TY - GEN

T1 - Simplification of the Burmister's problem by means of skew functions of discontinuum mechanics

AU - Yanqui Murillo, Calixtro

PY - 2008

Y1 - 2008

N2 - As a standard procedure, the dissipation of stresses in the Burmister's space is obtained from the Love's function, by using the method of the separation of variables, which has the advantage to allow for the excluding imposition of the boundary conditions in the horizontal plane and in the vertical direction. Unfortunately, the solution is so complicated that it is not directly applicable in engineering practice. In the present paper, the principle of the mean value to find a function of state in a statistically isotropic discontinuous substance is used to separate the variables of a strain potential by means of skew functions. By skewing the stresses, strains and Hooke's law, the Germain-Lagrange's equation is established for the horizontal plane, and two kinds of ordinary differential equation are gotten for the vertical direction: one biased and other systematic skewed. The solution to the first one coincides with the well-known polynomials for a thin plate that holds the Kirchhoff's simplifications. The solution to the second one is suitable for a slab of any thickness, comprises the well-known solution of the mechanics of materials when the layer thickness is comparatively small, and adjusts very well to the Boussinesq's solution when the layer thickness is very large.

AB - As a standard procedure, the dissipation of stresses in the Burmister's space is obtained from the Love's function, by using the method of the separation of variables, which has the advantage to allow for the excluding imposition of the boundary conditions in the horizontal plane and in the vertical direction. Unfortunately, the solution is so complicated that it is not directly applicable in engineering practice. In the present paper, the principle of the mean value to find a function of state in a statistically isotropic discontinuous substance is used to separate the variables of a strain potential by means of skew functions. By skewing the stresses, strains and Hooke's law, the Germain-Lagrange's equation is established for the horizontal plane, and two kinds of ordinary differential equation are gotten for the vertical direction: one biased and other systematic skewed. The solution to the first one coincides with the well-known polynomials for a thin plate that holds the Kirchhoff's simplifications. The solution to the second one is suitable for a slab of any thickness, comprises the well-known solution of the mechanics of materials when the layer thickness is comparatively small, and adjusts very well to the Boussinesq's solution when the layer thickness is very large.

KW - Discontinuum

KW - Layer

KW - Mean value

KW - Plate

KW - Skew

KW - Solid structure

KW - Stresses

UR - http://www.scopus.com/inward/record.url?scp=84869792463&partnerID=8YFLogxK

M3 - Contribución a la conferencia

AN - SCOPUS:84869792463

SN - 9781622761760

T3 - 12th International Conference on Computer Methods and Advances in Geomechanics 2008

SP - 546

EP - 554

BT - 12th International Conference on Computer Methods and Advances in Geomechanics 2008

Y2 - 1 October 2008 through 6 October 2008

ER -