A novel approach is employed to a general solution for one-dimensional steady-state thermal and mechanical stresses in a hollow thick cylinder made of a functionally graded material (FGM). The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the cylinder. The material properties, except Poisson’s ratio, are assumed to be exponentially-varying through the thickness. Forcing functions applied to the inner boundary are internal pressures which may be in form of steps. These conditions result in governing differential equations with variable coefficients. Analytical solutions to such equations cannot be obtained except for certain simple grading functions and pressures. Numerical approaches must be adopted to solve the problem in hand. The novelty of the present study lies in the fact that the Complementary Functions Method (CFM) is employed in the analysis. The Complementary Functions method (CFM) will be infused into the analysis to convert the problem into an initial-value problem which can be solved accurately. Benchmark solutions available in the literature are used to validate the results and to observe the convergence of the numerical solutions. The solution procedure is well-structured, simple and efficient and it can be readily applied to cylinders. It is also well suited for problems in which mechanical properties are graded.
W artykule opisano projekt, którego celem było opracowanie pakietu rootkit dla systemu Linux. Przedstawiono charakterystykę najważniejszych mechanizmów stosowanych w tego typu konstrukcjach, koncepcję rozwiązania i sposób implementacji. Zamieszczono również wybrane wyniki testów opracowanego oprogramowania. Opracowany pakiet przewidziany jest do zastosowania w wybranych maszynach wirtualnych wykorzystywanych w specjalistycznych laboratoriach komputerowych Wydziału Cybernetyki. Stąd przymiotnik „dydaktyczny” w tytule artykułu.
EN
The paper describes a project, whose aim was to develop a package rootkit for Linux. Characteristics of the most important mechanisms used in these types of structures, a solution concept, and a method of implementation are presented. The paper also contains selected results of tests of the developed software. The developed package is provided for the use in selected virtual machines that are used in specialized computer laboratories at the Faculty of Cybernetics.
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