Ratchet Boundary of a Beam With Arbitrary Cross Section

2013 ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Fundamental Idea ◽  
Shakedown Analysis ◽  
Component Structure ◽  
Elastic Range ◽  
Bending Loads ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “Non-Cyclic Method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan’s theorem). The fundamental idea behind the proposed method is to (conservatively) determine the stable and unstable boundary without going through the cyclic history. The method is used to derive the interaction diagrams for a beam subjected to primary membrane and bending with secondary bending loads. Various cross-sections including rectangular, solid circular and thin pipe are investigated.

Ratchet Limit Solution of a Beam With Arbitrary Cross Section

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Fundamental Idea ◽  
Component Structure ◽  
Elastic Range ◽  
Limit Solution ◽  
Thin Walled Pipe ◽  
Bending Loads ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “noncyclic method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan's theorem). The fundamental idea behind the proposed method is to (conservatively) determine the stable and unstable boundary without going through the cyclic history. The method is used to derive the interaction diagrams for a beam subjected to primary membrane and bending with secondary bending loads. Various cross-sections including rectangular, solid circular and thin-walled pipe are investigated.

Ratcheting/Shakedown Analysis of Cracked Structures

2011 ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Numerical Schemes ◽  
Shakedown Analysis ◽  
Component Structure ◽  
Elastic Range ◽  
Cracked Structures ◽  
Elastic Shakedown ◽  
Plastic Shakedown ◽  
Time Invariant ◽  
Mean Time

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a cracked component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “Non-Cyclic Method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan’s theorem). The proposed method is based on decomposing the loading into mean (time invariant) and fully reversed components. The applicability of the NCM has been demonstrated for several uncracked components and structures using both analytical and numerical schemes. The present paper extends the NCM further to analyze plastic shakedown for two simple cracked components.

Local vs. Global Ratcheting in Cracked Structures

2014 ◽  
Author(s):  
R. Adibi-Asl ◽  
Wolf Reinhardt
Keyword(s):  
Cyclic Loading ◽  
Component Structure ◽  
Elastic Range ◽  
Cracked Structures ◽  
Elastic Shakedown ◽  
Plastic Shakedown ◽  
Time Invariant ◽  
Global And Local ◽  
Mean Time ◽  
Cracked Structure

The classical approaches in shakedown analysis are based on the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a cracked component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. The Non-Cyclic Method (NCM) has been proposed recently to determine both the elastic and the plastic ratchet boundary of a component or structure under cyclic loading by generalizing the static shakedown theorem (Melan’s theorem). The proposed method is based on decomposing the loading into mean (time invariant) and fully reversed components. When a cracked structure is subjected to cyclic loading, the crack and its vicinity behave differently (local) than the rest of the structure (global). The crack may propagate during the application of cyclic loading. This will affect both local and global behavior of the cracked structure. This paper investigates global and local ratcheting of the cracked structures using the NCM and fracture mechanic parameters.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Analysis of shear lag in cylindrical tubes of arbitrary cross section

1983 ◽  
Vol 389 (1797) ◽  
pp. 259-277
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Bending Moment ◽  
General Purpose ◽  
Simple Eigenvalue ◽  
Arbitrary Cross Section ◽  
Longitudinal Distribution ◽  
Shear Lag ◽  
Cylindrical Tubes ◽  
Polynomial Distribution

A very general analysis is given of the phenomenon of shear lag in thin-walled cylindrical tubes, with single-cell cross sections of arbitrary shape, containing any number of concentrated longitudinal booms that carry direct stress only, and subjected to any longitudinal distribution of bending moment and torque. Two equations relating the distributions of direct and shearing stresses on the cross section are derived for the most general case where the tube is non-uniform because of an arbitrary longitudinal variation of wall thicknesses and boom areas. These equa­tions, which are remarkably simple in view of their generality, incor­porate all the requirements of equilibrium and compatibility and provide corrections to the stresses, curvature and twist calculated from the engineers’ theory of bending and torsion. They also govern the distri­bution of stresses arising from the application of self-equilibrating systems of tractions to the end cross sections. Exact solutions are ob­tained for the case of a uniform, but otherwise arbitrary, cross section under any polynomial distribution of bending moment and torque, and it is shown how conditions at the end cross sections can be satisfied with the aid of solutions of a simple eigenvalue problem. The equations are in a particularly ideal form for incorporating into a general purpose com­puter program for the automatic numerical solution of any problem of this type.

Pressure Distributions in Porous Ducts of Arbitrary Cross Section

1973 ◽  
Vol 95 (3) ◽  
pp. 342-348 ◽  
Author(s):  
J. C. P. Huang ◽  
H. S. Yu
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Cross Sections ◽  
Porous Plate ◽  
Porous Wall ◽  
Design Criterion ◽  
Arbitrary Cross Section ◽  
Solid Particles ◽  
Equivalent Diameter ◽  
Pressure Distributions

A general analytical method has been developed to approximate the pressure distribution along a porous duct of an arbitrary cross section with uniform fluid extraction or addition through the wall. Application of this method is made to a variety of cross sections including circular tubes, parallel plate channels, elliptical ducts, rectangular ducts, annular ducts, and isosceles triangular ducts. Comparisons have been made with results from existing literature on cases of the circular porous tube and the parallel porous plate channel in which exact solutions are available. A numerical solution for the case of a parallel channel consisting of an impermeable wall on one side and a porous wall on the other side is also presented. One important filter duct design criterion has been found for each of the above cases. At a critical wall Reynolds number, defined by flow velocity normal to the wall and the equivalent diameter of the duct, the pressure gradient along the filter duct approaches zero. The zero pressure gradient in a filter duct ensures uniform filtration of solid particles.

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

2010 ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Efficient Calculation ◽  
Asme Code ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavour, and demonstrates the connection to Melan’s theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

1995 ◽  
Vol 62 (3) ◽  
pp. 718-724 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Width Ratio ◽  
Cross Sectional ◽  
Hollow Cylinders ◽  
Displacement Based ◽  
Bending Modes

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

scholarly journals Analytical Method to Interpret Displacement in Elastic Anisotropic Soil due to a Tunnel Cavity with an Arbitrary Cross Section

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Qiongfang Zhang ◽  
Kang Cheng ◽  
Yadong Lou ◽  
Tangdai Xia ◽  
Panpan Guo ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Surface Displacement ◽  
Horizontal Displacement ◽  
Distribution Patterns ◽  
Mapping Method ◽  
Arbitrary Cross Section ◽  
Image Method ◽  
Variable Theory ◽  
Anisotropic Soil

Based on complex variable theory and conformal mapping method, the paper presents full plane elastic solutions around an unlined tunnel with arbitrary cross section in anisotropic soil. The solutions describe soil elastic solutions for assuming that the displacement vectors along the tunnel boundary are directed towards the center of the tunnel. Tunnels with different cross sections are used to illustrate the method and its correctness. An elliptical unlined tunnel case is discussed in detail in the paper. Using the image method, an approximate solution for predicting surface displacement and subsurface horizontal displacement around an unlined tunnel in anisotropic soil can be obtained. The results show anisotropic stiffness properties n n = E h / E v and m m = G v h / E v have a great effect on the displacement distribution patterns around an elliptical tunnel with certain shape.

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