Canonical polynomials in the problem about the bend of circular plate of variable thickness

The problem about the bend of circular plate of variable thickness under specifically selected laws of rigidity change is reduced to the ordinary differential equation with variable coefficients of polynomial kind. The construction of the approximate solution of equation that satisfies boundary conditions is realized by means of canonical polynomials and $\tau$-method of Lantzosh.

Heat and mass transfer on a stretching/shrinking and porous sheet of variable thickness with suction and injection

Heat and mass transfer in a viscous flow over a non-uniform porous plate of variable thickness is investigated in this paper. The variably heated plate is stretched/shrunk in a stagnant fluid with variable velocity and has the non-uniform species concentration. The governing partial differential equations are simplified and solved numerically. The transport of heat and mass in the flow regime is governed by a set of PDE’s satisfying certain necessary boundary conditions. The governing PDE’s are simplified by using boundary layer approximations and transformed into a set of ODE’s by invoking a set of new transformations. The system of ODE’s contains several dimensionless numbers (parameters) which demonstrates the behavior of all field quantities. All the unknown variables, rates of heat and mass transfer are evaluated and effects of the existing parameters are seen on them, whereas, they are significantly changed with the variation of these dimensionless quantities. New solutions and results are presented in graphs and tables, whereas, they are thoroughly examined and discussed. In addition to that the modeled problem and its solutions are exactly matched with the classical problems and their corresponding solutions for specific numerical values of the governing parameters involved in the current modeled problem. The engineering applications of heat and mass transfer problems are very famous in many industrial processes. Therefore, these two phenomena are widely discussed and analyzed, whereas, they are frequently utilized for the formation of metallic devices/objects while using additive manufacturing processes, cryogenics, formation of reasonable and suitable heat exchangers, falling film evaporation and the steam boilers. However, most of the engineering systems with or without magnetized and electrically conducting surfaces cannot be expressed in usual coordinates i.e. cartesian coordinate system, moreover, most of the engineering processes involve fluids of different nature and kinds, whereas, sometime they also require different physical and environmental conditions. Therefore, in such situations we need, to upgrade and modify the present modeled problem according to prevailing situations.

ANALYSIS OF COMBINED PLATES WITH ALLOWANCE FOR CONTACT WITH ELASTIC FOUNDATION

The paper covers the problems of combined plates with circular base and consisting of a few sections with different laws of thickness variation. Analytical methods of analysis of similar structures are not yet devel­oped. The present work suggests the analytical method for solving of the stated problems, the contact with the elas­tic subgrade is also considered. The above-mentioned approach is shown on the example of the analysis of the bot­tom of the cylindrical reservoir, resting on the elastic subgrade. The inner part of this construction is represented by the ring plate of variable thickness which increases along the direction from the internal boundary. The outer part is represented by the ring plate of the constant thickness. The influence of the elastic basis and the upper part of the reservoir is taken into consideration. The solutions for stresses and deflections of the combined plate are given in closed form in terms of Bessel functions. The conditions of the plate’s sections conjugation are fulfilled.

Comparative analysis and applicability of optimal composite sections for small to middle span girder bridges

<p>Paper reports findings from parametric analysis of open section constant height composite bridges with considered spans ranging from 20 to 70 m (for larger spans closed box girder section is recommended). For these spans, girder structural system is analyzed for permanent and traffic loads, and thus steel quantity determined according to Eurocode limit states. For each span, possible sections comprise various “<span>I</span>” girder types and various number of girders determined from variable bridge width, distinguishing two groups of sections – sections with only two main girders (comprising hunched deck plate of variable thickness) and sections with more than two girders (comprising constant thickness deck plate). Other considered parameters are section height, steel flange width and occurrence of web stiffeners for buckling verification. Analysis is performed on finite element models, according to typical construction stages, where composite section is activated only for loads applied after in‐situ concreating of deck slab. For each variable set, needed steel quantity is recorded. Graphical representation of all results is plotted in diagrams, showing section types and steel quantity for a given range of span lengths. In conclusion, comments are given for use of composite cross sections according to the bridge span length and width.</p>