Dynamics of three-layer cylindrical elements with an inhomogeneous core rested on the Pasternak elastic foundation is studied under various boundary conditions. The lightweight core is reinforced with ribs, the distance between them significantly exceeds the dimensions of ribs cross-sections. Because of this, the theory of independent static and kinematic hypotheses is applied for each layer. According to the Hamilton-Ostrogradsky variational principle, the equations of motion of three-layer cylindrical shells and natural boundary conditions have been obtained using the model of the Timoshenko theory of shells and rods. This made it possible to purposefully create an adequate finite element model for three-layer cylindrical shells consisting of several materials, and to obtain numerical results relative to the nature of the dynamic behavior of a three-layer structure on an elastic foundation using the finite-element method. It is studied how the physical and mechanical parameters of the layers of cylindrical structures, the methods of fastening their ends, and the parameter of the elastic foundation of shells effect on their dynamics under axisymmetric internal impulse loading.
An approximate solution to the optimization problem for the startup of a jib crane with simultaneous outreach variation and load hoisting with power and energy constraints is presented. The root-mean-square total power of the drive mechanisms for boom luffing, boom extension, and load hoisting with constraints on the driving forces and drive power is chosen as the optimization criterion. The constrained criterion is reduced to a generalized criterion, and the constrained optimization problem is transformed into unconstrained optimization. For the optimization, a dynamic model of the simultaneous movement of the boom system mechanisms is developed and represented by a system of nonlinear differential equations. The approximate solution to the optimization problem is represented by the sum of two polynomial functions, one of which satisfies the boundary conditions of motion and the other minimizes the criterion. The criterion is minimized using a modified particle swarm metaheuristic. Optimization of the motion profile for the crane mechanisms reduces the energy consumption of the drives, oscillations in the crane components, and loads on the flexible suspension.
The stress-strain state of multilayer plates resting on a rigid foundation has been investigated. A computational model of a transversely loaded plate has been developed by symmetrically mirroring the plate with respect to the contact surface with the foundation. The proposed model considers a plate/slab of doubled thickness subjected to a load that is symmetric with respect to its mid-surface. This approach has made it possible to model only in-plane deformation, thereby reducing the number of unknowns and the overall order of the differential system of governing equations. Importantly, this order does not depend on the number of layers. The refined continuous model has been developed to account for transverse shear and transverse compression deformations through higher-order iterative approximations. Perfect bonding between the foundation and the slab together with frictionless sliding along their contact surface has been assumed. Numerical calculations have confirmed the effectiveness of the proposed approach, which enables solutions that are qualitatively and quantitatively close to the corresponding three-dimensional solutions, while the problem has been formulated and solved in a simpler form than in other approaches reported in the literature.
A mathematical model of the contact interaction without friction between a heated rigid flat elliptical punch and a piezoelectric transversely isotropic half-space has been developed and analyzed. The surface of the half-space is assumed to coincide with the plane of isotropy of the piezoelectric transversely isotropic material. Explicit expressions for the contact stresses and displacements generated by the heated flat elliptical punch have been obtained. A simple inequality as a condition for preventing detachment of the piezoelectric material from the surface of the flat elliptical punch has been derived. Numerical calculations have been performed to assess the effect of the temperature field on the contact parameters of the flat elliptical punch interacting with the piezoelectric half-space.
This study addresses the numerical modelling of quasi-static flow-induced loading on thin-walled cylindrical shells of steel storage tanks. Axisymmetric geometric models of the shell structures have been developed. The gas flow has been simulated using the k–ω SST turbulence model. The dimensions of the computational domain have been determined empirically to minimize the influence of the boundary conditions on the predicted flow field. The inlet gas velocity has been adopted as the governing parameter for the quantitative assessment of shell buckling. The critical flow conditions required for evaluating the load-bearing capacity of the shells have been determined through an iterative numerical procedure. The computational fluid dynamics (CFD) simulations have been performed using the open-source software OpenFOAM.
