Annotation

One has examined the thin orthotropic deck on Winkler elastic foundation. A mathematical model of such deck is constructed. One has developed an analytical and numerical approach to the calculation of the elastic equilibrium of such structures. The calculation of structures is reduced to the solution of the differential equation in partial derivatives due to certain boundary conditions. The differential equation depends on the elastic constants of the material, such as the stiffness of the deck as to bending, torsion and lateral stiffness, as well as the stiffness coefficient of the foundation.

The solution of the differential equation is represented as a general solution of a homogeneous equation and some partial solution of an inhomogeneous equation. The general solution is presented as the sum of the products of the coordinate functions multiplied by the unknown coefficients by which the boundary conditions on the deck contour are satisfied. The meaning of these coefficients is the degree of freedom of the deck deflection. Their number is always equal to the number of boundary conditions recorded at individual points on the edges of the deck. Two boundary conditions are written at each point.

In turn, the partial solution of the basic differential equation is represented as the sum of the products of force functions on other unknown coefficients using which the conditions on the deck surface are satisfied.

Similarly, the relations on displacements, moments and transverse forces, expressed through their own coordinate and force functions, are obtained. The set of obtained expressions forms a computational model of the slab structure.

The fundamentals of the model are the basic functions of zero order, which is used to express the deflection of the deck. Tangential displacements are expressed using basic functions of the first order, bending and torsional moments – using basic functions of the second order, and transverse forces and generalized transverse forces – using functions of the third order. Basic functions of higher order are expressed using basic functions of lower orders and ultimately – using basic functions of zero order, that is deflections of the deck.

The proposed approach allows simulating static, kinematic and mixed boundary conditions on the polygonal contour of the deck.