Torsional Creep Buckling of Thin-Walled Open Tubes With a Cross Section Having an Axis of Symmetry

1962 ◽  
Vol 29 (1) ◽  
pp. 99-107
Author(s):  
George Lianis
Keyword(s):  
Cross Section ◽  
Closed Form Solution ◽  
Critical Time ◽  
Small Deformation ◽  
Form Solution ◽  
Creep Buckling ◽  
Thin Walled Tube ◽  
Axis Of Symmetry ◽  
Thin Walled ◽  
Stress Patterns

The variational theorem by Sanders, McComb, and Schlechte [1] is applied to find the critical collapse time of an open thin-walled tube with a cross section having an axis of symmetry subjected to torsional creep buckling. Large deformation strains are considered. It is shown that small deformation strains yield inaccurate results in predicting the critical time. A simplified stress distribution is introduced which gives a closed-form solution. More accurate stress patterns present considerable difficulties and a tedious numerical integration is needed. In examining most cases, however, the simplified stress configuration predicts the critical time very accurately.

Axially Symmetric Creep Buckling of Circular Cylindrical Shells in Axial Compression

1968 ◽  
Vol 35 (3) ◽  
pp. 530-538 ◽  
Author(s):  
N. J. Hoff
Keyword(s):  
Axial Compression ◽  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Critical Time ◽  
Form Solution ◽  
Large Displacements ◽  
Axially Symmetric ◽  
Initial Imperfections ◽  
Creep Buckling ◽  
Circular Cylindrical Shells

The creep-buckling phenomenon of circular cylindrical shells subjected to axial compression is studied in the presence of initial imperfections when the creep strain rate is proportional to a power of the stress with the exponent greater than unity. A closed-form solution is obtained for the critical time; that is, for the finite time at which the analysis predicts the development of indefinitely large displacements.

Bending and Twisting of Pipes With Strain Hardening

1984 ◽  
Vol 106 (2) ◽  
pp. 188-195 ◽  
Author(s):  
J. H. Lau ◽  
T. T. Lau
Keyword(s):  
Effective Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Small Deformation ◽  
Form Solution ◽  
Simultaneous Action ◽  
Deformation Analysis ◽  
Engineering Practice ◽  
Strain Diagram ◽  
Interaction Curves

A closed-form solution is presented for the small deformation analysis of a straight thin-walled circular cylinder subjected to the simultaneous action of bending and twisting moments. Dimensionless interaction curves and charts which relate the variables, bending moment, curvature, maximum effective strain, twisting moment, and shear strain are also provided for engineering practice convenience. The average stress-strain diagram of the cylinder is described by two straight lines. The result presented herein is not only a good approximation of a wide class of piping materials, but also provides a standard tool for estimating the accuracy of different direct schemes such as numerical integration, finite-difference, and finite-element methods.

scholarly journals Linearizing Control of a Distributed Actuation Magnetic Bearing for Thin-Walled Rotor Systems

Actuators ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 99
Author(s):  
Chakkapong Chamroon ◽  
Matthew O.T. Cole ◽  
Wichaphon Fakkaew
Keyword(s):  
Closed Form Solution ◽  
Magnetic Bearing ◽  
Form Solution ◽  
Electromagnetic Actuators ◽  
Control Approach ◽  
Zero Current ◽  
Improved Stability ◽  
Gradient Based ◽  
Thin Walled ◽  
Coil Winding

This paper describes an exact linearizing control approach for a distributed actuation magnetic bearing (DAMB) supporting a thin-walled rotor. The radial DAMB design incorporates a circular array of compact electromagnetic actuators with multi-coil winding scheme optimized for supporting thin-walled rotors. A distinguishing feature is that both the x and y components of the radial bearing force are coupled with all four of the supplied coil currents and so a closed form solution for the linearizing equations cannot be obtained. To overcome this issue, a gradient-based root-finding algorithm is proposed to solve the linearizing equations numerically in real-time. The proposed method can be applied with any chosen constraints on current values to achieve low RMS values while avoiding zero-current operating points. The approach is implemented and tested experimentally on a rotor system comprising two radial DAMBs and a uniform cylindrical shell rotor. The results show that the method achieves more accurate reproduction of demanded bearing forces, thereby simplifying the rotor suspension control design and providing improved stability and vibration control performance compared with implementations based on operating point linearization.

scholarly journals A Parametrical Analysis for the Rotational Ductility of Reinforced Concrete Beams

2013 ◽  
Vol 7 (1) ◽  
pp. 242-253
Author(s):  
Domenico Raffaele ◽  
Giuseppina Uva ◽  
Francesco Porco ◽  
Andrea Fiore
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Concrete Beams ◽  
Closed Form Solution ◽  
Form Solution ◽  
Reinforced Concrete Beams ◽  
Shear Cracks ◽  
Technical Standards ◽  
Mechanical Reinforcement ◽  
Plastic Rotation

The assessment of the plastic rotation of reinforced concrete beams is an essential aspect to avoid structural brittle collapses. The value actually available can be generally determined as sum of two different components. The first, due to bending, the second for inclined shear cracks. This paper presents a simplified model which provides the flexural plastic rotation of the rectangular beams with a ``closed-form solution''. The approach is substantially dimensionless and includes main influencing factors the cross -section, as mechanical material properties, ductility, geometrical and mechanical reinforcement ratio, confinement effects. In closing, in order to appreciate the reliability of the procedure, a comparison with models proposed by international technical standards is made.

scholarly journals Developed Mathematical Model for Indeterminate Elements with Variable Inertia and Curved Elements with Constant Cross-Section

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Mohamed A. El Zareef ◽  
Mohamed E. El Madawy ◽  
Mohamed Ghannam
Keyword(s):  
Mathematical Models ◽  
Numerical Integration ◽  
Cross Section ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimum Number ◽  
Fe Model ◽  
Constant Cross Section ◽  
Structural Elements ◽  
Good Agreement

Issues such as analysis of indeterminate structural elements that have variable inertia as well as a curved shape still have no closed form solution and are considered one of the major problems faced by design engineers. One method to cope with these issues is by using suitable the finite element (FE) software for analyzing these types of elements. Although it saves time, utilization of FE programs still needs professional users and not all engineers are familiar with it. This paper has two main objectives; first, to develop simple mathematical models for analyzing indeterminate structural elements with variable inertia and that have a curved shape with constant cross section, this model is much easier to be used by engineers compared to the FE model. For simplicity and saving time, a MATLAB program is developed based on investigated mathematical models. The force method combined with numerical integration technique is used to develop these models. The developed mathematical models are verified using the suitable FE software; good agreement was observed between the mathematical and the FE model. The second objective is to introduce a mathematical formula to determine the accurate number of divisions that would be used in the mathematical models. The study proves that the accuracy of analysis depends on the number of divisions used in the numerical integration. The optimum number of divisions is obtained by comparing the output results for both FE and developed mathematical models. The developed mathematical models show a good agreement with FE results with faster processing time and easier usage.

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