In this paper, a new algorithm for solving the vehicle/track dynamic interaction problem is developed, aimed at reducing the computational cost. The algorithm called Advanced Solver Algorithm (ASA) uses the full Newton–Raphson incremental-iterative method in conjunction with the Newmark integration scheme to solve the equilibrium equations of the coupled vehicle/track system in time domain. Considering the track as a beam resting on a viscoelastic foundation and each vehicle as a wagon with ten degrees of freedom, the governing differential equations of motion of the vehicle/track system were derived. The wheel/rail contact was considered as a nonlinear Hertz spring and consequently the vehicle/track nonlinear dynamic interaction problem was solved. A comparison between the results of the ASA and those of the most advanced algorithm available was made to evaluate the efficiency of the ASA. It is confirmed that using the ASA can result in 40–70 % of reduction in computational cost.
In this study, a new sub-parametric strip element is developed to simulate the axially loaded composite cylindrical panel with arbitrary cutout. For this purpose, a code called SSFSM is developed in FORTRAN to analyze the buckling of panels. The first order shear deformation theory is used to form the straindisplacement relations. Spline and Lagrangian functions are used to derive element shape functions in the longitudinal and transverse directions, respectively. The computational cost of the SSFSM is decreased dramatically, as mapping functions of the strip element are very simple. The results obtained from the SSFSM are compared with those of the literature and the results obtained by ABAQUS to show the validity of the proposed approach. A parametric study is performed to show the capability of the SSFSM in calculating the panel buckling load. Results indicate that increasing the panel thickness and panel central angles cause an increase in panel buckling load. The cutout shape is an important factor influencing the panel buckling load. For instance, when the angle between the direction of big chord of the elliptical cutout and compressive load direction are 0 and 90 degrees, the panel buckling load reaches its minimum and maximum magnitude, respectively.
Linearized buckling analysis of functionally graded shells of revolution subjected to displacement-dependent pressure, which remains normal to the shell's middle surface throughout the deformation process, is described in this work. Material properties are assumed to be varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and a metal. The governing equations are derived based on the first-order shear deformation theory, which accounts for through the thickness shear flexibility with Sanders type of kinematic nonlinearity. Displacements and rotations in the shell's middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix, also known as the pressure stiffness matrix, which accounts for the variation of load direction, is derived for each strip and after assembling resulted in the global load stiffness matrix of the shell, which may be unsymmetric. The load stiffness matrix can be divided into two unsymmetric parts (i.e., load nonuniformity and unconstrained boundary effects) and a symmetric part. The main part of this research is to quantify the effects of these unsymmetries on the follower action of lateral pressure. A detailed numerical study is carried out to assess the influence of various parameters such as power law index of functionally graded material (FGM) and shell geometry interaction with load distribution, and shell boundary conditions on the follower buckling pressure reduction factor. The results indicate that, when applied individually, unconstrained boundary effect and longitudinal nonuniformity of lateral pressure have little effect on the follower buckling reduction factor, but when combined with each other and with circumferentially loading nonuniformity, intensify this effect.
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