Thermal stresses in a rotating, nonhomogeneous, anisotropic disk of varying thickness and density

1975 ◽  
Vol 10 (3) ◽  
pp. 137-142 ◽  
Author(s):  
G V Gurushankar
Keyword(s):  
Thermal Loading ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Annular Disk ◽  
Varying Thickness ◽  
Principal Axes ◽  
Rotationally Symmetric ◽  
Anisotropic Disk

Closed form solution is obtained for stresses in a rotationally symmetric, nonhomogeneous, anisotropic, annular disk of varying thickness and density, subjected to thermal loading. Analysis is presented for a particular type of anisotropy, namely Polar Orthotropy, in which axes of anisotropy coincide with the principal axes of stresses at each point in the disk. The variations of homogenity, density and thickness are assumed to be hyperbolic. Numerical results in the form of graphs presented show the effect of nonhomogenity, density and degree of orthotropy on the stress distribution in a disk subjected to constant and varying temperature gradients. Homogeneous, varying density anisotropic rotating disk of varying thickness forms a special case of the analysis.

Thermal stresses in a functionally graded rotating disk: An approximate closed form solution

2020 ◽  
Vol 44 (1) ◽  
pp. 20-50
Author(s):  
Surja Deka ◽  
Ashis Mallick ◽  
Pratyush P. Behera ◽  
Prakash Thamburaja
Keyword(s):  
Closed Form ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Functionally Graded

Thermal Stress Measurement of Solder Joints in BGA Packages: Theoretical and Experimental

2008 ◽  
Author(s):  
H. X. Shang ◽  
J. X. Gao ◽  
P. I. Nicholson
Keyword(s):  
Thermal Stresses ◽  
Solder Joints ◽  
Stress Measurement ◽  
Closed Form Solution ◽  
Dissimilar Materials ◽  
Form Solution ◽  
Bga Packages ◽  
Reliability Characteristics ◽  
Bga Package ◽  
Graded Interlayer

In this study, an analytical model to obtain a closed-form solution for thermomechanical behaviours of BGA (Ball Grid Array) package was derived and experimentally validated. In the theoretical analysis, the BGA package was represented by a three-layer axisymmetrical model: two layers of dissimilar materials jointed by a graded interlayer. Based on the classical bending theory, the thermal stresses induced by temperature changes were calculated accurately. 2-D FE (Finite Element) meshes of BGA packages subjected to high temperature were used to verify the theoretical solutions. Furthermore, two types of BGA samples, each with eutectic (63wt%Sn/37wt%Pb) and Pb-free SAC387 (95.5wt%Sn/3.8wt%Ag/0.7wt%Cu) solder joints respectively, were experimentally investigated by high resolution Moire´ Interferometry (MI). Thermal cycling tests were performed on each package with temperature variation from 25°C to 125°C. It was found that the thermal deformation obtained from moire´ tests matched well with those from analytical solutions and FE analyses. Based on the shear strain values, the reliability characteristics of BGA assemblies were also assessed.

A closed-form solution for thermal stresses of structures using generalized variational principles

2018 ◽  
Vol 41 (6) ◽  
pp. 748-757 ◽  
Author(s):  
Zou-Qing Tan ◽  
Xue-Dong Jiang ◽  
Yun-Song He ◽  
Shu-Hao Ban ◽  
Ren-Qiang Xi ◽  
...  
Keyword(s):  
Closed Form ◽  
Thermal Stresses ◽  
Variational Principles ◽  
Closed Form Solution ◽  
Form Solution ◽  
Generalized Variational Principles

Large Amplitude Thermo-Mechanical Vibration Analysis of Asymmetrically Laminated Composite Beams

2011 ◽  
Vol 471-472 ◽  
pp. 745-750 ◽  
Author(s):  
Ali Fallah ◽  
Hamid Shahsavari Alavijeh ◽  
Abdoreza Pasharavesh ◽  
Mohammad Mohammadi Aghdam
Keyword(s):  
Large Amplitude ◽  
Vibration Analysis ◽  
Thermal Loading ◽  
Closed Form Solution ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Beams ◽  
Form Solution ◽  
Simple Analytical Expression ◽  
Laminated Composite Beams

In this paper, simple analytical expression is presented for large amplitude thermo-mechanical free vibration analysis of asymmetrically laminated composite beams. Euler-Bernoulli assumptions together with Von Karman's strain-displacement relation are employed to derive the nonlinear governing partial differential equation (PDE) of motion. He's variational method is employed to obtain a simple and efficient approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of presented technique. Some new results for the nonlinear natural frequencies of the laminated beams such as the effect of vibration amplitude, lay-up configuration and thermal loading are presented for future references.

Nonlinear Thermo-Mechanical Vibration Analysis of Functionally Graded Beams

2011 ◽  
Author(s):  
Ali Fallah ◽  
Keikhosrow Firoozbakhsh ◽  
Abdolreza Pasharavesh
Keyword(s):  
Vibration Analysis ◽  
Vibration Amplitude ◽  
Thermal Loading ◽  
Natural Frequencies ◽  
Mechanical Vibration ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Form Solution ◽  
Functionally Graded ◽  
Material Inhomogeneity

In this paper, nonlinear thermo-mechanical free vibration analysis of functionally graded (FG) beams investigated. Euler-Bernoulli assumptions together with Von Karman’s strain-displacement relation are employed to derive the nonlinear governing partial differential equation (PDE) of motion. He’s variational method is employed to obtain a simple and efficient approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of presented technique. Some new results for the nonlinear natural frequencies of the FG beams such as the effect of vibration amplitude, material inhomogeneity and thermal loading are presented for future references.

