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.

Creep of Thin-Walled Circular Cylinder Under Axial Force, Bending, and Twisting Moments

1984 ◽  
Vol 106 (1) ◽  
pp. 79-83 ◽  
Author(s):  
J. H. Lau ◽  
S. S. Jung ◽  
T. T. Lau
Keyword(s):  
Circular Cylinder ◽  
Strain Rate ◽  
Axial Force ◽  
Effective Strain ◽  
Bending Moment ◽  
Constitutive Relationship ◽  
Engineering Practice ◽  
Shear Strain Rate ◽  
Thin Walled ◽  
Interaction Curves

An exact analysis is presented for the creep deformation of a thin-walled circular cylinder subjected to the simultaneous actions of axial force, bending, and twisting moments. Dimensionless interaction curves and charts which relate the variables, axial force, location of neutral-axis, bending moment, maximum effective strain rate, twisting moment, and shear strain rate are also provided for engineering practice convenience. The constitutive relationship of the cylinder is described by Prandtl-Nadai creep law.

scholarly journals Green's functions for unsymmetric composite laminates with inclusions

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190437
Author(s):  
Chia-Wen Hsu ◽  
Chyanbin Hwu
Keyword(s):  
Composite Laminates ◽  
Green's Functions ◽  
Green’S Functions ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Displacement Discontinuity ◽  
Computational Time ◽  
Out Of Plane ◽  
Logarithmic Functions

It is known that the stretching and bending deformations will be coupled together for the unsymmetric composite laminates under in-plane force and/or out-of-plane bending moment. Although Green's functions for unsymmetric composite laminates with elliptical elastic inclusions have been obtained by using Stroh-like formalism around 10 years ago, due to the ignoring of inconsistent rigid body movements of matrix and inclusion, the existing solution may lead to displacement discontinuity across the interface between matrix and inclusion. Due to the multi-valued characteristics of complex logarithmic functions appeared in Green's functions, special attention should be made on the proper selection of branch cuts of mapped variables. To solve these problems, in this study, the existing Green's functions are corrected and a simple way to correctly evaluate the mapped complex variable logarithmic functions is suggested. Moreover, to apply the obtained solutions to boundary element method, we also derive the explicit closed-form solution for Green's function of deflection. Since the continuity conditions along the interface have been satisfied in Green's functions, no meshes are required along the interface, which will save a lot of computational time and the results are much more accurate than any other numerical methods.

Bending and Twisting of 60Sn40Pb Solder Interconnects With Creep

1994 ◽  
Vol 116 (2) ◽  
pp. 154-157
Author(s):  
John H. Lau
Keyword(s):  
Creep Deformation ◽  
Material Properties ◽  
Bending Moment ◽  
Engineering Practice ◽  
Solder Material ◽  
Solder Interconnects ◽  
Exact Analysis ◽  
Twist Rate ◽  
Thin Walled ◽  
Interaction Curves

An exact analysis is presented for the creep deformation of a thin-walled circular solder cylinder under the actions of bending and twisting moments. Dimensionless interaction curves and charts which relate the variables, interconnect geometry, solder material properties, bending moment, twisting moment, curvature rate, and twist rate are also provided for engineering practice convenience.

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.

Local PWB and Component Bowing of an Assembly Subjected to a Bending Moment

1994 ◽  
Vol 116 (2) ◽  
pp. 92-97 ◽  
Author(s):  
D. B. Barker ◽  
Sidharth
Keyword(s):  
Cross Sections ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Printed Wiring Board ◽  
Axial Forces ◽  
Beam Equations ◽  
Wiring Board ◽  
Component Assembly ◽  
Array Format

An analytical model is developed for determining the bowing of a component mounted on a printed wiring board (PWB) that is subjected to a bending moment. The model assumes a uniform elastic attach, between the component and the board. The elastic attach is assumed to transmit axial forces and restrain cross-sections of the component against rotation. The closed form solution to the beam equations directly determines the bowing of the component and the board. The solution is then used for computing the forces and moments, and hence, stresses in the leads that can occur in static or vibrational loading of a PWB/component assembly. The present analysis applies to electronic components with uniformly distributed leads in an array format, such as some PGA components, or to the class of components with parallel rows of leads such as a DIP or a SOIC. To demonstrate the solution and whether or not the rotational stiffness of the component leads needs to be considered, three different types of packages are analyzed.

Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Hardening ◽  
Plane Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Hardening Law

Finite deformation elastic-plastic analysis of plane-strain pure bending of a strain hardening sheet is presented. The general closed-form solution is proposed for an arbitrary isotropic hardening law assuming that the material is incompressible. Explicit relations are given for most popular conventional laws. The stage of unloading is included in the analysis to investigate the distribution of residual stresses and springback. The paper emphasizes the method of solution and the general qualitative features of elastic-plastic solutions rather than the study of the bending process for a specific material. In particular, it is shown that rigid-plastic solutions can be used to predict the bending moment at sufficiently large strains.

A Generalized Impact-Sliding Fretting Wear Model Based on Fracture Mechanics Approach

2004 ◽  
Author(s):  
Yemane Gessesse ◽  
Helmi Attia ◽  
M. O. M. Osman
Keyword(s):  
Fracture Mechanics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fretting Wear ◽  
Simultaneous Action ◽  
Wear Process ◽  
Inconel 600 ◽  
Order Of Magnitude ◽  
Flow Induced Vibrations ◽  
Physical Attributes

Impact-sliding fretting wear is a complex phenomenon due to the random nature of the flow-induced vibrations, and the self-induced tribological changes. Available models, which relate wear losses to the process variables, are empirical in nature and bear no physical similarity to the actual mathematical and physical attributes of the wear process. A generalized model is developed in the present work to mathematically describe the fretting wear process under various modes of motion, namely, impact, sliding and oscillatory. This model, which is based on the findings from the fracture mechanics analysis of the crack initiation and propagation processes, takes into consideration the simultaneous action of both the surface adhesion and subsurface fatigue mechanisms. The model also accounts for the micro-, and macro- contact configuration of the tube-support system. The closed form solution requires the calibration of single parameter, using a limited number of experiments, to account for the effect of environment and the support material. The model was validated using experimental data that are generated for Inconel 600 and Incology 800 tube materials at room and high temperature environment, and for different types of motion. The results showed that model can accurately predict wear losses within a factor of < ±3. This narrow range presents better than an order of magnitude improvement over the current state-of-the-art models.

Creep Deflection of Thick-Walled Piping due to Combined Bending and Internal Pressure

1990 ◽  
Vol 112 (3) ◽  
pp. 251-255 ◽  
Author(s):  
I. Finnie ◽  
M. Shirmohamadi
Keyword(s):  
Internal Pressure ◽  
Closed Form ◽  
Satisfactory Agreement ◽  
Correction Factor ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Piping System

A closed-form solution is derived for the creep deflection in thick-walled piping subjected to combined internal pressure and bending moment. The solution is limited to the situation usually encountered in practice with sustained gravity loads and support forces in which the additional stresses due to bending are small compared to those due to internal pressure. For this case, it is shown that a simple correction factor may be applied to an elastic computation of pipe deflections to include the effect of creep. Predictions using this factor show satisfactory agreement with observations on a thick-walled piping system which had been in service for 20 years.

Deformation of Curved Bars With Creep

1985 ◽  
Vol 107 (1) ◽  
pp. 225-230 ◽  
Author(s):  
J. H. Lau ◽  
C. K. Hu
Keyword(s):  
Axial Force ◽  
Maximum Stress ◽  
Bending Moment ◽  
Neutral Axis ◽  
Constitutive Relationship ◽  
Engineering Practice ◽  
Stress And Strain ◽  
Interaction Curves ◽  
Stress And Strain Rate ◽  
Relationship Of

An exact analysis is presented for the creep deformation of a curved bar subjected to the simultaneous actions of bending moment and axial force. Dimensionless interaction curves and charts, which relate the variables, axial force, location of neutral axis, maximum stress and strain rate, bending moment, and change in curvature rate, are also provided for engineering practice convenience. The constitutive relationship of the curved bar is described by the Prandtl-Nadai Creep Law.

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