Exploiting hybrid parallelism in the kinematic analysis of multibody systems based on group equations

Computational kinematics is a fundamental tool for the design, simulation, control, optimization and dynamic analysis of multibody systems. The analysis of complex multibody systems and the need for real time solutions requires the development of kinematic and dynamic formulations that reduces computational cost, the selection and efficient use of the most appropriated solvers and the exploiting of all the computer resources using parallel computing techniques. The topological approach based on group equations and natural coordinates reduces the computation time in comparison with well-known global formulations and enables the use of parallelism techniques which can be applied at different levels: simultaneous solution of equations, use of multithreading routines, or a combination of both. This paper studies and compares these topological formulation and parallel techniques to ascertain which combination performs better in two applications. The first application uses dedicated systems for the real time control of small multibody systems, defined by a few number of equations and small linear systems, so shared-memory parallelism in combination with linear algebra routines is analyzed in a small multicore and in Raspberry Pi. The control of a Stewart platform is used as a case study. The second application studies large multibody systems in which the kinematic analysis must be performed several times during the design of multibody systems. A simulator which allows us to control the formulation, the solver, the parallel techniques and size of the problem has been developed and tested in more powerful computational systems with larger multicores and GPU.This work was supported by the Spanish MINECO, as well as European Commission FEDER funds, under grant TIN2015-66972-C5-3-

Computer-aided methods for analysis and synthesis of supersonic cruise aircraft structures

Computer-aided methods are reviewed which are being developed by Langley Research Center in-house work and by related grants and contracts. Synthesis methods to size structural members to meet strength and stiffness (flutter) requirements are emphasized and described. Because of the strong interaction among the aerodynamic loads, structural stiffness, and member sizes of supersonic cruise aircraft structures, these methods are combined into systems of computer programs to perform design studies. The approaches used in organizing these systems to provide efficiency, flexibility of use in an iterative process, and ease of system modification are discussed

Integrated control/structure optimization by multilevel decomposition

A method for integrated control/structure optimization by multilevel decomposition is presented. It is shown that several previously reported methods were actually partial decompositions wherein only the control was decomposed into a subsystem design. One of these partially decomposed problems was selected as a benchmark example for comparison. The system is fully decomposed into structural and control subsystem designs and an improved design is produced. Theory, implementation, and results for the method are presented and compared with the benchmark example

Simultaneous structural and control optimization via linear quadratic regulator eigenstructure assignment

A method for simultaneous structural and control design of large flexible space structures (LFSS) to reduce vibration generated by disturbances is presented. Desired natural frequencies and damping ratios for the closed loop system are achieved by using a combination of linear quadratic regulator (LQR) synthesis and numerical optimization techniques. The state and control weighing matrices (Q and R) are expressed in terms of structural parameters such as mass and stiffness. The design parameters are selected by numerical optimization so as to minimize the weight of the structure and to achieve the desired closed-loop eigenvalues. An illustrative example of the design of a two bar truss is presented

Optimal design and optimal control of structures undergoing finite rotations and elastic deformations

In this work we deal with the optimal design and optimal control of structures undergoing large rotations. In other words, we show how to find the corresponding initial configuration and the corresponding set of multiple load parameters in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures.Comment: 35 pages, 11 figure

Structural sensitivity analysis: Methods, applications, and needs

Some innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. These techniques include a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Finally, some of the critical needs in the structural sensitivity area are indicated along with Langley plans for dealing with some of these needs

Control and structural optimization for maneuvering large spacecraft

Presented here are the results of an advanced control design as well as a discussion of the requirements for automating both the structures and control design efforts for maneuvering a large spacecraft. The advanced control application addresses a general three dimensional slewing problem, and is applied to a large geostationary platform. The platform consists of two flexible antennas attached to the ends of a flexible truss. The control strategy involves an open-loop rigid body control profile which is derived from a nonlinear optimal control problem and provides the main control effort. A perturbation feedback control reduces the response due to the flexibility of the structure. Results are shown which demonstrate the usefulness of the approach. Software issues are considered for developing an integrated structures and control design environment

A disturbance based control/structure design algorithm

Some authors take a classical approach to the simultaneous structure/control optimization by attempting to simultaneously minimize the weighted sum of the total mass and a quadratic form, subject to all of the structural and control constraints. Here, the optimization will be based on the dynamic response of a structure to an external unknown stochastic disturbance environment. Such a response to excitation approach is common to both the structural and control design phases, and hence represents a more natural control/structure optimization strategy than relying on artificial and vague control penalties. The design objective is to find the structure and controller of minimum mass such that all the prescribed constraints are satisfied. Two alternative solution algorithms are presented which have been applied to this problem. Each algorithm handles the optimization strategy and the imposition of the nonlinear constraints in a different manner. Two controller methodologies, and their effect on the solution algorithm, will be considered. These are full state feedback and direct output feedback, although the problem formulation is not restricted solely to these forms of controller. In fact, although full state feedback is a popular choice among researchers in this field (for reasons that will become apparent), its practical application is severely limited. The controller/structure interaction is inserted by the imposition of appropriate closed-loop constraints, such as closed-loop output response and control effort constraints. Numerical results will be obtained for a representative flexible structure model to illustrate the effectiveness of the solution algorithms

Freeze-drying modeling and monitoring using a new neuro-evolutive technique

This paper is focused on the design of a black-box model for the process of freeze-drying of pharmaceuticals. A new methodology based on a self-adaptive differential evolution scheme is combined with a back-propagation algorithm, as local search method, for the simultaneous structural and parametric optimization of the model represented by a neural network. Using the model of the freeze-drying process, both the temperature and the residual ice content in the product vs. time can be determine off-line, given the values of the operating conditions (the temperature of the heating shelf and the pressure in the drying chamber). This makes possible to understand if the maximum temperature allowed by the product is trespassed and when the sublimation drying is complete, thus providing a valuable tool for recipe design and optimization. Besides, the black box model can be applied to monitor the freeze-drying process: in this case, the measurement of product temperature is used as input variable of the neural network in order to provide in-line estimation of the state of the product (temperature and residual amount of ice). Various examples are presented and discussed, thus pointing out the strength of the too