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A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that the structure and steady-state growth velocity of spatially periodic precipitation fronts strongly depend on the relative magnitudes of the diffusion coefficients. Steady-state solutions always exist for a range of interlamellar spacings that is limited by a fold singularity for low spacings, and by the onset of tip-splitting or oscillatory instabilities for large spacings. A detailed analysis of the simulation data reveals that the hypothesis of local equilibrium at interfaces, used in previous theories, is not valid for the typical conditions of discontinuous precipitation., Comment: 24 pages, 9 figures, submitted to Acta Materialia

This research focuses on the computational dynamics of flexible constrained multibody systems. At first a recursive mapping formulation of the kinematical expressions in a minimum dimension as well as the matrix representation of the equations of motion are presented. The method employs Kane's equation, FEM, and concepts of continuum mechanics. The generalized active forces are extended to include the effects of high temperature conditions, such as creep, thermal stress, and elastic-plastic deformation. The time variant constraint relations for rolling/contact conditions between two flexible bodies are also studied. The constraints for validation of MBS simulation of gear meshing contact using a modified Timoshenko beam theory are also presented. The last part deals with minimization of vibration/deformation of the elastic beam in multibody systems making use of time variant boundary conditions. The above methodologies and computational procedures developed are being implemented in a program called DYAMUS.

In this paper a generalized algorithmic procedure is presented for handling constraints in mechanical transmissions. The latter are treated as multibody systems of interconnected rigid/flexible bodies. The constraint Jacobian matrices are generated automatically and suitably updated in time, depending on the geometrical and kinematical constraint conditions describing the interconnection between shafts or gears. The type of constraints are classified based on the interconnection of the bodies by assuming that one or more points of contact exist between them. The effects due to elastic deformation of the flexible bodies are included by allowing each body element to undergo small deformations. The procedure is based on recursively formulated Kane's dynamical equations of motion and the finite element method, including the concept of geometrical stiffening effects. The method is implemented on an IBM-3090-600j vector processor with pipe-lining capabilities. A significant increase in the speed of execution is achieved by vectorizing the developed code in computationally intensive areas. An example consisting of two meshing disks rotating at high angular velocity is presented. Applications are intended for the study of the dynamic behavior of helicopter transmissions.

In this paper an automated algorithmic method is presented for the dynamic analysis of geared trains/transmissions. These are treated as a system of interconnected flexible bodies. The procedure developed explains the switching of constraints with time as a result of the change in the contacting areas at the gear teeth. The elastic behavior of the system is studied through the employment of three-dimensional isoparametric elements having six degrees-of-freedom at each node. The contact between the bodies is assumed at the various nodes, which could be either a line or a plane. The kinematical expressions, together with the equations of motion using Kane's method, strain energy concepts, are presented in a matrix form suitable for computer implementation. The constraint Jacobian matrices are generated automatically based on the contact information between the bodies. The concepts of the relative velocity at the contacting points at the tooth pairs and the subsequent use of the transmission ratios in the analysis is presented.

This paper presents an innovative method for minimizing the vibration of structures with time-variant boundary conditions (supports). The elastic body is modeled in two ways: (1) the first model is a letter seven type beam with a movable mass not to exceed the lower tip; (2) the second model has an arm that is a hollow beam with an inside mass with adjustable position. The complete solutions to both problems are carried out where the body is undergoing large rotation. The quasi-static procedure is used for the time-variant boundary conditions. The method developed employs partial differential equations governing the motion of the beam, including the effects of rigid-body motion, time-variant boundary conditions, and calculus of variations. The analytical solution is developed using Laplace and Fourier transforms. Examples of elastic robotic arms are given to illustrate the effectiveness of the methods developed.

A computational algorithmic procedure is developed and implemented for the dynamic analysis of a multibody system with rigid/flexible interconnected bodies. The algorithm takes into consideration the large rotation/translation and small elastic deformations associated with the rigid-body degrees of freedom and the flexibility of the bodies in the system respectively. Versatile three-dimensional isoparametric brick elements are employed for the modeling of the geometric configurations of the bodies. The formulation of the recursive dynamical equations of motion is based on the recursive Kane's equations, strain energy concepts, and the techniques of component mode synthesis. In order to minimize CPU-intensive matrix multiplication operations and speed up the execution process, the concepts of indexed arrays is utilized in the formulation of the equations of motion. A spin-up maneuver of a space robot with three flexible links carrying a solar panel is used as an illustrative example.

A generalized algorithmic procedure is presented for handling the constraints in transmissions, which are treated as a multibody system of interconnected rigid/flexible bodies. The type of constraints are classified based on the interconnection of the bodies, assuming one or more points of contact to exist between them. The method is explained through flow charts and configuration/interaction tables. A significant increase in speed of execution is achieved by vectorizing the developed code in computationally intensive areas. The study of an example consisting of two meshing disks rotating at high angular velocity is carried out. The dynamic behavior of the constraint forces associated with the generalized coordinates of the system are plotted by selecting various modes. Applications are intended for the study of dynamic and subsequent prediction of constraint forces at the gear teeth contacting points in helicopter transmissions with the aim of improving performance dependability.

An improved technique for the identification and extraction of the exact quantities associated with the degrees of freedom at the element as well as the flexible body level is presented. It is implemented in the dynamic equations of motions based on the recursive formulation of Kane et al. (1987) and presented in a matrix form, integrating the concepts of strain energy, the finite-element approach, modal analysis, and reduction of equations. This technique eliminates the CPU intensive matrix multiplication operations in the code's hot spots for the dynamic simulation of the interconnected rigid and flexible bodies. A study of a simple robot with flexible links is presented by comparing the execution times on a scalar machine and a vector-processor with and without vector options. Performance figures demonstrating the substantial gains achieved by the technique are plotted.

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed.

The objective is to address the continuity of motion when a dynamical system is suddenly subjected to constraint conditions. Motion discontinuity due to the initial constraint violation is avoided by prior control forces that adjust the motion and yield velocity and acceleration consistent at the point of application of the constraint. The optimum control forces are determined for a specified control interval. The method proposed provides an optimum adjustment of the system's motion and assures that the stresses developed at the system components are kept within acceptable limits. The procedures developed will be illustrated making use of inequality constraints applied to obstacle avoidance problems in robotics.