An Interval Parametric Approach for the Solution of One Dimensional Generalized Thermoelastic Problem

Subject Areas : Mechanics of Solids

S Mandal ¹ , S Pal Sarkar ² , T Kumar Roy ³

1 - Department of Mathematics, Sitananda College, Nandigram, Purba Medinipur-721631, India ---Department of Mathematics, IIEST, Shibpur, Howrah-711103, India
2 - Department of Mathematics, IIEST, Shibpur, Howrah-711103, India
3 - Department of Mathematics, IIEST, Shibpur, Howrah-711103, India

Received: 2021-09-10 Accepted : 2021-12-10 Published : 2022-03-30

Keywords:

References:

1.  Nowacki W., 1981, Theory of Assymatric Elasticity, Pergamon Press.


2.  Love A.E.H., 2013, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press.


3.  Sokolnikoff S., 1956,  Mathematical Theory of Elasticity, McGraw-Hill, Book Company.


4.  McCarthy E.K., Bellew A.T., 2014, Poisson’s ratio of individual metal nanowires, Nature Communications 5: 4336.


5.  Muhanna R.L., Mullen RL., 2001, Uncertainty in mechanics problems-Interval–based approach, Journal of Engineering Mechanics127(6): 557-566.


6.  Rao S.S., Berke L., 1997, Analysis of uncertain structural systems using interval analysis, AIAA Journal 35(4): 727-735.


7.  Dinkle J.J., Tretter J., 1987, An interval arithmetic approach to sensitivity analysis in geometric programming, Operetion Research 35: 859-866.


8.  Pal D., Mahapatra G.S., Samanta G.P., 2015, Bifurcation analysis of predator-prey model with time delay and Harvesting efforts using interval parameter, International Journal of Dynamics and Control 3:199-209.


9.  Lord H., Shuman Y., 1967, A generalized dynamical theory of elasticity, Journal of the Mechanics and Physics of Solids 15:299-309.


10.  Green A.E., Lindsey K.A., 1972, Thermoelasticity, Journal of Elasticity2: 1-7.


11.  Lahiri A., Das B., Sarkar B., 2010, Thermal stresses in an isotropic elastic slab due to prescribed surface temperature, Advances in Theoretical and Applied Mechanics 3: 451-467.


12.  Dhaliwal R.S., Sherif H.H., 1981, Generalized one-dimensional thermal shock problem for small times,
    Journal of Thermal Stresses 4: 407-420.


13.  Noda N., Furukawa T., Ashida F., 1989, Generalized thremoelasticity in an infinite solid with a hole, Journal of Thermal Stresses 12: 385-402.


14.  Bahar Y.L., Hetnarski R.B., 1979, Connection between the thermoelastic potential and the state space formulation of thermoelasticity, Journal of Thermal Stresses 2: 283-290.


15.  Das N.C., Lahiri A., Giri R.R., 1997, Eigenvalue approach to generalized thermoelasticity, Indian Journal of Pure and Applied Mathematics 28(12): 1573-1594.


16.  Das N.C., Lahiri, Bhakta P.C., 1998, Some one dimensional problems in generalized thermoelasticity, Bulletin of the Calcutta Mathematical Society 90: 239-250.


17.  Lahiri A., Das N.C., 2009, Matrix method of solution of coupled differential equations and its applications in generalized thremoelasticity, Bulletinof the Calcutta Mathematical Society 101(6): 571-590.


18.  Wilms E.V., Cohen H., 1985, Some one dimensional problems in coupled thermoelasticity, Mechanics Research Communications 12: 41-47.


19.  Youssef H.M., Al-Lehaibi E.A., 2007, State-space approach of two temperature generalized thermoelasticity of one dimensional problem, International Journal of Solids and Structures 44: 1550-1562.


20.  Zakian V., 1969, Numerical inversion of laplace transform, Electronic Letters 5(6): 120-122.


21.  Zakian V., 1970a, Rational approximation to transform function matrix of distributed system, Electronic Letters 6(15): 474-476.


22.  Zakian V., 1970b, Optimisation of numerical inversion of laplace transform, Electronic Letters 6(21): 677-679.