Frictionless Supports Research Articles

Modeling of solitary breaking wave force absorption by coastal trees

Tall vegetation in the form of green belt along the shorelines is considered an environmentally friendly and cost-effective strategy against large coastal wave damages. Comprehensive experiments were carried out to determine the effects of green belt on attenuation of solitary wave height and force. A novel technique based on momentum approach was used to measure direct wave force absorbed by simulated green belt. Using artificial trees with different densities, the simulated coastal forest was exposed to the breaking waves with different heights. The green belt was simulated on a movable section of a flume. The movable section with 1-m length was mounted on frictionless supports at the middle of the flume to allow direct transfer of the absorbed horizontal wave force to the load cell between moveable and stationary sections of the flume. Instantaneous wave height was measured using recorded video and pressure transducers in five points before and after the vegetation section. Results indicated a considerable effect of green belt on the reduction of the wave force and inundation depth. For example, inundation depth decreases 14%, 18%, and 29% in average for the coastal vegetation density of 30%, 50%, and 100%, respectively.

On the Stability of Rigid Multibody Systems With Applications to Robotic Grasping and Locomotion

This paper shows that the equilibria of a wide class of multibody systems with quasi-rigid, frictional, or frictionless supports correspond to local minima of their potential energy; hence they are stable against small perturbations of external forces. This is a generalization of a theorem by Howard and Kumar on the stability of a single rigid body held by a gripper. It is also demonstrated that ambiguous equilibria (those, which coexist with the possibility of accelerating motion) may be stable. These results help finding safe grasps on nonrigid objects and assessing the stability of quasi-static robots moving over complex terrains.

Nonlinear static analysis of a dual-track multi-span continuous cable car system

This paper presents a nonlinear static analysis of a dual-track, multi-span continuous cable system for cable cars and ski lifts. The end supports are assumed to be frictionless bull wheels and the intermediate supports are assumed to be frictionless pulley supports. As geometrical and contact nonlinearities are involved, a nonlinear finite element solver ABAQUS is adopted for the static analysis of the cable system. The interfaces between cables and frictionless supports are modelled by frictionless interaction in normal direction and “hard contact” that allows for separation after contact in the tangential direction. Load cases due to different arrangements of cable cars are considered in the nonlinear analysis of the cable system. The proposed method for analysis used herein should be useful for solving various engineering problems involving cables undergoing large geometrical deformation and contact nonlinearity.

The solution of open and closed elasticas using intrinsic coordinate finite elements

The determination of the deflected shape of a bar bent through frictionless supports using finite elements is addressed. The finite element procedure uses intrinsic coordinates, which are computationally efficient and produce solutions in a convenient form. Variables include node rotations, Lagrange multipliers and bar lengths between supports, which are determined simultaneously using Newton-Raphson iteration. Linear, quadratic and cubic Lagrangian elements are considered. The method may find use in a range of applications, from pipeline analysis, curve fitting, computer aided design and wave guide optimisation. Two examples are considered.

Vibrations of a Beam Moving Over Supports with Clearance

The transverse vibration of a beam moving over two supports with clearance is analyzed using Euler beam theory. The equations of motion are formulated based on a Lagrangian approach and the assumed mode method. The supports with clearance are modeled as frictionless supports with piecewise-linear stiffness. A feature of the present formulation is that its complexity does not increase with increased number of supports. Results of numerical simulations are presented for various prescribed motions of the beam. The effect of support clearance on the stability of the beam is investigated.

Vibrations of a Beam Moving Over Supports with Clearance

The transverse vibration of a beam moving over two supports with clearance is analyzed using Euler beam theory. The equations of motion are formulated based on a Lagrangian approach and the assumed mode method. The supports with clearance are modeled as frictionless supports with piecewise-linear stiffness. A feature of the present formulation is that its complexity does not increase with increased number of supports. Results of numerical simulations are presented for various prescribed motions of the beam. The effect of support clearance on the stability of the beam is investigated.

