Closed-form solution to the residual stresses in ion-exchanged silicate glass including concentration-dependent material properties

2020 ◽  
Vol 536 ◽  
pp. 120012
Author(s):  
Roberto Dugnani
2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.


Author(s):  
Youn-Young Jang ◽  
Nam-Su Huh ◽  
Ik-Joong Kim ◽  
Cheol-Man Kim ◽  
Young-Pyo Kim

Abstract Crack assessment for pipe components of a nuclear power plant or oil/gas pipeline is one of the essential procedures to ensure safe operation services. To assess cracked pipes, J-integral has been considered as a theoretically robust and useful elastic-plastic fracture parameter, so that the estimations of J-integral for various pipe geometries, material properties and loading conditions are highly needed. For this reason, many engineering predictive solutions for J-estimations based on finite element (FE) analyses have been developed. Generally, many engineering predictive solutions have been suggested as a tabular-form or closed-form. Among them, the closed-form solution is more preferred than a tabular-form solution for its convenience when many lots of interpolation are required to use it. However, the accuracy of the closed-form solution tends to be significantly reduced as the number of design parameters increases. Moreover, since there is no strict rule to define the form of functions as well, the accuracy of the closed-form solution is inevitably dependent on the rule of thumb. Therefore, it is highly required to suggest a new approach for J-estimation of cracked pipes with various geometries, material properties and loading conditions. In this paper, we propose an efficient approach based on a machine learning technique to estimate J-integral for surface cracked pipes with various geometric sizes and material properties under axial displacement loading condition. Firstly, parametric FE analysis studies were systematically performed to produce the coefficients representing the engineering J-estimation for the corresponding cracked pipe. Secondly, artificial neural network (ANN) models based on deep multilayer perceptron technique were trained based on FE results. The five input neurons (pipe geometries and material properties) and the two output neurons (the coefficients representing the engineering J-estimation) were considered. Lastly, the accuracy of the trained ANN model was studied by comparing to that of the closed-form solution from multi-variable regressions.


2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Armanj D. Hasanyan ◽  
Anthony M. Waas

With the recent development of micromechanics in micropolar solids, it is now possible to characterize the macroscopic mechanical behavior of cellular solids as a micropolar continuum. The aim of the present article is to apply these methods to determine the micropolar constitutive relation of various cellular solids. The main focus will be on the hexagonal packed circular honeycomb to demonstrate how its constitutive relationship is obtained. In addition, the same method will be applied to determine the material properties of a grid structure and a regular hexagon honeycomb. Since we model the cellular solid as an assembly of Euler–Bernoulli beams, we know that the macroscopic material properties will depend on the cell wall thickness, length, and Young's modulus. From this, and in conjunction with nondimensional analysis, we can provide a closed form solution, up to a multiplicative constant, without resorting to analyzing the governing equations. The multiplicative constant is evaluated through a single numerical simulation. The predicted values are then compared against assemblies with different local properties, using the numerical result as a benchmark since it takes into account higher order thickness effects. It is concluded that our closed form expressions vary from the numerical predictions only when the thickness of the beams increase, as expected since shear effects must be taken into account. However, for most engineering applications, these expressions are practical since our closed form solution with the Euler–Bernoulli assumption only produces about 10% error for most extreme cases. Our results are also verified by comparing them against those reported in the literature.


2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.


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