STRENGTH OF SHIPS’ GRILLAGES UNDER LATERAL LOAD AND IN-PLANE COMPRESSION

The paper deals with strength of a grillage loaded by lateral load and in-plane compression load (in one direction). It consists of a system of prismatic girders crossing under 90°. The compression load is taken by the longitudinal girders that are elastically fixed on rigid supports. The system of aggregated differential equations is derived for solution of the problem using the Lagrange method. It allows for replacement of the system of aggregated differential equations by a system of independent differential equations. These equations for the case of simultaneous action of lateral and longitudinal compression load have the form of differential equations for bending of prismatic girders laying on elastic foundation and loaded with lateral and longitudinal compression forces. When only lateral load exists, the form of these equations coincides with the form of differential equations for bending of girders laying on elastic foundation and loaded with lateral load alone. When only longitudinal compression load exists, the form of these equations coincides with the form of differential equations for buckling of girders laying on elastic foundation. Solutions are given for bending of a grillage (the first two problems). Formulas are derived for calculation of the parameters of longitudinal girders’ bending when girders’ end sections are elastically fixed. Also, formulas are derived for calculation of the reaction forces at cross-points of transverse and longitudinal girders. When only longitudinal compression load exists (third problem), a solution is given for the connection between the coefficient of elastic foundation’s rigidity and the Euler force. Results obtained by using the proposed method are compared with FEA simulations.

Migration Behavior of Low-Density Particles in Lab-on-a-Disc Devices: Effect of Walls

The effect of the lateral walls of a Lab-On-a-Disc device on the dynamics of a model system of particles with a density lower than that of the solvent (modelling parasites eggs) is analyzed theoretically and experimentally. In the absence of lateral walls, a particle always moves in the direction of the centrifugal force, while its trajectory is deflected in the tangential direction by the inertial Coriolis and Euler forces. Lateral walls, depending on the angle forming with the radial direction, can guide the particle either in the same or in the opposite direction to the centrifugal force, thus resulting in unusual particle trajectories including zig-zag or backwards particle motion. The effect is pronounced in the case of short operation times when the acceleration of the angular rotation, and thus the Euler force, is considerable. The predicted unusual motion is demonstrated by numerically solving the equation of motion in the presence of lateral walls and verified in the experiment with particles of density lower than that of the solvent. Our analysis is useful for design and operational considerations of Lab-On-a-Disc devices aiming for or involving (bio)particle handling.

Multi-objective optimization and linear buckling of serial chain of a medical robot tool for soft tissue surgery

<p>The slender structures of a medical robot may have a tendency to buckling when a force equal to the critical Euler force and an additional disturbance will work on their structures. In this work, eigenvalue problem that describes the linear buckling, is under consideration. The main goal of the article is to check when linear buckling phenomenon appears in construction of a medical robot with serial chain due to the fact that for safety reasons of a robot’s work, it is necessary to answer the question, whether the buckling may occur in the robot’s structure. For this purpose, a numerical calculation model was defined by using the finite element method. The values of load factor coefficients that are eigenvalue are determinated and also the eigenvectors that have shapes of deformation for the next eigenvalues are presented. The multi-criteria optimization model was determined to aim for the minimum mass of the effector and the buckling coefficient, from which the Euler force results, for the maximum. The solution was obtained on the basis of Pareto fronts and the MOGA genetic algorithm.</p>

Fictitious forces in yarn during unwinding from packages

In this paper we discuss the general equation of motion for yarn in a rotating coordinate system. This equation is often used to describe the motion of yarn that is unwinding from packages. The rotating coordinate system is non-inertial and the equation of motion therefore contains fictitious forces. We comment on the physical significance of fictitious forces that appear in a non-inertial frame and we devote particular attention to a less known Euler force that only appears in non-uniformly rotating frames. We show that this force should be taken into account when the unwinding point is near the edges of the package, when the quasi-stationary approximation is not valid because the angular velocity is changing with time. The additional force has an influence on the yarn dynamics in this transient regime, where the movement of yarn becomes complex and can lead to yarn slipping and even breaking.

Strength of Ships’ Grillages Under Lateral Load and In-Plane Compression

The paper deals with strength of a grillage loaded by lateral load and in-plane compression load (in one direction). It consists of a system of prismatic girders crossing under 90°. The compression load is taken by the longitudinal girders that are elastically fixed on rigid supports. The system of aggregated differential equations is derived for solution of the problem using the Lagrange method. It allows for replacement of the system of aggregated differential equations by a system of independent differential equations. These equations for the case of simultaneous action of lateral and longitudinal compression load have the form of differential equations for bending of prismatic girders laying on elastic foundation and loaded with lateral and longitudinal compression forces. When only lateral load exists, the form of these equations coincides with the form of differential equations for bending of girders laying on elastic foundation and loaded with lateral load alone. When only longitudinal compression load exists, the form of these equations coincides with the form of differential equations for buckling of girders laying on elastic foundation. Solutions are given for bending of a grillage (the first two problems). Formulas are derived for calculation of the parameters of longitudinal girders’ bending when girders’ end sections are elastically fixed. Also, formulas are derived for calculation of the reaction forces at cross-points of transverse and longitudinal girders. When only longitudinal compression load exists (third problem), a solution is given for the connection between the coefficient of elastic foundation’s rigidity and the Euler force. Results obtained by using the proposed method are compared with FEA simulations.