Design for Buckle-Free Shapes in Pressure Vessels

1985 ◽  
Vol 107 (4) ◽  
pp. 387-393 ◽  
Author(s):  
W. Szyszkowski ◽  
P. G. Glockner
Keyword(s):  
Pressure Vessel ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Numerical Procedure ◽  
Pressure Vessels ◽  
Form Solution ◽  
Loading Conditions ◽  
Loading Case ◽  
Present Design ◽  
Axisymmetric Structures

There are many applications of thin-walled axisymmetric structures as pressure vessels in which buckle-free in-service behavior can only be guaranteed by reinforcements, such as stringers and girths, which not only raise the weight of the structure but also increase its cost. Buckle-free behavior, however, can also be assured by “correcting” the shape of the pressure vessel by a small amount in the area of impending instability. This paper proposes the use of the theory of inflatable membranes to obtain the shape of a pressure vessel subjected to tension only stress state, whereby the possibility of buckling is excluded. Such a shape will be referred to as the “buckle-free” shape. A set of nonlinear differential equations are derived which are valid for any axisymmetric pressure vessel subjected to axisymmetric loadings. The shape obtained from the solution of the equations is an “extremum” to possible stable shapes under the given loading conditions; i.e., there are other stable shapes, for which the circumferential compressive stiffness of the structure has to be relied upon. A closed-form solution for the set of equations was obtained for the constant pressure loading case. For hydrostatic pressure a numerical procedure is applied. Results on “buckle-free” shapes for typical pressure vessel strucures for these two loading conditions are presented. It is established that the deviation of such shapes from the shapes obtained by present design methods and code specifications is small so that this proposed method and the resulting “corrections’ leading to “buckle-free” inservice behavior should not present an aesthetic problem in design.

scholarly journals Stress Intensity Factors for Layered Pressure Vessel Inner Layer Through Cracks

2019 ◽  
Author(s):  
Joel R. Hobbs
Keyword(s):  
Elastic Modulus ◽  
Stress Intensity ◽  
Closed Form ◽  
Stress Intensity Factors ◽  
Pressure Vessel ◽  
Closed Form Solution ◽  
Pressure Vessels ◽  
Form Solution ◽  
Intensity Factors ◽  
Friction Forces

Abstract A difficulty encountered when performing Fitness-for-Service assessments for layered pressure vessels (LPVs) is the lack of stress intensity factor solution in literature that produce accurate results for inner layer longitudinal through cracks. Using surrogate solutions such as a through crack in a plate or cylinder produce results that can be overly conservative especially for longer cracks. This is largely due to the ability of a layered pressure vessel to redistribute hoop load to other layers, the restricted radial movement of the cracked layer, and the friction forces applied in the cracked region. To understand this problem, a parametric finite element model (FEM) generator was developed that is capable of producing layered pressure vessel models with inner layer through cracks. The results from the FEMs were used to create a dataset of inner layer through crack stress intensity factors (Ki) for layered pressure vessels corresponding to variations of internal pressure, radius, layer thicknesses, friction factor, and crack length. The elastic modulus of the material also has an effect on Ki but, for this dataset, the elastic modulus was fixed at the typical value for steel – 29,500 ksi (203 GPa). Finally, a non-dimensional model was developed and calibrated using the dataset. This allows Ki to be calculated without the need of a FEM using a closed-form equation. The results of the closed-form solution were then compared to FEM results showing accuracy was generally within 10%.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Isaiah Ramos ◽  
Young Ho Park ◽  
Jordan Ulibarri-Sanchez
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Structural Damage ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Analytical Results ◽  
Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

Postbuckling Analysis of a Nonlocal Nanorod Under Self-Weight

2020 ◽  
Vol 12 (04) ◽  
pp. 2050035
Author(s):  
Chinnawut Juntarasaid ◽  
Tawich Pulngern ◽  
Somchai Chucheepsakul
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Nonlocal Elasticity ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Constraint Equation ◽  
Form Solution ◽  
Postbuckling Behavior ◽  
Euler Beam ◽  
Softening Behavior

This paper presents the postbuckled configurations of simply supported and clamped-pinned nanorods under self-weight based on elastica theory. Numerical solution is considered in this work since closed-form solution of postbuckling analysis under self-weight cannot be obtained. The set of nonlinear differential equations of a nanorod including the effect of nonlocal elasticity are investigated. The constraint equation at boundary condition technique is introduced for the solution of postbuckling analysis. In order to solve the set of nonlinear differential equations, the shooting method is utilized, where the set of these equations along with boundary conditions are integrated by the fourth-order Runge-Kutta algorithm. Numerical results are obtained and the highlighting influences of the nonlocal elasticity on postbuckling behavior of nanorods are discussed. The obtained results indicate that the rotation angle and the postbuckled configurations of nanorods are varied by changing the nonlocal elasticity parameter. The effect of nonlocal elasticity shows the softening behavior in comparison with the Euler beam. The present formulation together with constraint boundary condition technique is an effective solution for postbuckling analysis of a nanorod under self-weight including the effect of nonlocal elasticity.

