THIN ELASTIC PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE THE VON KARMAN LIMITS

Thin elastic plates (homogeneous or composite) experiencing large deflections are considered. The deflections are much larger than the plate thickness. The geometrically nonlinear elasticity theory and the Kirchhoff assumptions are employed. Small elongations and shears are assumed. Following Novozhilov, the strain expressions are derived. Then, under a small in-plane rotation assumption and using the virtual work principle, the equilibrium equations and the boundary conditions are obtained. The equations/conditions become the known von Karman ones for the case of moderate deflections. The solutions of the obtained equations may be used as benchmarks for the nonlinear structural analysis (e.g., FEM) software in the case of large deflections.

Torque Analysis for Rotational Devices with Nonmagnetic Rotor Driven by Magnetic Fluid Filled in Air Gap

In magnetomechanical applications, it is necessary to calculate the magnetic force or torque of specific objects. If the magnetic fluid is involved, the force and torque also include the effect of pressure caused by the fluid. The standard method is to solve the Navier–Stokes equation. However, obtaining magnetic body force density is still under controversy. To resolve this problem, this paper shows that the calculation of the torque of these applications should not only use the magnetic force calculation method, but also consider the mechanical pressure using an indirect approach, such as the virtual work principle. To illustrate this, we use an experimental motor made of a nonmagnetic rotor immersed in a magnetic fluid. Then, we show that the virtual work principle in appropriate approach can calculate the output torque of the nonmagnetic rotor due to pressure of the magnetic fluid. Numerical analysis and experimental results show the validity of this approach. In addition, we also explain how the magnetic fluid transmits its magnetic force to the stator and rotor, respectively.

Multi-objective optimal design of a novel 6-DOF spray-painting robot

This paper deals with the multi-objective optimal design of a novel 6-degree of freedom (DOF) hybrid spray-painting robot. Its kinematic model is obtained by dividing it into serial and parallel parts. The dynamic equation is formulated by virtual work principle. A performance index for evaluating the compactness of robot is presented. Taking compactness, motion/force transmissibility, and energy consumption as performance indices, the optimal geometric parameters of the robot are selected in the Pareto-optimal set by constructing a comprehensive performance index. This paper is very useful for the development of the spray-painting robot.

Energy Consumption Comparison of a Novel Parallel Tracker and Its Corresponding Serial Tracker

A novel two-axis solar tracker with parallel mechanism is proposed in this paper. A dynamic model is derived by using the virtual work principle and the consumed energy including the mechanical energy and motor energy loss is computed. Taking Beijing as the working location of the solar tracker, the energy consumptions of the parallel solar tracker and its corresponding serial solar tracker are compared based on the premise that the proposed solar tracker and its corresponding serial solar tracker have similar static stiffness. Mechanical energy consumption of the proposed tracker is reduced by 7.55% compared to the serial solar tracker. The motor energy loss of the parallel solar tracker is also significantly lower. This simple and low-energy consumption solar tracker is a good alternative to the traditional solar tracker with large energy consumption.

A PD Computed Torque Control Method with Online Self-gain Tuning for a 3UPS-PS Parallel Robot

SUMMARY In this paper, an online self-gain tuning method of a PD computed torque control (CTC) is used for a 3UPS-PS parallel robot. The CTC is applied to the 3UPS-PS parallel robot based on the robot dynamic model which is established via a virtual work principle. The control system of the robot comprises a nonlinear feed-forward loop and a PD control feedback loop. To implement real-time online self-gain tuning, an adjustment method based on the genetic algorithm (GA) is proposed. Compared with the traditional CTC, the simulation results indicate that the control algorithm proposed in this study can not only enhance the anti-interference ability of the system but also improve the trajectory tracking speed and the accuracy of the 3UPS-PS parallel robot.

Funicularity in elastic domes: Coupled effects of shape and thickness

An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes. It is realized how the static and kinematic matrix operators are one the ad-joint of the other, and, on the other hand, it can be rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without ‚exural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membrane one.

On FEM analysis of Cosserat-type stiffened shells: static and stability linear analysis

The present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod, respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam FE with 6 DoFs (including the drilling rotation for shells) in each node. Examples of static and stability linear analyses are included. Novel design formulas for the stability of stiffened shells are included.

Equivalent Axial Stiffness of Horizontal Stays

Cable-stayed structures are widely employed in several fields of civil, industrial, electrical and ocean engineering. Typical applications are cable-stayed building roofs, bridges, guyed masts, overhead electrical lines, and floating device anchorages. Since the cable behavior is often highly nonlinear, suitable equivalent mechanical cable models are often adopted in analyzing this kind of structures. Usually, like in the classical Dischinger’s approach, stays are treated as straight rods offering an equivalent axial tangent stiffness, so that each of them can be substituted with an appropriate equivalent nonlinear spring or truss element. Formulae expressing equivalent stiffness provided by classical methods are satisfactory only when the cable is highly stressed, and therefore its sag is small with respect to its chord; on the contrary, when the cable is slack, they give often contradictory or meaningless results. Aiming to remove that limitation, a more refined approach based on the application of the virtual work principle is discussed. Important products of that original rational criterion are accurate and closed form innovative expressions of the tangent stiffness of the cable, whose field of application is independent on the sag to chord ratio of the cable, as well as on the magnitude of the normal stresses. Referring to some relevant case studies, the results obtained applying these new formulae are critically discussed for cables made of different materials, also in comparison with the approximate expressions provided by simplified methods.

On a consistent rod theory for a linearized anisotropic elastic material: I. Asymptotic reduction method

An asymptotic reduction method is introduced to construct a rod theory for a linearized general anisotropic elastic material for space deformation. The starting point is Taylor expansions about the central line in rectangular coordinates, and the goal is to eliminate the two cross-section spatial variables in order to obtain a closed system for displacement coefficients. This is first achieved, in an ‘asymptotically inconsistent’ way, by deducing the relations between stress coefficients from a Fourier series for the lateral traction condition and the three-dimensional (3D) field equation in a pointwise manner. The closed system consists of 10 vector unknowns, and further refinements through elaborated calculations are performed to extract bending and torsion terms and to obtain recursive relations for the first- and second-order displacement coefficients. Eventually, a system of four asymptotically consistent rod equations for four unknowns (the three components of the central-line displacement and the twist angle) are obtained. Six physically meaningful boundary conditions at each edge are obtained from the edge term in the 3D virtual work principle, and a one-dimensional rod virtual work principle is also deduced from the weak forms of the rod equations.