Identifying the characteristics of finite element analysis convergence curves

Given the mathematical idealization of a structure, modeling introduces all the approximations which vanish as the number of unconstrained degrees of freedom of the finite element grid approaches infinity. As a practical matter, the computer code selected to support the analysis limits the definition of the idealized model and hence, the accuracy of the analysis. Sensitivity analysis can furnish information on the effect of these limitations on structural response. However, by definition, the judgement exercised by the analyst in idealization is unassailable by the computer program. That is, we assume that during a finite element analysis the computer has no access to alternative unprogrammed idealizations. A very important example of idealization is the choice of the constitutive equations and the choice of the coefficients of its particularization. Choices affecting the relevance of the element model include use of Euclidean geometry to define the length, volume, and deformations of the structure and the coefficients chosen to particularize the geometry. The assumption of frictionless pins or spring supports, the limitation of the distribution of applied loadings, and the mathematical model of nodal displacement constraints are other examples of idealization choices. Examples of modeling approximations include element and/or node approximations. Use of straight lines to represent curves, polygons or hyperbolas to model circular edges, and stepped surface thicknesses typify approximations to the original geometry. Use of polynomials with few terms to represent deformations is the most important modeling approximation of the deformed geometry. Modeling applied loading and settlements by linear functions of element local coordinates illustrates modeling approximations of boundary conditions. By definition, when the modeling is optimum, the required computer solution accuracy is developed with a minimum of computer resources. The parameters of this optimization problem are the modeling choices, the analysis strategy and the efficiency of the computer configuration in implementing the choices. In this study, we assume that the constraint on the optimum is evaluation of the external work in the structure to a prespecified number of significant digits. We measure the efficiency of the computer configuration by the relative number of degrees of freedom in the analysis. Melosh [1] emphasizes that conventional analysis with element models satisfying minimum convergence requirements can be much less efficient than analysis using curve fitting. Examples suggest that use of fitting can reduce the number of calculations by more than two orders of magnitude and the storage requirements by more than three orders. Furthermore, the previous study indicates that using rational polynomials or hyperbolic estimating functions for curve fitting offers no advantage over polynomials.

Dynamics of a beam moving over multiple supports

The equations of motion of a beam moving over multiple supports are formulated based on Hamilton's principle and the assumed mode method. The supports are either roller supports which impart motion to the beam or frictionless supports with the beam being pushed or pulled over them. In both cases, the supports are regarded as very stiff springs acting on the moving beam. A feature of the present formulation is that its complexity does not increase with an increased number of supports. Results of numerical simulations are presented for various prescribed motions of the beam.

Motion of a rectangular bar under traction on a horizontal plane

This paper forms part of a study into how components move when pushed or pulled. It extends previous work by other authors, who have studied quasi-static pushing, by addressing the dynamics of pulling. In particular, dynamic models are developed for a rectangular bar lying flat on a horizontal planar support and acted upon by a tractive force. Initially, the equations of motion of the bar, a set of six coupled non-linear first order ODEs, are derived by ignoring friction between the bar and the support. The results of numerically integrating the equations to find the bar's trajectory are presented. The integration was implemented using the Bulirsch-Stoer Method. The numerical results show good agreement with closed-form solutions obtained by linearising the equations of motion for small angular displacements. The problem of rough support surfaces is then treated. Expressions for the frictional force and moment exerted on the bar are found in terms of R and α, the polar coordinates of the centre of mass (C.M.) of the bar relative to its instantaneous centre of rotation (C.O.R.). These expressions are used to construct a new set of equations of motion. Two methods of obtaining the trajectory of the bar are described. The first involves direct numerical integration of the equations of motion, as in the case of frictionless supports. The second is based on explicitly searching for R and α using the equations of motion.

The finite element solution of a class of elastica problems

Abstract A finite element procedure for the analysis of an inextensional elastica bent through frictionless supports is presented. Element displacements are expressed in terms of cubic Hermite polynomials with nodal displacements and derivatives being determined to minimise the strain energy. It is shown that the axial force at any point is proportional to the square of the bending moment, which enables member incremental stiffness matrices to be expressed in a similar form to those used in stability analysis. The iterative procedure proposed for solving the nonlinear stiffness equations may readily be incorporated into any continuous beam program by the modification and addition of very few statements. An example is considered which indicates that accurate solutions may be obtained to a wide range of practical problems using the proposed technique.

Large deflections of bars bent through frictionless supports

A procedure enabling the numerically exact solution of the deflected shape of a bar bent through frictionless supports is presented. It is shown that the axial force at any point is proportional to the square of the bending moment, and based on this property, coefficients relating end rotations and end moments for a single member are presented. A non-linear analysis using Newton-Raphson iteration is then adopted for solving the overall problem.