W. Szyszkowski

Controlling angular oscillations through mass reconfiguration: a variable length pendulum case

The control of angular oscillations or energy of a system through mass reconfiguration is examined using a variable length pendulum. Control is accomplished by sliding the end mass towards and away from the pivot as the pendulum oscillates. The resulting attenuation or amplification of the angular oscillations are explained using the Coriolis inertia force and by examining the energy variation during an oscillation cycle. Simple rules relating the sliding motion to the angular oscillations are proposed and assessed using numerical simulations. An equivalent viscous damping ratio is introduced to quantify the attenuation/amplification phenomena. Sliding motion profiles for achieving attenuation have been simulated with the results being discussed in detail.

Effects of surface geometry of composites on thermal stress distribution: a numerical study

The fiber/matrix interaction is analyzed from the viewpoint of micro-mechanics by using the finite-element method. The effects of various parameters characterizing the free surface of the composite on the thermal stress distribution are examined. The paper aims at obtaining a better understand of the nature of stress concentrations and how these stresses contribute to the cracking which is often observed on the free surface of a fiber-reinforced composite if the temperature changes. The results indicate that it is possible to minimize the stress concentration occurring at the end of the fiber, thereby reducing the tendency of the composite to crack.

On Systematic Errors of Two-Dimensional Finite Element Modeling of Right Circular Planar Flexure Hinges

This paper discusses the finite element method (FEM) based modeling of the behavior of typical right circular flexure hinges used in planar compliant mechanisms. Such hinges have traditionally been approximated either by simple beams in the analytical approach or very often by two-dimensional (2D) plane stress elements when using the FEM. The three-dimensional (3D) analysis presented examines these approximations, focusing on systematic errors due to 2D modeling. It is shown that the 2D models provide only the lower (assuming the plane stress state) or the upper (assuming the plane strain state) limits of the hinge’s stiffness. The error of modeling a particular hinge by 2D elements (with either the plane stress or the plane strain assumptions) depends mainly on its depth-to-height ratio and may reach up to about 12%. However, this error becomes negligible for hinges with sufficiently high or sufficiently low depth-to-height ratios, in which either the plane strain or stress states dominate respectively. It is also shown that the computationally intensive 3D elements can be replaced, without sacrificing accuracy, by numerically efficient 2D elements if the material properties are appropriately manipulated.

Influence of the free surface on the thermal stresses in unidirectional composites

Abstract Thermal stresses in a continuous carbon fiber reinforced polymer matrix composite are determined using the finite element method (FEM) and 3-D FEM models. The zone close to the free surface (the end zone) and the zone far from the free surface (the inner zone) are analyzed. These two zones have substantially different stress characteristics. The analysis of the end zone revealed significant radial and hoop stress concentrations. These concentrations are sensitive to meshing indicating the stress singularity localized at the free surface on the fibre/matrix matrix interface. Qualitative investigations of the effect of meshing on the stress concentration permits determination of the order of singularity which, in general, depends on the composite parameters. It is shown that this order is mostly effected by the transverse Youngs modulus and the Poissons ratio of the fiber.

An Algorithm for Time-Optimal Control Problems

A numerical procedure to compute nonsingular, time-optimal solutions for nonlinear systems, which have fixed initial and final states, and are linear and bounded in control, is presented. Using the Pontryagins Minimum Principle, the corresponding nonlinear two-point boundary-value problem is formulated and solved by combination of the forward-backward and the shooting methods. The forward-backward procedure generates a good guess of the initial costates, which is crucial for the convergence of the shooting method. Numerical example of a two-link manipulator illustrates the proposed approach and the convergence of the procedure.

Stress concentrations due to thermal loads in composite materials

The thermal stress concentration at the surface of the composite is analyzed using the ADINA program. The fibres in the composite are assumed to be arranged in a regular array. Making use of symmetry only one cell of such an array is considered. When a composite is cooled down, a high tensile radial stress is detected at the interface, creating a condition for crack initiation at this location. Numerical experimentation, using various meshings, reveals that the magnitude of this stress depends on the size of element used, indicating a stress singularity. The order of the singularity is determined numerically and appears to be different for different stress components.

An effective method for non-linear viscoelastic structural analysis

Abstract A numerical analysis of structures made of polymeric-type materials is discussed. Material response, dependent on the stress history, is modelled by means of single Volterra integrals. The integrals are handled using an approximate method which utilizes Pronys series and requires storing only the current stress and some internal strain components. Also, an efficient semi-direct time-integration scheme providing a stable integration process, even for relatively large time-steps, is derived and used for analysis of a polypropylene beam.

Multimodal optimality criterion for maximum fundamental frequency of free vibrations

Abstract A multimodal optimality criterion is derived and used for numerical optimization of elastic structures with respect to the fundamental frequency of free vibrations. An arbitrarily large number of vibration modes can be assumed at the beginning of the iterative optimization procedure. The real modality of the problem, that is the number of modes participating in the final optimal design, is determined iteratively. The procedure is convergent in a sense of the Newtons scheme.

Bimodal optimization of frames for maximum stability

Abstract A bimodal iterative procedure for optimizing frames of constant volume for maximum stability is discussed. An optimality condition derived in the paper plays the role of the objective function in the numerical optimization process. The procedure uses the finite element technique and permits treatment of the optimized structure as a potentially bimodal one. For a single mode optimal design the influence of the second mode is automatically eliminated by the iterative procedure. The numerical examples presented illustrate the convergence of the procedure for frames with both single mode and bimodal buckling failures.

Parameter identification and trajectory following of a two-link rigid manipulator

Abstract An adaptive controller for rigid manipulators is discussed in this paper. The scheme presented is applied to a two-link rigid manipulator. It takes full advantage of the known parameters of the manipulator while estimating the unknown parameters. In deriving the dynamic equations of motion, all the physical parameters of the manipulator, including the distributed masses of the links, are taken into account. The overall control system maintains the structure of the computed torque system with an adaptive element. The convergence of the control is considered in detail. A method of selecting the best combination of the various gains is presented. Some simulation results of the manipulator with unknown payload masses following a desired trajectory are presented.