Three-Dimensional Generalized Thermoelasticity with Fractional Order Heat Conduction of a Half-Space Subjected to Rectangular Thermal Pulse: State-Space Approach

2018 ◽  
Vol 7 (6) ◽  
pp. 833-841
Author(s):  
A. K. Khamis ◽  
A. A. El-Bary ◽  
Allam. A. Allam ◽  
Allalbakali
Keyword(s):  
Heat Conduction ◽  
State Space ◽  
Half Space ◽  
Fractional Order ◽  
Three Dimensional ◽  
Generalized Thermoelasticity ◽  
State Space Approach ◽  
Thermal Pulse ◽  
Space Approach

Theory of Fractional Order Generalized Thermoelasticity

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Hamdy M. Youssef
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
State Space ◽  
Uniqueness Theorem ◽  
Half Space ◽  
Fractional Order ◽  
Elastic Material ◽  
Generalized Thermoelasticity ◽  
New Model ◽  
One Dimensional

In this work, a new model of thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with fractional order, and its uniqueness theorem has been approved also. One-dimensional application for a half-space of elastic material, which is thermally shocked, has been solved by using Laplace transform and state-space techniques. According to the numerical results and its graphs, conclusion about the new theory of thermoelasticity has been constructed.

GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

2020 ◽  
Vol 9 (11) ◽  
pp. 9769-9780
Author(s):  
S.G. Khavale ◽  
K.R. Gaikwad
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Order Derivative ◽  
Laplace Inversion ◽  
State Space Approach ◽  
Spherical Region ◽  
Fractional Order Derivative ◽  
Numerical Laplace Inversion ◽  
Mathcad Software ◽  
Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

Assessment of cross-laminated timber panels by the state-space approach

2019 ◽  
Vol 22 (11) ◽  
pp. 2375-2391
Author(s):  
Asad S Albostami ◽  
Zhangjian Wu ◽  
Lee S Cunningham
Keyword(s):  
State Space ◽  
Three Dimensional ◽  
The State ◽  
Composite Panel ◽  
State Space Approach ◽  
Cross Laminated Timber ◽  
Practical Applications ◽  
The Cross ◽  
Analytical Approaches ◽  
Space Approach

In this article, cross-laminated timber panels are investigated as a novel engineering application of the state-space approach. As cross-laminated timber is a laminated composite panel, the three-dimensional analytical method provided by the state-space approach offers the potential for improved accuracy over existing common approaches to the analysis of cross-laminated timber. Before focusing on the specific application to cross-laminated timber, the general theory of the state-space approach is outlined. The method is then applied to describe the behaviour of a number of cross-laminated timber panel configurations previously examined experimentally and analytically. In order to demonstrate the capability of the state-space approach in this application, the results are compared with those from various two-dimensional and three-dimensional analytical approaches and finite element modelling briefly. With a view to design, different failure criteria are explored to assess the ultimate strength of the cross-laminated timber panels. The state-space approach demonstrates its superior capability in capturing the nonlinear distribution of the elastic stresses through the thickness of the cross-laminated timber panels over a range of span-to-thickness ratios common in practical applications.

Modeling of memory-dependent derivatives with the state-space approach

2019 ◽  
Vol 16 (4) ◽  
pp. 657-677
Author(s):  
Siddhartha Biswas
Keyword(s):  
Time Delay ◽  
State Space ◽  
Kernel Function ◽  
Generalized Thermoelasticity ◽  
Inversion Method ◽  
Two Dimensional ◽  
State Space Approach ◽  
Content Type ◽  
Coupled Equations ◽  
Space Approach

Purpose The purpose of this paper is to deal with a new generalized model of thermoelasticity theory with memory-dependent derivatives (MDD). Design/methodology/approach The two-dimensional equations of generalized thermoelasticity with MDD are solved using a state-space approach. The numerical inversion method is employed for the inversion of Laplace and Fourier transforms. Findings The solutions are presented graphically for different values of time delay and kernel function. Originality/value The governing coupled equations of the new generalized thermoelasticity with time delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to a two-dimensional problem of an isotropic plate.

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