On Transverse Vibrations of a Rotating Disk of Uniform Strength

1992 ◽  
Vol 59 (1) ◽  
pp. 234-235 ◽  
Author(s):  
Ugˇur Gu¨ven
Keyword(s):  
Closed Form ◽  
Hypergeometric Functions ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Transverse Motion ◽  
Confluent Hypergeometric Functions ◽  
Transverse Vibrations ◽  
Uniform Strength

Transverse, axisymmetric vibrations of a rotating disk of uniform strength is studied. Closed-form solution for the equation of transverse motion is obtained in terms of confluent hypergeometric functions.

Effect of temperature variation on the plate-end debonding of FRP-strengthened beams: A theoretical study

2021 ◽  
pp. 136943322110463
Author(s):  
Dong Guo ◽  
Wan-Yang Gao ◽  
Dilum Fernando ◽  
Jian-Guo Dai
Keyword(s):  
Temperature Variation ◽  
Thermal Loading ◽  
Closed Form Solution ◽  
Form Solution ◽  
Effect Of Temperature ◽  
Shear Stresses ◽  
Limited Information ◽  
Element Analysis ◽  
Bond Slip ◽  
Loading Effects

Steel/concrete structures strengthened with externally bonded FRP plates may be subjected to significant temperature variations during their service time. Such temperature variation (i.e., thermal loading) may significantly influence the debonding mechanism in FRP-strengthened structures due to the thermal incompatibility between the FRP plate and the substrate as well as the temperature-induced bond degradation at the FRP-to-steel/concrete interface. However, limited information is available on the effect of temperature variation on the debonding failure in FRP-strengthened beams. This paper presents a new and closed-form solution to investigate the plate-end debonding failure of the FRP-strengthened beam subjected to combined thermal and mechanical (i.e., flexural) loading. A bilinear bond-slip model is used to describe the bond behavior of the FRP-to-substrate interface. The analytical solution is validated through comparisons with finite element analysis results regarding the distributions of the interfacial shear stresses, the interfacial slips and the axial stresses of the FRP plate. Given that a constant bond-slip relationship is adopted, it is observed that an increase in service temperature will lead to an increased interfacial slip at the plate end and consequently a reduced plate-end debonding load, and vice versa. Further parametric studies have indicated that the thermal loading effects become more significant when shorter and stiffer FRP plates are applied for strengthening.

Thermal Induced Stresses in Bridge-Wire Initiator Glass-to-Metal Seals

2006 ◽  
Vol 129 (3) ◽  
pp. 300-306 ◽  
Author(s):  
Luke M. Thompson ◽  
Michael R. Maughan ◽  
Karl K. Rink ◽  
Donald M. Blackketter ◽  
Robert R. Stephens
Keyword(s):  
Closed Form ◽  
Plane Stress ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Manufacturing Processes ◽  
Material Degradation ◽  
Element Analysis ◽  
Parametric Plane ◽  
Lumped Models

Cracks have been observed in the insulating glass of bridge-wire initiators that may allow moisture to penetrate the assembly, potentially leading to the corrosion and degradation of the bridge wire and the pyrotechnic material. Degradation of the pyrotechnic or the bridge wire may result in initiator failure or diminished performance. The goal of this research is to determine if the manufacturing processes could produce thermal stresses great enough to crack the glass. A parametric plane stress closed-form solution was used to determine the effects of changing material properties and dimensions of the initiator, and to determine potential stresses within the initiator from two different manufacturing scenarios. To verify and expand the plane stress closed-form solution, a two-dimensional axisymmetric finite element analysis was performed. To reproduce the two manufacturing scenarios, lumped models and models that included the effects of cooling the initiator were used. Both models showed that if the manufacturing process involves pouring molten glass into the initiator, the potential for cracking exists. Furthermore, if the surface of the initiator cools faster than the center, cracking is more likely.

Closed-Form Solution of the Frictional Sliding Contact Problem for an Orthotropic Elastic Half-Plane Indented by a Wedge-Shaped Punch

2014 ◽  
Vol 618 ◽  
pp. 203-225 ◽  
Author(s):  
Aysegul Kucuksucu ◽  
Mehmet A. Guler ◽  
Ahmet Avci
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Contact Problems ◽  
Form Solution ◽  
Orthotropic Materials ◽  
Principal Axes ◽  
The Coefficient Of Friction ◽  
Processing Techniques

In this paper, the frictional contact problem of a homogeneous orthotropic material in contact with a wedge-shaped punch is considered. Materials can behave anisotropically depending on the nature of the processing techniques; hence it is necessary to develop an efficient method to solve the contact problems for orthotropic materials. The aim of this work is to develop a solution method for the contact mechanics problems arising from a rigid wedge-shaped punch sliding over a homogeneous orthotropic half-plane. In the formulation of the plane contact problem, it is assumed that the principal axes of orthotropy are parallel and perpendicular to the contact. Four independent engineering constants , , , are replaced by a stiffness parameter, , a stiffness ratio, a shear parameter, , and an effective Poisson’s ratio, . The corresponding mixed boundary problem is reduced to a singular integral equation using Fourier transform and solved analytically. In the parametric analysis, the effects of the material orthotropy parameters and the coefficient of friction on the contact stress distributions are investigated.

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