Support Analysis of Horizontal Pressure Vessel Using FEA

2014 ◽  
Vol 592-594 ◽  
pp. 1220-1224
Author(s):  
Navin Kumar ◽  
Surjit Angra ◽  
Vinod Kumar Mittal
Keyword(s):  
Stress Analysis ◽  
Pressure Vessel ◽  
Theoretical Basis ◽  
Pressure Vessels ◽  
Loading Conditions ◽  
Ansys Software ◽  
Support Design ◽  
Horizontal Pressure ◽  
The Given

Saddles are used to support the horizontal pressure vessels such as boiler drums or tanks. Since saddle is an integral part of the vessel, it should be designed in such a way that it can withstand the pressure vessel load while carrying liquid along with the operating weight. This paper presents the stress analysis of saddle support of a horizontal pressure vessel. A model of horizontal pressure vessel and saddle is created in Ansys software. For the given boundry and loading conditions, stresses induced in the saddle support are analyzed using Ansys software. After analysis it is found that maximum localized stress arises at the saddle to vessel interface near the saddle horn area. The results obtained shows that the saddle support design is safe for the given loading conditions and provides the theoretical basis for furthur optimisation.

Using Isochronous Method to Calculate Creep Damage in Pressure Vessel Components: Part 2

2017 ◽  
Author(s):  
Chithranjan Nadarajah ◽  
Benjamin F. Hantz ◽  
Sujay Krishnamurthy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Pressure Vessel ◽  
Closed Form Solution ◽  
Creep Damage ◽  
Form Solution ◽  
Creep Model ◽  
Stress Strain ◽  
Element Analysis ◽  
Good Agreement

This paper is Part 2 of two papers illustrating how isochronous stress strain curves can be used to calculate creep stresses and damage for pressure vessel components. Part 1 [1], illustrated the use of isochronous stress strain curves to obtain creep stresses and damages on two simple example problems which were solved using closed form solution. In Part 2, the isochronous method is implemented in finite element analysis to determine creep stresses and damages on pressure vessel components. Various different pressure vessel components are studied using this method and the results obtained using this method is compared time explicit Omega creep model. The results obtained from the isochronous method is found to be in good agreement with the time explicit Omega creep model.

Improved Parker-Sochacki Approach for Closed Form Solution of Enzyme Catalyzed Reaction Model

2017 ◽  
Vol 8 (1-2) ◽  
pp. 90
Author(s):  
Babatunde Sunday Ogundare ◽  
Saheed O Akindeinde ◽  
Adebayo O Adewumi ◽  
Adebayo A Aderogba
Keyword(s):  
Closed Form ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Processing Technique ◽  
Reaction Model ◽  
Form Solution ◽  
Post Processing ◽  
Analytical Technique ◽  
Comparison Of The Results

In this article, a new analytical technique called Improved Parker-Sochacki Method (IPSM) for solving nonlinear Michaelis-Menten enzyme catalyzed reaction model is proposed. The global form of the solution for the concentrations of the substrate, enzyme and the enyzme-free product are obtained. Employing the Laplace-Pade resummation as a post processing technique on the computed series solution, the domain of convergence of the solution is greatly extended. The solution is therefore devoid of limited convergence interval that is typical of series solution of nonlinear differential equations.  The proposed method showed a significant improvement  over the conventional Parker-Sochacki Method (PSM). Furthermore, comparison of the results with numerically computed solutions elucidated the simplicity and accuracy of the proposed method.

Slope Discontinuities in Pressure Vessels

1970 ◽  
Vol 37 (3) ◽  
pp. 587-595 ◽  
Author(s):  
C. R. Steele ◽  
J. Skogh
Keyword(s):  
Significant Variation ◽  
Weld Seam ◽  
Closed Form Solution ◽  
Pressure Vessels ◽  
Form Solution ◽  
Edge Zone ◽  
Slope Discontinuity ◽  
Theoretical Results ◽  
Maximum Stresses ◽  
Slope Discontinuities

A closed-form solution is obtained for the problem of a shell of revolution with a meridional slope discontinuity, which might occur at a weld seam in a pressure vessel. The effect of significant variation in the slope occurring within the usual “edge zone” and the nonlinear pressurization effect are taken into consideration. Graphs are presented from which maximum stresses can be easily computed for a wide variation of the parameters. The theoretical results agree with numerical values obtained from a computer program, even for shells that are relatively thick, for slope discontinuities that are relatively severe, and for high pressurization.

