in the thickness of longitudinal stiffeners (stringers) and a slight decrease in the number of ribs. In addition, it should be noted that the general case of buckling and the first special one turned out to be decisive in choosing optimal shell parameters.

Optimal Design of an Elastic Column of Thin-Walled Cross Section

1968 ◽  
Vol 35 (2) ◽  
pp. 285-288 ◽  
Author(s):  
N. C. Huang ◽  
C. Y. Sheu
Keyword(s):  
Optimal Design ◽  
Cross Section ◽  
Wall Thickness ◽  
Cross Sections ◽  
Unit Length ◽  
Compressive Load ◽  
Median Line ◽  
Vertical Column ◽  
Thin Walled ◽  
Allowable Compressive Stress

This paper treats the optimal design of a vertical column that is built-in at the lower end. In addition to its own weight, the column is to carry an axial compressive load at its unsupported upper end. The column is to be designed as a thin-walled tube. The median line is to be the same for all cross sections; the wall thickness, though constant along the median line of any cross section, is allowed to vary along the length of the tube. Accordingly, the weight per unit length of the tube is proportional to the bending stiffness. For given length and total weight, the variation of the wall thickness along the column is to be determined to maximize the critical value of the compressive load at the upper end. The influence of a maximum allowable compressive stress on the design is also investigated.

scholarly journals Optimum Design of Reinforced Cylindrical Shells Under Combined Axial Compression and Internal Pressure

2021 ◽  
Vol 24 (2) ◽  
pp. 50-58
Author(s):  
Heorhii V. Filatov ◽  
Keyword(s):  
Mathematical Programming ◽  
Internal Pressure ◽  
Objective Function ◽  
Programming Problem ◽  
Random Search ◽  
Cylindrical Shells ◽  
Mathematical Programming Problem ◽  
Stability Conditions ◽  
Search Area ◽  
Critical Stresses

This paper discusses the use of the random search method for the optimal design of single-layered rib-reinforced cylindrical shells under combined axial compression and internal pressure with account taken of the elastic-plastic material behavior. The optimality criterion is the minimum shell volume. The search area for the optimal solution in the space of the parameters being optimized is limited by the strength and stability conditions of the shell. When assessing stability, the discrete rib arrangement is taken into account. In addition to the strength and stability conditions of the shell, the feasible space is subjected to the imposition of constraints on the geometric dimensions of the structural elements being optimized. The difficulty in formulating a mathematical programming problem is that the critical stresses arising in optimally-compressed rib-reinforced cylindrical shells are a function of not only the skin and reinforcement parameters, but also the number of half-waves in the circumferential and meridional directions that are formed due to buckling. In turn, the number of these half-waves depends on the variable shell parameters. Consequently, the search area becomes non-stationary, and when formulating a mathematical programming problem, it is necessary to provide for the need to minimize the critical stress function with respect to the integer wave formation parameters at each search procedure step. In this regard, a method is proposed for solving the problem of optimally designing rib-reinforced shells, using a random search algorithm whose learning is carried out not only depending on the objective function increment, but also on the increment of critical stresses at each extremum search step. The aim of this paper is to demonstrate a technique for optimizing this kind of shells, in which a special search-system learning algorithm is used, which consists in the fact that two problems of mathematical programming are simultaneously solved: that of minimizing the weight objective function and that of minimizing the critical stresses of shell buckling. The proposed technique is illustrated with a numerical example.

Optimal design of ring stiffened cylindrical shells using multiple stiffener sizes

AIAA Journal ◽  
1980 ◽  
Vol 18 (8) ◽  
pp. 1020-1022 ◽  
Author(s):  
Michael Pappas ◽  
Jacob Moradi
Keyword(s):  
Optimal Design ◽  
Cylindrical Shells ◽  
Stiffened Cylindrical Shells

scholarly journals Dynamical analysis of multilayered reinforced composite cylindrical shells

2005 ◽  
Vol 27 (4) ◽  
pp. 220-228
Author(s):  
Dao Huy Bich ◽  
Tran Thanh Tuan
Keyword(s):  
Linear Problem ◽  
Cylindrical Shells ◽  
Dynamical Analysis ◽  
Dynamical Equations ◽  
Fundamental Frequencies ◽  
Reinforced Composite ◽  
Longitudinal Stiffeners ◽  
Shell Vibration ◽  
Shell Geometry ◽  
Composite Cylindrical Shells

In the present paper the governing dynamical equations for multilayered reinforced composite cylindrical shells based on Kirchhoff-Love's theory and Lekhnitsky's smeared stiffeners technique are derived. The shell is reinforced by longitudinal and ring stiffeners. The longitudinal stiffeners may be composite or sleeves with SMA wire. The linear problem of shell vibration is considered for illustrating the effects of the stiffeners, the shell geometry and altering the lamination scheme on fundamental frequencies of the shell.

