Analytical Solution of Cattaneo and Thermal Stress Equations

2013 ◽  
pp. 85-119 ◽  
Author(s):  
Bekir S. Yilbas ◽  
Ahmad Y. Al-Dweik ◽  
Nasser Al-Aqeeli ◽  
Hussain M. Al-Qahtani
Keyword(s):  
Thermal Stress ◽  
Analytical Solution

Ratchet Boundary for Superimposed Biaxial Membrane Stress States

2018 ◽  
Author(s):  
Wolf Reinhardt
Keyword(s):  
Thermal Expansion ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Pressure Vessels ◽  
Stress Fields ◽  
Design Codes ◽  
Bending Stress ◽  
Membrane Stress ◽  
Asme Code ◽  
Stress States

Thermal membrane and bending stress fields exist where the thermal expansion of pressure vessel components is constrained. When such stress fields interact with pressure stresses in a shell, ratcheting can occur below the ratchet boundary indicated by the Bree diagram that is implemented in the design Codes. The interaction of primary and thermal membrane stress fields with arbitrary biaxiality is not implemented presently in the thermal stress ratchet rules of the ASME Code, and is examined in this paper. An analytical solution for the ratchet boundary is derived based on a non-cyclic method that uses a generalized static shakedown theorem. The solutions for specific applications in pressure vessels are discussed, and a comparison with the interaction diagrams for specific cases that can be found in the literature is performed.

An Analysis of Thermo-Mechanical Behavior in a Multilayer Composite Pipe Under Temperature Variation

2010 ◽  
Author(s):  
Wei Yang ◽  
Jyhwen Wang
Keyword(s):  
Finite Element ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Mechanical Behavior ◽  
Temperature Change ◽  
Thermal Stresses ◽  
Element Model ◽  
Functionally Graded ◽  
Element Analysis ◽  
Graded Materials

A generalized analytical solution of mechanical and thermal induced stresses in a multi-layer composite cylinder is presented. Based on the compatibility condition at the interfaces, an explicit solution of mechanical stress due to inner and outer surface pressures and thermal stress due to temperature change is derived. A finite element model is also developed to provide the comparison with the analytical solution. It was found that the analytical solutions are in good agreement with finite element analysis result. The analytical solution shows the non-linear dependency of thermal stress on the diameters, thicknesses and the material properties of the layers. It is also shown that the radial and circumferential thermal stresses depend linearly on the coefficients of thermal expansion of the materials and the temperature change. As demonstrated, this solution can also be applied to analyze the thermo-mechanical behavior of pipes coated with functionally graded materials.

scholarly journals Thermal Load and Heat Transfer in Dental Titanium Implants: an Exact Analytical Solution to the ‘Heat Equation’

2021 ◽  
Author(s):  
Ziyad S. Haidar
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Heat Equation ◽  
Exposure Time ◽  
Thermal Load ◽  
Exact Analytical Solution ◽  
Titanium Implants ◽  
Surrounding Tissue ◽  
Temperature Changes

Introduction: Heat is a kinetic process whereby energy flows from between two systems; hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and -drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury; this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants upon hot-liquid intake. Materials and Methods: We investigate the impact of the material, the location point along implant length, and the exposure time of the thermal load on temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of knowledge, this is the first introduction of the intrinsic time, a “proper” time that characterizes the geometry of the dental implant, where we show, mathematically and graphically, how the interplay between “proper” time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability and success rates, whether for immediate or delayed loading strategies.

Uncoupled Dynamic Thermal Stress Distribution on the Section of a Flow Channel Occupied Filling Medium

2013 ◽  
Vol 394 ◽  
pp. 185-191
Author(s):  
Jie Liu ◽  
Xiao Ling Jia ◽  
Neng Qiang Chai
Keyword(s):  
Thermal Stress ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Elliptic Flow ◽  
Flow Channel ◽  
Two Dimensional ◽  
Coordinate Axis ◽  
Rotation Method ◽  
Thermal Stress Distribution ◽  
Dimensional Section

Throught translation and rotation method of coordinate axis, a problem of the dynamic thermal stress distribution on the two-dimensional section of a flow channel occupied filling medium was studied theoretically. A general analytical solution with related computional process was described in detailed. As an illustration sample, some numberical results are shown in the figure about the dynamical thermal stress distribution on the section of an elliptic flow channel occupied filling medium.

The Shakedown Boundary for Parabolic Stress Distribution in NB-3222.5

2013 ◽  
Author(s):  
W. Reinhardt ◽  
A. Asadkarami
Keyword(s):  
Thermal Stress ◽  
Temperature Distribution ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Thermal Loading ◽  
Exact Analytical Solution ◽  
Second Order ◽  
Fe Model ◽  
Membrane Stress ◽  
Shakedown Analysis

The rules for the prevention of thermal stress ratchet in NB-3222.5 address the interaction of general primary membrane stress with two types of cyclic thermal loading. The first is a linear through-wall temperature gradient, for which the shakedown boundary is given by the well-known Bree diagram. The Code provides a second shakedown boundary for the interaction of general primary membrane stress with a “parabolic” temperature distribution. The corresponding ratchet boundary is fully defined in the elastic range, but only three points are given in the elastic-plastic regime. The range of validity of this ratchet boundary in terms of the thermal stress distribution (does “parabolic” mean second-order in the thickness coordinate or any polynomial of degree greater than one? If it is second-order, are there any further restrictions?) is not well defined in NB-3222.5. Using a direct lower bound method of shakedown analysis, the non-cyclic method, an exact analytical solution is derived for the shakedown boundary corresponding to the interaction of general primary membrane stress with a cyclic “parabolic” temperature distribution. By comparison to what is given in NB-3222.5, the thermal condition for which the Code equation is valid is defined and its range of validity is established. To study the transition behavior to the steady state and to confirm the analytical solution, numerical results using an FE model are also obtained.

scholarly journals An exact analytical solution of non-Fourier thermal stress in cylindrical shell under periodic boundary condition

2014 ◽  
Vol 2 (4) ◽  
pp. 293-302 ◽  
Author(s):  
Mohammad Reza Talaee ◽  
Mansoor Alizadeh ◽  
Sadra Bakhshandeh
Keyword(s):  
Boundary Condition ◽  
Cylindrical Shell ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Exact Analytical Solution
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