CONTINUATION METHOD APPLIED IN KINEMATICS OF PARALLEL ROBOT

Continuation method solving forward kinematics problem of parallel robot was discussed. And through a coefficient-parameter continuation method the efficiency and feasibility of continuation method were improved. Using this method all forward solutions of a new parallel robot model which was put forward lately by Robot Open Laboratory of Science Institute of China were obtained. Therefore it provided the basis of mechanism analysis and real-time control for new model.

A GLOBAL LINEAR AND LOCAL QUADRATIC SINGLE-STEP NONINTERIOR CONTINUATION METHOD FOR MONOTONE SEMIDEFINITE COMPLEMENTARITY PROBLEMS

A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.

A Combined Feasible-Nonfeasible Point Continuation Method for Strongly Monotone Variational Inequalities

In this paper, we discuss the variational inequality problems VIP(X, F), where Fis a strongly monotone function and the convex feasible set X is described by some inequality eonstraints. We present a continuation method for VIP(X. F). which solves a sequence ofperturbed variational inequality problems PVIP(X. F, ε. μ) depending on two parameters ε≥ 0and μ＞0. It is worthy to point out that the method will be a feasible point type whenε = 0 and a nonfeasible point type when ε＞0, i.e., it is a combined feasible-nonfeasible point(CFNFP for short) method. We analyse the existence, uniqueness and continuity of the solutionto PVIP(X, F, ε,μ), and prove that any sequence generated by this method converges to theunique solution of VIP(X, F).

Solving a Class of Nonlinear Programming Problems via a Homotopy Continuation Method

In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is effective. It should be pointed out that we extend the results of Lin et al. （see Appl. Math. Comput., 80（1996）, 209-224） to a broader class of non-convex programming problems.

Downward continuation of airborne geomagnetic data based on two iterative regularization methods in the frequency domain

Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed to realize effective continuation. According to the Poisson integral plane approximate relationship between observation and continuation data, the computation formulae combined with the fast Fourier transform（FFT）algorithm are transformed to a frequency domain for accelerating the computational speed. The iterative Tikhonov regularization method and the iterative Landweber regularization method are used in this paper to overcome instability and improve the precision of the results. The availability of these two iterative regularization methods in the frequency domain is validated by simulated geomagnetic data, and the continuation results show good precision.

Design optimization of unsteady airfoils with continuous adjoint method

In this paper, a new unsteady aerodynamic design method is presented based on the Navier-Stokes equations and a continuous adjoint approach. A basic framework of time-accurate unsteady airfoil optimization which adopts time-averaged aerodynamic coefficients as objective functions is presented. The time-accurate continuous adjoint equation and its boundary conditions are derived. The flow field and the adjoint equation are simulated numerically by the finite volume method （FVM）. Feasibility and accuracy of the approach are perfectly validated by the design optimization results of the plunging NACA0012 airfoil.

Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method

Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.

ICM Method Combined with Meshfree Approximation for Continuum Structure

The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.

EFFICIENT ANALYSIS OF ELECTROMAGNETIC RADIATION FROM MICROSTRIP ANTENNA USING VOLUME-SURFACE CURRENT CONTUNUITY METHOD

The Volume-Surface Current Continuity Method (VSCCM) is presented to analyze electromagnetic radiation from microstrip antenna. The microstrip antenna is discretized into small triangular patches on conducting surface and tetrahedral volume cells in dielectric region. The Method of Moments (MoM) is applied to solve the integral equation. An equation contains the restriction relation between the volume and surface current coefficient is derived from the current continuity equation at those parts where the conducting surface is in contact with the dielectric material. A simple equivalent strip model is introduced in the treatment of the feeding probe in VSCCM. The VSCCM can reduce the unknowns required to be solved in MoM, as well as the condition number of the matrix equation. Numerical results are given to validate the accuracy and efficiency of this method.

Continuous finite element methods for Hamiltonian systems

By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo- symplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agree-ment with theory.

Stepwise Method Based on Confidence Bound and Information Incorporation for Identifying the Maximum Tolerable Dose

The primary goal of a phase I clinical trial is to find the maximum tolerable dose of a treatment. In this paper, we propose a new stepwise method based on confidence bound and information incorporation to determine the maximum tolerable dose among given dose levels. On the one hand, in order to avoid severe even fatal toxicity to occur and reduce the experimental subjects, the new method is executed from the lowest dose level, and then goes on in a stepwise fashion. On the other hand, in order to improve the accuracy of the recommendation, the final recommendation of the maximum tolerable dose is accomplished through the information incorporation of an additional experimental cohort at the same dose level. Furthermore, empirical simulation results show that the new method has some real advantages in comparison with the modified continual reassessment method.

ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.

Cable Sliding at Supports in Cable Structures

To develop an effective numerical method for the cable sliding problem in cable structures, two-node catenary cable element was built to model the cables based on analytical solution of elastic catenary. Cooperated with Newton method, continuation method was used to solve the nonlinear equations. This approach is more efficient than using Newton method only and has a wider range to select initial values for the process to converge. The relationship between the tension on a cable segment and its unstrained length was derived and used to calculate the unbalanced cable tensions at the supports. An example is presented to show the correctness and efficiency of the proposed method.

EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.

FindingSymbolicandAllNumericalSolutionsforDesignOptimizationBasedonMonotonicityAnalysisandSolvingPol

A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.

A LOWER BOUND OF STABLE STATIONARY TRAJECTORIES

It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectorlies.

SHARED VALUE IN A FINITE-DIMENSIONAL BANACH MANIFOLD

Sufficient conditions are given to assert that two C1-mappings share only one value in a connected compact Banach manifold modelled over Rn. The proof of the result, which is based upon continuation methods, is constructive.

FREDHOLM AND COMPACT MAPPINGS SHARING A VALUE

Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.

STABLE AND UNSTABLE STATIONARY TRAJECTORIES

The stability of stationary trajectories of a particular autonomous system is studied.The proof of the result is based upon continuation methods.