STATIC ANALYSIS OF A PLATE ON ELASTIC FOUNDATION WITH THE MODELING IN PC “LIRA” AND WITH THE CALCULATION BY VARIATIONAL-DIFFERENCE METHOD

Static analysis of a plate on elastic foundation is made in two ways on the example of a reinforced concrete road plate 2PP30.18-30 series B3.503.1-1 intended for temporary roads. The plate are calculated on the PC «LIRA». Also the plate are calculated by the variational-difference method like a construction on linearly elastic inhomogeneous foundation (in the form of criss-crossed reinforced concrete tapes). When setting up a contact problem, hypotheses and assumptions of the theory of elasticity and structural mechanics are used. The hypotheses of the theory of bending are valid for a plate. When the deformation energy functional is compiled, the work of the forces of the intrinsic weight of the elastic foundation is not taken into account. In the contact zone, the equality of the displacements of the foundation to the deflections of the plate is valid. When calculating a layered elastic medium is replaced by a rectangular design area, which is approximated by a rectangular grid of finite dimensions. For unknowns are accepted vertical and horizontal movements of the nodes of the calculation area and reactive pressures (contact stresses) in the contact zone of the plate with the base. Based on the calculated values of nodal displacements the intensity of deformations and the intensity of stresses are identifying. When calculating in a PC «LIRA», 6 loading options are considered (central and edge). When calculating the variational-difference method, only central loading is considered. There are given the results of numerical studies in comparison to the two variants of calculations in this article.

REINFORCED CONCRETE COATING PLATES OF HIGHWAYS ON AN ELASTIC HALF-SPACE

Static analysis of the stress-strain state of a plate on elastic foundation is made in two ways on the example of a reinforced concrete road plate 2PP30.18-30 series B3.503.1-1 intended for temporary roads. These plates are considered as a planar structure on an elastic foundation. The plates are calculated by the method of B.N. Zhemochkin using the Ritz method to determine plate deflections in the main system using the mathematical package «MathCad». Also the plates are calculated on the PC «LIRA». There are given the results of experimental and numerical studies in this article

Refined General Theory of Stress Analysis for Tubesheet

The stress analysis method for fixed tubesheet (TS) heat exchangers (HEX) in pressure vessel codes such as ASME VIII-1, EN13445, and GB151 is based on the classical theory of thin plate on elastic foundation. In addition, these codes all assume a geometric and loading plane of symmetry at the midway between the two TSs so that only half of the unit or one TS is needed to be considered. In this study, a refined general theory of stress analysis for TS is presented which also considers unequal thickness for two TSs, different edge conditions, pressure drop and deadweight on two TSs, the anisotropic behavior of the TS in thickness direction, and transverse shear deformation in TS. Analysis shows floating and U-tube heat exchangers are the two special cases of the refined theory. Theoretical comparison shows that ASME method can be obtained from the special case of the simplified mechanical model of the refined theory. Numerical comparison results indicate that predictions given by the refined theory agree well with finite element analysis (FEA) for both thin and thick TS heat exchangers, while ASME results are not accurate or not correct. Therefore, it is concluded that the presented refined general theory provides a single unified method, dealing with both thin and thick TSs for different type (U type, floating, and fixed) HEXs in equal detail, with confidence to predict design stresses.