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.

Flow Analysis and Modeling of Field-Controllable, Electro- and Magneto-Rheological Fluid Dampers

2005 ◽  
Vol 74 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Xiaojie Wang ◽  
Faramarz Gordaninejad
Keyword(s):  
Theoretical Model ◽  
Flow Analysis ◽  
Closed Form Solution ◽  
Nonlinear Behavior ◽  
Form Solution ◽  
Proposed Model ◽  
Fluid Dampers ◽  
Magneto Rheological ◽  
Er Fluid ◽  
Theoretical Results

This study combines a fluid mechanics-based approach and the Herschel-Bulkley constitutive equation to develop a theoretical model for predicting the behavior of field-controllable, magneto-rheological (MR), and electro-rheological (ER) fluid dampers. The goal is to provide an accurate theoretical model for analysis, design, and development of control algorithms of MR/ER dampers. Simplified explicit expressions for closed-form solution of the pressure drop across a MR fluid valve are developed. The Herschel-Bulkley quasi-steady flow analysis is extended to include the effect of fluid compressibility to account for the nonlinear dynamic behavior of MR/ER fluid dampers. The advantage of this model is that it only depends on geometric and material properties of the MR/ER material and the device. The theoretical results are validated by an experimental study. It is demonstrated that the proposed model can effectively predict the nonlinear behavior of field-controllable fluid dampers.

scholarly journals Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluids

1976 ◽  
Vol 43 (2) ◽  
pp. 325-329 ◽  
Author(s):  
S. S. Chen ◽  
M. W. Wambsganss ◽  
J. A. Jendrzejczyk
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Cylindrical Shell ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Viscous Fluids ◽  
Series Of Experiments ◽  
Theoretical Results ◽  
Good Agreement

This paper presents an analytical and experimental study of a cylindrical rod vibrating in a viscous fluid enclosed by a rigid, concentric cylindrical shell. A closed-form solution for the added mass and damping coefficient is obtained and a series of experiments with cantilevered rods vibrating in various viscous fluids is performed. Experimental data and theoretical results are in good agreement.

Wave Number-Based Technique for Detecting Slope Discontinuity in Simple Beams Using Moving Test Vehicle

2017 ◽  
Vol 17 (06) ◽  
pp. 1750060 ◽  
Author(s):  
J. D. Yau ◽  
Judy P. Yang ◽  
Y. B. Yang
Keyword(s):  
Numerical Simulation ◽  
Closed Form Solution ◽  
Element Model ◽  
Beam Element ◽  
Form Solution ◽  
Wave Number ◽  
Test Vehicle ◽  
Promising Alternative ◽  
Alternative Approach ◽  
Slope Discontinuity

The wavelength characteristic is a useful clue for locating and assessing the severity of slope discontinuity in beams. In this study, the slope discontinuity of a beam is represented by an internal hinge restrained by elastic springs, and the wavelength of the beam is calculated indirectly from the vertical response of a test vehicle during its travel over the beam. The key parameters of the problem at hand are first unveiled using an approximate, closed-form solution for the response of the vehicle moving at low speeds over the bridge. Then a two-beam element model with slope discontinuity is formulated for the vehicle–bridge interaction (VBI) system for use in numerical simulation. In the examples, the wavenumber-based response of the test vehicle is used to identify the location and severity of the discontinuity in the beam. It is demonstrated that the wavelength-based technique presented herein by using the moving test vehicle as a moving sensor system offers a promising, alternative approach for damage detection in girder type bridges.

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.

Dual quaternion-based inverse kinematics of the general spatial 7R mechanism

2008 ◽  
Vol 222 (8) ◽  
pp. 1593-1598 ◽  
Author(s):  
D Gan ◽  
Q Liao ◽  
S Wei ◽  
J S Dai ◽  
S Qiao
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Dual Quaternion ◽  
Whole Process ◽  
Inverse Kinematic Analysis ◽  
Angular Displacements ◽  
Output Equation ◽  
Theoretical Results

The theory of dual quaternion and its use in serial mechanisms are described in this paper. A closed-form solution to the inverse kinematic analysis of the general 7-link 7R mechanism is presented. Dixon's resultant is used and the input—output equation is expressed in the form of a 6×6 determinant equated to zero, and the formulae to determine other angular displacements are expressed in the closed form. Numerical example confirms these theoretical results. The whole process is very simple and easy to program, which supplies a new method for the real use of the 7R mechanism.

scholarly journals Energy-saving optimization method for point-to-point trajectories planned via standard primitives in 1-DoF mechatronic systems

2021 ◽  
Author(s):  
Giovanni Carabin ◽  
Renato Vidoni
Keyword(s):  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Motor Drives ◽  
Mechatronic Systems ◽  
Analytical Methodology ◽  
Point Trajectories ◽  
Point To Point ◽  
Theoretical Results ◽  
Energy Formulation

AbstractIn this work, an analytical methodology to minimize the energy expenditure of mechatronic systems performing point-to-point (PTP) trajectories based on well-known motion primitives is developed and validated. Both PTP trajectory profiles commonly used in industrial motor drives and more complex ones are investigated. Focusing on generic 1-DoF mechatronic systems moving a constant inertia load (e.g., elevators, cranes, CNC machines, Cartesian axis) and possibly equipped or retrofitted with regenerative devices, the consumed energy formulation is firstly derived. Then, the analytical optimization considering all the selected PTP trajectory profiles is computed and a generic closed-form solution is determined. Finally, numerical and experimental evaluations are done showing the effectiveness of the theoretical results and proposed methodology. In addition, all the different trajectories are compared with respect to energy consumption.

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%.

Simplified External Pressure Design of ASME Pressure Vessels Using Closed Form Solution

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Sandip Vinayka
Keyword(s):  
Closed Form ◽  
Cylindrical Shells ◽  
Closed Form Solution ◽  
External Pressure ◽  
Pressure Vessels ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Simplified Procedure

Abstract The procedure of design of cylindrical shells under external pressure as outlined in ASME Sec VIII Div.1 is iterative and tedious, not suitable for quick hand calculations. This paper provides an alternative simplified procedure to calculate the required thickness for shells under external pressure, as well as to size the stiffeners as required using closed form solutions. An example is provided to demonstrate the working of the procedure and to validate the results with the current ASME Sec VIII Div.1 methodology.

On the Transverse Twisting of Shallow Spherical Ring Caps

1980 ◽  
Vol 47 (1) ◽  
pp. 101-105 ◽  
Author(s):  
E. Reissner
Keyword(s):  
Boundary Layer ◽  
Stress Concentration ◽  
Spherical Shell ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Relevant Parameter ◽  
Edge Zone ◽  
Concentration Problem ◽  
Layer Behavior

The problem of transverse twisting of a shallow spherical shell with a small circular hole is solved, in generalization of the corresponding problem of a flat plate. The solution is of interest as a closed-form solution of an unsymmetrical stress concentration problem, with quantitative features depending on its boundary-layer behavior for large values of a relevant parameter. The problem is also of interest as an example of applicability of a previously proposed asymptotic procedure where interior contributions and edge-zone contributions are determined in sequence rather than simultaneously.

Forward Displacement Analysis of Parallel Mechanisms: Closed Form Solution of PRR-3S and PPR-3S Structures

1992 ◽  
Vol 114 (1) ◽  
pp. 68-73 ◽  
Author(s):  
V. Parenti-Castelli ◽  
C. Innocenti
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
Forward Displacement ◽  
Form Analysis ◽  
Displacement Analysis ◽  
Theoretical Results ◽  
Forward Displacement Analysis

The forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multiloop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR-3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degree 16 and 12, respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results.

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