Application of Artificial Neural Network to Multi-Variables Regression for Estimations of J-Integral for Surface Cracked Pipes

2020 ◽  
Author(s):  
Youn-Young Jang ◽  
Nam-Su Huh ◽  
Ik-Joong Kim ◽  
Cheol-Man Kim ◽  
Young-Pyo Kim
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Closed Form ◽  
Material Properties ◽  
Closed Form Solution ◽  
Form Solution ◽  
J Integral ◽  
Loading Conditions ◽  
Tabular Form ◽  
J Estimation

Abstract Crack assessment for pipe components of a nuclear power plant or oil/gas pipeline is one of the essential procedures to ensure safe operation services. To assess cracked pipes, J-integral has been considered as a theoretically robust and useful elastic-plastic fracture parameter, so that the estimations of J-integral for various pipe geometries, material properties and loading conditions are highly needed. For this reason, many engineering predictive solutions for J-estimations based on finite element (FE) analyses have been developed. Generally, many engineering predictive solutions have been suggested as a tabular-form or closed-form. Among them, the closed-form solution is more preferred than a tabular-form solution for its convenience when many lots of interpolation are required to use it. However, the accuracy of the closed-form solution tends to be significantly reduced as the number of design parameters increases. Moreover, since there is no strict rule to define the form of functions as well, the accuracy of the closed-form solution is inevitably dependent on the rule of thumb. Therefore, it is highly required to suggest a new approach for J-estimation of cracked pipes with various geometries, material properties and loading conditions. In this paper, we propose an efficient approach based on a machine learning technique to estimate J-integral for surface cracked pipes with various geometric sizes and material properties under axial displacement loading condition. Firstly, parametric FE analysis studies were systematically performed to produce the coefficients representing the engineering J-estimation for the corresponding cracked pipe. Secondly, artificial neural network (ANN) models based on deep multilayer perceptron technique were trained based on FE results. The five input neurons (pipe geometries and material properties) and the two output neurons (the coefficients representing the engineering J-estimation) were considered. Lastly, the accuracy of the trained ANN model was studied by comparing to that of the closed-form solution from multi-variable regressions.

scholarly journals Closed-Form Solution of Large Deflected Cantilever Beam a gainst Follower Loading Using Complex Analysis

2017 ◽  
Vol 11 (12) ◽  
pp. 12 ◽  
Author(s):  
Ibrahim Mousa Abu-Alshaikh
Keyword(s):  
Numerical Methods ◽  
Closed Form ◽  
Cantilever Beam ◽  
Complex Analysis ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Beam Deflection ◽  
Integral Approach ◽  
Loading Conditions

The literature reveals that the non-conservative deflection of an elastic cantilever beam caused by applying follower tip loading was investigated and solved by various numerical methods like: Runge Kutta, iterative shooting, finite element, finite difference, direct iterative and non-iterative numerical methods. This is due to the fact that the Euler–Bernoulli nonlinear differential equation governing the problem contains the “slope at the free end”, this slope however needs special numerical treatment. On the other hand, some of these methods fail to find numerical solutions for extremely large loading conditions. Hence, this paper is aimed to obtain a closed-form solution for solving the large deflection of a cantilever beam opposed to a concentrated point follower load at its free end. This closed-form solution when compared with other conventional numerical approaches is characterized by simplicity, stability and straightforwardness in getting the beam deflection and slopes even for extremely large loading conditions. The closed-form solution is obtained by applying complex analysis along with elliptic-integral approach. Very good results were obtained when the elastica of the beam compared with that of various numerical methods which are used in analyzing similar problem.

A Numerical Procedure for Designing Profiled Rolling Elements

1976 ◽  
Vol 98 (4) ◽  
pp. 547-551 ◽  
Author(s):  
K. P. Oh ◽  
E. G. Trachman
Keyword(s):  
Closed Form Solution ◽  
Numerical Procedure ◽  
Potential Method ◽  
Form Solution ◽  
Geometric Constraints ◽  
Stress Distributions ◽  
Elastic Bodies ◽  
Rolling Elements ◽  
Quadratic Programming Method ◽  
Quadratic Surfaces

A numerical procedure is developed for studying the pressure and stress distributions resulting from the contact of two elastic bodies. The pressure distribution is obtained by a quadratic programming method such that the resulting displacements satisfy the geometric constraints of the contact problem, and the bodies are in a state of minimum potential energy. The potential method is used to calculate the subsurface stresses due to a constant pressure over a rectangular element. The stresses due to the contact pressure are then obtained by superposition of the contributions of all the elements in the contact area. A small number of elements (5 × 5) provides pressure and stress solutions within two percent of the closed-form solution for quadratic surfaces. For surfaces with abrupt changes in geometry, more elements are required. This procedure can be used to locate an optimum profile for rolling element bearings.

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