REINFORCEMENT OF AGEING SHIP STRUCTURES

2021 ◽  
Vol 160 (A3) ◽  
Author(s):  
D Chichì ◽  
Y Garbatov
Keyword(s):  
Monte Carlo Simulation ◽  
Finite Element ◽  
Ultimate Strength ◽  
Steel Plate ◽  
Plate Thickness ◽  
Compressive Load ◽  
Finite Element Models ◽  
Uniform Corrosion ◽  
Finite Element Analyses ◽  
Longitudinal Stiffeners

The objective of the present study is to investigate the possibility to recover the ultimate strength of a rectangular steel plate with a manhole shape opening subjected to a uniaxial compressive load and non-uniform corrosion degradation reinforced by additional stiffeners. Finite element analyses have been carried out to verify the possible design solutions. A total of four finite element models are generated, including 63 sub-structured models. The non-uniform corrosion has been generated by the Monte Carlo simulation. The reinforcement process covers three scenarios that include mounting of two longitudinal stiffeners, two longitudinal and two transverse stiffeners and the flange on the opening. The positioning of the stiffeners has also been studied. A total of 10 cases has been selected and tested for the numerical experiment. Three different assessments have been performed to evaluate the ultimate strength, weight and cost. Two additional studies on the effect of the plate thickness and slenderness have been also carried out.

The Role of Modal Coupling on the Non-Linear Response of Cylindrical Shells Subjected to Dynamic Axial Loads

2000 ◽  
Author(s):  
Paulo B. Gonçalves ◽  
Zenón J. G. N. Del Prado
Keyword(s):  
Dynamic Instability ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Parametric Instability ◽  
Compressive Load ◽  
Basins Of Attraction ◽  
Dynamic Component ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Low Dimensional

Abstract This paper discusses the dynamic instability of circular cylindrical shells subjected to time-dependent axial edge loads of the form P(t) = P0+P1(t), where the dynamic component p1(t) is periodic in time and P0 is a uniform compressive load. In the present paper a low dimensional model, which retains the essential non-linear terms, is used to study the non-linear oscillations and instabilities of the shell. For this, Donnell’s shallow shell equations are used together with the Galerkin method to derive a set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. To study the non-linear behavior of the shell, several numerical strategies were used to obtain Poincaré maps, stable and unstable fixed points, bifurcation diagrams and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric instability and escape from the pre-buckling potential well. The numerical results obtained from this investigation clarify the conditions, which control whether or not instability may occur. This may help in establishing proper design criteria for these shells under dynamic loads, a topic practically unexplored in literature.

Linear Bending Theory of Laminated Cylindrical Shells Under Axisymmetric Load

1963 ◽  
Vol 30 (1) ◽  
pp. 98-102 ◽  
Author(s):  
B. Paul
Keyword(s):  
Wall Thickness ◽  
First Principles ◽  
Flexural Rigidity ◽  
Cylindrical Shells ◽  
Laminated Shell ◽  
Axisymmetric Loading ◽  
Axisymmetric Load ◽  
Column Type ◽  
Simple Dependence ◽  
Laminated Cylindrical Shells

The linear bending theory of laminated elastic cylindrical shells under axisymmetric loading is developed from first principles. It is shown that a spontaneous “beam-column” type of deformation may develop even in the absence of end loads. Generally, however, this effect is shown to be small for metallic cylinders, in which case the laminated shell deforms in the same manner as a homogeneous shell, where the effective flexural rigidity and effective extensional rigidity are both shown to have a simple dependence upon the “elasticity distribution” throughout the wall thickness. The influence of edge loads on a pressurized semi-infinite shell are determined and applied to find the stresses in a titanium shell with a steel reinforcing band.

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