Combinative Algorithms for the Multidisciplinary Collaborative Simulation of Complex Mechatronic Products Based on Major Step and Convergent Integration Step

Multidisciplinary collaborative simulation （MCS） is an important area of research in the domain of multidisciplinary design optimization （MDO）.Although previous research for MCS has to some extent addressed some issues like using of multiple tools,integration stability,control of step size,data synchronization,etc,further work is still necessary to study how to achieve improved precision.A theoretical model is formulated to describe and analyze the integration process of MCS.A basic algorithm with equal major steps is proposed based on the model,along with two methods of implementation for the model,namely the serial method and the parallel method.A further algorithm based on convergent integration step is proposed,which has a more flexible strategy for run-time integration.The influence of interpolation techniques on simulation performance is studied as well.Simulations of the performance of various algorithms with different interpolation techniques are performed for both a simple numerical example and a complex mechatronic product.The novel algorithm based on convergent integration step,when used with a high-order interpolation technique,has better performance in terms of precision and efficiency.The innovation of this paper is mainly on the validation of high precision of the proposed convergent integration step algorithm.

Modified precise time step integration method of structural dynamic analysis

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.

On time-step in structural seismic response analysis under ground displacement/acceleration

There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.

RETHINKING TO FINITE DIFFERENCE TIME-STEP INTEGRATIONS

The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.

Excited response of granular ores in vibrating field

The dynamical theory was utilized to probe into the law of the excited response of granular ores generated by the exciting action of exciter and the influence of wave propagation in vibrating field. The exciter with double axes was presented as an example, and the principle of exciter and its mathematical expression of the excitation force were given. The granular ores have viscidity and damping speciality, on the basis of which the motion equation of excited response of ores was established and the approximate expression of mode displacement by harmonic excitation and the steady effect solution of coordinate response were deduced. Utilizing the step by step integration method, the recursion relation matrix of displacement, velocity and acceleration of the excited response of ores were obtained, and the computational flow chart and a computational example were given. The results show that the excited response can change the dynamical character and the flowing characteristic of granular ores.

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.

Integration of nine steps for producing ammonia and liquid-fuel synthesis gases in one membrane reactor

Subject Code:B03With the support by the National Natural Science Foundation of China and the Chinese Academy of Sciences,the research team led by Prof.Yang Weishen(杨维慎)and Prof.Zhu Xuefeng(朱雪峰)at the State Key Laboratory of Catalysis,Dalian Institute of Physical Chemistry,Chinese Academy of Sciences,proposed a new catalytic membrane reactor for one-step producing the ammonia synthesis gas(ASG,H_2/