Recommended by Agnes MuszynskaThis paper is concerned with the dynamic behavior of the rotating composite shaft on rigid bearings. A p-version, hierarchical finite element is employed to define the model. A theoretical study allows the establishment of the kinetic energy and the strain energy of the shaft, necessary to the result of the equations of motion. In this model the transverse shear deformation, rotary inertia and gyroscopic effects, as well as the coupling effect due to the lamination of composite layers have been incorporated. A hierarchical beam finite element with six degrees of freedom per node is developed and used to find the natural frequencies of a rotating composite shaft. A program is elaborate for the calculation of the eigenfrequencies and critical speeds of a rotating composite shaft. To verify the present model, the critical speeds of composite shaft systems are compared with those available in the literature. The efficiency and accuracy of the methods employed are discussed.

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The h-p version of the finite element method (FEM) is considered to determine the transient temperature distribution in functionally graded materials (FGM). The h-p version may be regarded as the marriage of conventional h-version and p-version. The graded Fourier p-element is used to set up the two-dimensional heat conduction equations. The temperature is formulated in terms of linear shape functions used generally in FEM plus a variable number of trigonometric shape functions representing the internal degrees of freedom (DOF). In the graded Fourier p-element, the function of the thermal conductivity is computed exactly within the conductance matrix and thus overcomes the computational errors caused by the space discretization introduced by the FEM. Explicit and easily programmed trigonometric enriched capacitance, conductance matrices and heat load vectors are derived for plates and cylinders by using symbolic computation. The convergence properties of the h-p version proposed and the results of the numbers of test problems are in good agreement with the analytical solutions. Also, the effect of the non-homogeneity of the FGM on the temperature distribution is considered.

For their high mechanical characteristic (capacity resistance, hardness and impact resistance), the stainless steels remain not easily replaceable materials. This material can be used in significant fields such as the nuclear power, the storage of the chemical products. This work presents fatigue crack growth of austenitic stainless steel 316L at constant amplitude loading. The double through crack at hole specimen is used where the influence of dimension of hole, maximum amplitude loading and stress ratio are studied. The Nasgro model was used to prevent the fatigue crack growth. The effect of the stress ratio is highlighted, where one notices a shift of the curves of crack growth. The increasing of dimension of hole and the maximum amplitude loading decrease the fatigue life. Different situations permit to select the optimized hole.