This paper attempts to model a plate-fin element. The cooperation of the rib and the plate is provided by satisfying the equation of static equilibrium subjected to axial and tangent forces. The forces occur in bottom and top surfaces of the rib. Moreover, description of the plate element is generalized considering unknown horizontal displacements. The obtained equation of deflection of the fin element contains unknown forces of reactions of the bottom surface of the plate. A sum of general integral of homogeneous equation and particular integral of non-homogeneous equation is a solution of the equation. It can be assumed that the general integral is in symmetric form. Particular integral is solved by decompositions in functional series of loads of the plate and interaction forces. Next stage of modeling considers the above process for the rib. Putting these two descriptions together –the plate and the rib, allows to define the plate-rib element method.

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