相关论文: Equilibrium Configurations of Cantilever under Ter…
The article discusses six problems which can arise in the determination of the equilibrium configuration of an elastic cantilever rod pulled by an inextensible cable. The discussions are illustrated with graphs of equilibrium shapes and…
The application of variational principles for analyzing problems in the physical sciences is widespread. Cantilever-like problems, where one end is fixed and the other end is free, have received less attention in terms of their stability…
In the paper a solution for equilibrium configurations of an elastic beam subject to three points bending is given in terms of Jacobi elliptical functions. General equations are derived and the domain of solution is established. Several…
The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The deduced…
The design of compliant mechanisms is crucial in several technologies and relies on the availability of solutions for nonlinear structural problems. One of these solutions is given and experimentally validated in the present article for a…
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…
In the article, we investigate the influence of spring on the large deflections and stability of a spring-hinged cantilever subject to conservative tip force. Using the closed form solution of the equilibrium equation and closed form…
A highly deformable rod, modelled as the extensible elastica, is connected to a movable clamp at one end and to a pin sliding along a frictionless curved profile at the other. Bifurcation analysis shows that axial compliance provides a…
Two equal and opposite distributed dead loads are applied orthogonally to the axis of an elastic rod in its rectilinear reference configuration, one at the extrados and the other at the intrados, such that the resultant applied force per…
The discovery of configurational forces acting on elastic structures and its initial applications are reviewed. Configurational forces are related to the possibility that an elastic structure can change its configuration, thus inducing a…
The problem of determining equilibrium configurations of the free surface of a conducting liquid is considered with allowance for a finite interelectrode distance. The analogy is established between this electrostatic problem and that of…
An analytical form of the characteristic equation for a vertically mounted cantilever beam with an end rigid body is obtained and solved for the eigenvalues of the structure. The effect of the weight of the structure is taken into…
The bifurcation problem of a circular Euler-Bernoulli rod subject to a uniform radial force distribution is investigated under three distinct loading conditions: (i.) hydrostatic pressure, (ii.) centrally-directed, and (iii.) dead load.…
For the planar four-vortex problem, we show that there are finitely many stationary configurations consisting of equilibria, rigidly translating configurations, relative equilibria (uniformly rotating configurations) and collapse…
The dynamics of a cantilever plate clamped at its trailing edge and placed at a moderate angle ($\alpha \leq 30^{\circ}$) to a uniform flow are investigated experimentally and numerically, and a large experimental data set is provided. The…
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…
The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…
Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and…
An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…