Axisymmetric vibrations of temperature-dependent functionally graded moderately thick circular plates with two-dimensional material and temperature distribution

2020 ◽  
Author(s):  
Rahul Saini ◽  
Roshan Lal
Keyword(s):  
Temperature Distribution ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Circular Plates ◽  
Temperature Dependent

Nonlinear Bending of the FGM Circular Plates with Temperature-Dependent Properties

2008 ◽  
Vol 575-578 ◽  
pp. 1020-1024 ◽  
Author(s):  
Lian Sheng Ma ◽  
Chun Zhi Deng ◽  
Zhi Ying Ou
Keyword(s):  
Shooting Method ◽  
Plate Theory ◽  
Material Constant ◽  
Functionally Graded ◽  
Circular Plates ◽  
Power Law Distribution ◽  
Temperature Dependent ◽  
Nonlinear Bending ◽  
Bending Behavior ◽  
Temperature Dependent Properties

Axisymmetric nonlinear bending of the functionally graded circular plates is investigated in the present work. The material properties of plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. Based on the classical nonlinear plate theory, the governing equations for the problem are derived, and then a shooting method is employed to numerically solve the equations. Effects of material constant, temperature- dependent properties and boundary conditions on the nonlinear bending behavior of the FGM plate are discussed in details.

Modelling of Temperature Distribution of Semiconductors During Rapid Thermal Processing

1994 ◽  
Vol 342 ◽  
Author(s):  
Andreas Tillmann
Keyword(s):  
Temperature Distribution ◽  
Material Property ◽  
Thermal Processing ◽  
Rapid Thermal Processing ◽  
Two Dimensional ◽  
Temperature Uniformity ◽  
Temperature Dependent ◽  
Incident Intensity ◽  
Circular Test ◽  
Contour Plots

ABSTRACTThe modelling of temperature distribution on semiconductor wafers in common RTP-equipment is described. The incident intensity distribution on the wafer is calculated using raytracing. Based on this distribution the temperature distribution on the wafer is determined solving the two-dimensional heat conduction equation. If the dependence of a considered material property on the process temperature is known, the calculated temperature distribution can be convened to a distribution of this parameter.The distinctive feature of the described algorithms is the two-dimensional treatment of the distributions using a grid of ring segments, each with equal area. This grid is identical to the usual circular test patterns of multipoint measurement equipment. This is convenient since the evaluation of temperature uniformity in RTP equipment is done mostly by mapping an appropriate temperature dependent material property. All calculated distributions can be presented by contour plots as well as 3-D plots. This results in a very suitable method to compare simulated and experimental wafer maps.The agreement between simulated and experimental temperature distributions is shown.

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