Search

The motion equations of a rolling flexible circular ring are derived using a Lagrangian formulation. The in-plane flexural and out-of-plane twist-bending free vibrations are modeled using the Rayleigh-Ritz method. The motion equations of a flexible circular ring translating and rotating in space are first developed and then constrained to roll on aflat surface by introducing Lagrange multipliers. The motion equations developed capture the nonholonomic nature of the circular ring rolling without slip on a flat suiface. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the circular ring on its trajectory. The vibrations of the circular ring are observed to impact the ring's motion. [ABSTRACT FROM AUTHOR]

The zeroth-order parametric finite-volume direct averaging micromechanics (FVDAM) theory is further extended in order to model the evolution of damage in periodic heterogeneous materials. Toward this end, displacement discontinuity functions are introduced into the formulation, which may represent cracks or traction-interfacial separation laws within a unified framework. The cohesive zone model (CZM) is then implemented to simulate progressive separation of adjacent phases or subdomains. The new capability is verified in the linear region upon comparison with an exact elasticity solution for an inclusion surrounded by a linear interface of zero thickness in an infinite matrix that obeys the same law as CZM before the onset of degradation. The extended theory's utility is then demonstrated by revisiting the classical fiber/matrix debonding phenomenon observed in SiC/Ti composites, illustrating its ability to accurately capture the mechanics of progressive interfacial degradation. [ABSTRACT FROM AUTHOR]

Spiral spring is widely used in mechanisms, such as mechanical watch movements and clocks where the spiral spring is used for timekeeping. According to literature, there are only a few studies on spiral springs. In this paper, the mechanics of spiral springs is analyzed in details, and its dynamic performance in mechanical watch movements is further studied to find out its natural fre-quency, which is the most critical parameter for mechanical watch movements. Based on Castigliano's theorem, the mathemat-ical model of dynamic deformation and natural frequency of the spiral spring under external axial torque is developed, and com-puter simulation with MATLAB® is also conducted. Experimental validations are carried out, which confirm the simulation results. Experiments show that the analytical method in this paper can be used to guide and facilitate the design of spiral spring. [ABSTRACT FROM AUTHOR]

A simple transformation is used to obtain the first integrals and the solutions of the Duffing--van der Pol type equation under certain conditions. It is shown that the system can be totally integrable and this total integrability admits new solutions. The new solutions require weaker conditions on the system's parame-ters than hereto known. [ABSTRACT FROM AUTHOR]

A least action principle for damping motion has been previously proposed with a Hamilto-nian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties persist about the appropriate variational calculus and the nature (maxima, minima, and inflection) of the stationary action. The aim of this work is to make a numerical simulation of the damped motion and to compare the actions of different paths in order to obtain evidence of the existence and the nature of stationary action. The model is a small particle subject to conservative and friction forces. Two conservative forces and three friction forces are considered. The comparison of the actions of the perturbed paths with that of the Newtonian path reveals the existence of extrema of action which are minima for zero or very weak friction and shift to maxima when the motion is overdamped. In the intermediate case, the action of the Newtonian path is neither least nor most, meaning that the extreme feature of the Newtonian path is lost. In this situation, however, no reliable evidence of stationaiy action can be found from the simulation result. [ [ABSTRACT FROM AUTHOR]

A nonlinear, planar model of a slack cable with bending stiffness and arbitrarily moving ends is developed. The model uses the slope angle of the centroid line of the cable to describe the motion of the cable, and the resulting integropartial differential equation with constraints is derived using Hamilton's principle. A new method is developed to obtain the spatially discretized equations, and the Baumgarte stabilization procedure is used to solve the resulting differential-algebraic equations. The model can be used to calculate the equilibria and corresponding free vibration characteristics of the cable, as well as the dynamic response of the cable under arbitrarily moving ends. The results for an equilibrium and free vibration characteristics around the equilibrium are experimentally validated on a laboratory steel band. The methodology is applied to elevator traveling and compensation cables. It is found that a vertical motion of the car can introduce a horizontal vibration of a traveling or compensation cable. The results presented are verified by a commercial finite element software. The current method is shown to be more efficient than the finite element method as it uses a much smaller number of elements to reach the same accuracy. Some other interesting features include the condition for a traveling or compensation cable equilibrium to be closest to a natural loop and a direct proof that the catenary solution is unique. [ABSTRACT FROM AUTHOR]

