Abstract
Residual stress in continuum has not been quantified because time relationship with residues has not been proven analytically. This is achieved in this paper by analyzing a two component mixture with the non-homogeneous equation of statics in the theory of elastic mixture, and second order differential equations with variable coefficients. A dry mixture of sand and cement is transformed into a continuum, which is been determined as an entire or a meromorphic function, as a result of the existence of residues that are contained in the principal component of the mixture obtained directly from the earth. The time relationship with residue, in these two functions are determined. Our result shows that time places a limit on residues, making the meromorphic function prone to implosion..
Highlights
The theories of mixtures in the framework of continuum mechanics have been developed throughout the sixties and seventies, and subsequent development in various constitutive theories and continuum analysis are too numerous to document [ 1 ]
A dry mixture of sand and cement is transformed into a continuum, which is been determined as an entire, or a meromorphic functions, due to the existence of residues that are domiciled in the principal component of the mixture obtained directly from the earth
(i) A transformed mixture [w = u(x1, x2) + iv(x1, x2)] is an entire function (y) when it is analytic at every point in a given domain; that is, it contains no pole, represented by Taylor series, which gives an infinite radius of convergence [13 ]
Summary
The theories of mixtures in the framework of continuum mechanics have been developed throughout the sixties and seventies, and subsequent development in various constitutive theories and continuum analysis are too numerous to document [ 1 ]. [2,5] discussed the entropy flux of transversely isotropic elastic bodies of homogeneous type, while [6, 7, 8] gave a solution of a non-classical problem of oscillation of two component mixtures. Time impact on residue in a non-homogeneous equation of statics in the theory of elastic mixture has not been solved. We analyze the time impact on residues in a two component mixture using special functions. This study is aimed at analyzing the time impact on these two forms of functions, resulting from a single mixture, using second order differential equations with variable coefficient, and graphs. “Time Impact on Residue in a Non-homogeneous Equation of Statics in the Theory of Elastic Mixture”.
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