Elastic-plastic indentation of a single-crystal half-space by a rigid cylinder was analyzed by discrete dislocation plasticity. Short-range dislocation interactions were modeled by a set of constitutive rules of dislocation emission, glide, pinning (by obstacles), and annihilation. The occurrence of the first dislocation dipole, multiplication of dislocations, and evolution of subsurface stress field were examined in terms of contact load, dislocation source density, slip-plane distance and orientation angle, and indenter radius. In the presence of defects (dislocation sources), the critical load for dislocation initiation is less than that of a defect-free medium and depends on dislocation source density, slip-plane distance, and indenter radius. The critical indenter radius resulting in deformation under the theoretical material strength is determined from numerical results, and the role of dislocation obstacles is interpreted in terms of their spatial density. Simulations provide insight into yielding and plastic deformation of indented single-crystal materials, and establish a basis for developing coarse-grained plasticity models of localized contact deformation in polycrystalline solids. [ABSTRACT FROM AUTHOR]

Bone is similar to fiber-reinforced composite materials made up of distinct phases such as osteons (fiber), interstitial bone (matrix), and cement lines (matrix-fiber interface). Microstructural features including osteons and cement lines are considered to play an important role in determining the crack growth behavior in cortical bone. The aim of this study is to elucidate possible mechanisms that affect crack penetration into osteons or deflection into cement lines using fracture mechanics-based finite element modeling. Cohesive finite element simulations were performed on two-dimensional models of a single osteon surrounded by a cement line interface and interstitial bone to determine whether the crack propagated into osteons or deflected into cement lines. The simulations investigated the effect of (i) crack orientation with respect to the loading, (ii) fracture toughness and strength of the cement Une, (iii) crack length, and (iv) elastic modulus and fracture properties of the osteon with respect to the interstitial bone. The results of the finite element simulations showed that low cement line strength facilitated crack deflection irrespective of the fracture toughness of the cement line. However, low cement line fracture toughness did not guarantee crack deflection if the cement line had high strength. Long cracks required lower cement line strength and fracture toughness to be deflected into cement lines compared with short cracks. The orientation of the crack affected the crack growth trajectory. Changing the fracture properties of the osteon influenced the crack propagation path whereas varying the elastic modulus of the osteon had almost no effect on crack trajectory. The findings of this study present a computational mechanics approach for evaluating microscale fracture mechanisms in bone and provide additional insight into the role of bone microstructure in controlling the microcrack growth trajectory. [ABSTRACT FROM AUTHOR]

In this paper, we study the deformation of a thin elastic rod constrained inside a cylindrical tube and under the action of an end twisting moment. The ends of the rod are clamped in the lateral direction. Unlike the previous works of others, in which only the fully developed line-contact spiral was considered, we present a complete analysis on the deformation when the dimensionless twisting moment Mx is increased from zero. It is found that the straight rod buckles into a spiral shape and touches the inner wall of the tube at the midpoint when Mx reaches 8.987. As Mx increases to 11.472, the contact point in the middle splits into two, leaving the midpoint floating in the air. As Mx increases to 13.022, the midpoint returns to touch the tube wall and the two-point-contact deformation evolves to a three-point-contact deformation. Starting from Mx = 13.098, the point contact in the middle evolves to a line contact, cmd the deformation becomes a point-line-point contact configuration and remains so thereafter. In the case when the linecontact pattern is fully developed, it is possible to predict the spiral shape analytically. The numerical results are found to agree very well with those predicted analytically. Finally, an experimental setup is constructed to observe the deformation evolution of the constrained rod under end twist. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear approach with regard to the dynamic stability of an isotropic metal foam circular cylindrical shell subjected to combined loads. The mechanical properties of metal foam vary in the thickness direction. Combinations of external pressure and axial load are taken into account. A nonlinear hypothesis of deformation of a plane cross section is formulated. The system of partial differential equations of motion for a shell is derived on the basis of Hamilton's principle. The system of equations is analytically solved by Galerkin 's method. Numerical investigations of dynamic stability for the family of cylindrical .shells with regard to analytical solution are carried out. Moreover, finite element model analysis is presented, and the results of the numerical calculations are shown in figures. [ABSTRACT FROM AUTHOR]

A procedure for calculating contact loads on a dovetail surface for given engine performance parameters such as speed and temperature is described. The procedure requires a small number of predetermined calibrating finite element analyses to obtain empirical constants. Verification is provided by detailed finite element analyses. Contact loads can be calculated for an entire mission history in near real-time. The contact load histories could be used to calculate local stress necessary for fatigue life prediction. [ABSTRACT FROM AUTHOR]

The article discusses the isotropic clamped-free thin annular circular plate which is subjected to a concentrated load. It is noted that the null-field integral formulation was employed to verify the accuracy of Adewale's results and the examine the response of the clamped-free annular plate subjected to a concentrated load. Moreover, the agreements between the analytical results and those of ABAQUS were made but deviated from Adewale's data. It is concluded that the outcome of Adewale's results may not be correct.

This paper suggests an analytical approach to investigating vibrations of a laminated plate with a noncanonical shape in plan view under impact with an impactor having a semispherical end. The approach suggested is based on the immersion method. The dynamic behavior of the plate is described by the first-order theory accounting for trans- verse shear strain, thickness reduction, and normal element rotation inertia in each layer. Impact has been analyzed for different points of the plate whose contour consists of straight lines and circle arcs. The theoretical results are consistent with experimental data obtained with the dynamic wide-range strain measurement technique. [ABSTRACT FROM AUTHOR]

Background. Many papers on the elastic stability of both thin-walled and massive (three-dimensional) bodies regard the bifurcation of equilibrium in the case of compressive loads. Although, the elastic instability may also occur under tensile stresses. Method of Approach. In the present paper on the basis of three-dimensional equations of the nonlinear elasticity the instability of a stretched infinite hollow cylinder under torsion and inflation is investigated. The bifurcational method of stability analysis is used. Results. The critical surfaces and stability region in the space of loading parameters are defined for a Biderman material and special model of incompressible medium, which possess essential material nonlinearity. The influence of a wall thickness on the instability of a hollow cylinder is analyzed. Conclusions. Based on the obtained results, a simple and efficient practical criterion of stability under tension is formulated. This criterion can be represented in the form of the Drucker postulate, given in terms of external loads. [ABSTRACT FROM AUTHOR]

The characteristics of the frequency response function of a nonviscously damped linear oscillator are considered in this paper. It is assumed that the nonviscous damping force depends on the past history of velocity via a convolution integral over an exponentially decaying kernel function. The classical dynamic response properties, known for viscously damped oscillators, have been generalized to such nonviscously damped oscillators. The following questions of fundamental interest have been addressed: (a) Under what conditions can the amplitude of the frequency response function reach a maximum value?, (b) At what frequency will it occur?, and (c) What will be the value of the maximum amplitude of the frequency response function? Introducing two nondimensional factors, namely, the viscous damping factor and the nonviscous damping factor, we have provided exact answers to these questions. Wherever possible, attempts have been made to relate the new results with equivalent classical results for a viscously damped oscillator. It is shown that the classical concepts based on viscously damped Systems can "be extended to a nonviscously damped system only under certain conditions. [ABSTRACT FROM AUTHOR]

Based on the surface elasticity theory and using a local asymptotic approach, we analyzed the influences of surface energy on the stress distributions near a blunt crack tip. The dependence relationship of the crack-tip stresses on surface elastic parameters is obtained for both mode-I and mode-III cracks. It is found that when the curvature radius of a crack front decreases to nanometers, surface energy significantly affects the stress intensities near the crack tip. Using a kind of surface elements, we also performed finite element simulations to examine the surface effects on the near-tip stresses. The obtained analytical solution agrees well with the numerical results. [ABSTRACT FROM AUTHOR]

Presents a study that constructed a reduced-order model for nonlinear dynamical systems with many fewer degrees-of-freedom at nanoscale in relation to the field of applied mechanics. Review of related literature on reduced-order models which rely substantially on the existence of global modes such as eigenmodes; Investigation of the use of alternative modal models; Suggestions with regard to the capacity of the reduced-order models to offer the possibility of reducing computational model size and cost by several orders of magnitude.

Presents a procedure to calculate natural frequencies of in-plane loaded, thin, slightly curved, simply supported rectangular plates. Solutions to equilibrium equation and linear shell vibration equation; Static and vibration analysis; Results and discussion.

Presents the general form of the explicit equations of motion for mechanical systems. Formulation of the problem of constrained motion; Discussion on the general form of the explicit equation of motion for any constrained mechanical systems; Proof of the general form of the equations of motion for constrained systems.

Focuses on a study in which probabilistic and nonprobabilistic anti-optimization approaches are contrasted to evaluate their relative advantages and disadvantages while solving a mechanical problem in the presence of vector uncertainty. Description of two-dimensional case uncertainty vector; Equations used; Numerical results; Concluding remarks.

Presents a study in which the transient response of a propagating in-plane crack interacting with half-plane boundaries is investigated in detail. What will make the analysis very difficult; How the complete transient solutions are constructed; Insight into the dynamic stress intensity factors of a propagating crack in a configuration with boundaries.

Presents a study in which a fracture initiated at a corner between two different isotropic materials is considered. Modeling of a `small crack' located well within the region dominated by the asymptotic stress fields of the noncracked corner; How the stress intensities associated with the tip of the small crack was determined.

Announces the Eighteenth Freeman Scholar Program of the American Society of Mechanical Engineers (ASME). Criteria for the candidates; Application requirements; Information on the most recent Freeman lectures of ASME.