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Computer Modeling in Engineering & Sciences 2025年第1期142卷 329-355页

作者： yufeng xing Ye Yuan Gen Li Institute of Solid Mechanics Beihang University(BUAA)Beijing100191China

The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical *** taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue ***,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are *** is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.

关键词： Separation-of-variable method Rayleigh quotient nodal line eigenvalue equation bisection method

Analytical solution methods for eigenbuckling of symmetric cross-ply composite laminates

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Chinese Journal of Aeronautics 2017年第1期30卷 282-291页

作者： xing yufeng Xiang Wei Institute of Solid Mechanics Beihang University School of Mechanical Engineering Southwest Jiaotong University

Based on the first-order shear deformation theory, this paper explores the analytical methods for eigenbuckling of symmetric cross-ply rectangular composite laminates with a pair of parallel edges simply supported and the remaining two edges arbitrarily constrained. The main contribution of present paper lies in two aspects： one is to present a simple and effective analytical method, namely, the separation-of-variables method, which can generate the closed-form buckling solutions without any computational difficulty; the other is to incorporate the accurate computation method of exponential matrix into the state space technique to avoid the inevitable numerically illconditioned problems reported in several literatures. The results obtained via both analytical methods are identical, and a good agreement with their counterparts in literature is observed. The separation-of-variables method can generate exact solutions within 1 s, which is impossible if the state space method is employed. Besides, the combination of the accurate computation method of exponential matrix and the state space method greatly improves the computational efficiency and gives correct results compared with the straightforward use of state space method.

关键词： Accurate computation Analytical solution Composite laminates Eigenbuckling Separation of variablesState space

Multiscale eigenelement method for periodical composites: A review

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Chinese Journal of Aeronautics 2019年第1期32卷 104-113页

作者： yufeng xing Yahe GAO Institute of Solid Mechanics Beihang University

Based on the eigenvector expansion idea, the Multiscale Eigenelement Method(MEM)was proposed by the author and co-workers. MEM satisfies two equivalent conditions, one condition is the equivalence of strain energy, and the other is the deformation similarity. These two equivalent conditions character the structure-preserving property of a multiscale analysis method. The equivalence of strain energy is necessary for achieving accurate macro behaviors such as lower order frequencies, while the deformation similarity is essential for predicting accurate micro behaviors such as stresses. The MEM has become a powerful multiscale method for the analysis of composite structures because of its high accuracy and efficiency. In this paper, the research advances of MEM are reviewed and all types of eigenelement methods are compared, focusing on superiorities and deficiencies from practical viewpoint. It is concluded that the eigenelement methods with smooth shape functions are more suitable for the analysis of macro behaviors such as lower order frequencies, and the eigenelement methods with piecewise shape functions are suitable for the analysis of both macro and micro behaviors.

关键词： Composite Deformation similarity Eigenelement Energy equivalence Mechanical analysis Multiscale

A three-parameter single-step time integration method for structural dynamic analysis

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Acta Mechanica Sinica 2019年第1期35卷 112-128,I0004页

作者： Huimin Zhang yufeng xing Institute of Solid Mechanics Beihang University (BUAA)Beijing 100083China

The existing three-parameter single-step time integration methods, such as the Generalized-a method, improve numerical dissipation by modifying equilibrium equation at time points, which cause them to lose accuracy due to the interpolation of load vectors. Moreover, these three-parameter methods do not present an available formulation applied to a general secondorder non linear differential equatio n. To solve these problems, this paper proposes an innovative three-parameter single-step method by introducing an additional variable into update equations. Although the present method is spectrally identical to the Generalized-cx method for undamped systems, it possesses higher accuracy since it strictly satisfies the equilibrium equation at time points, and can be readily used to solve nonlinear equations. By the analysis of accuracy, stability, numerical dissipation and dispersion, the optimal second-order implicit and explicit schemes are generated, which can maximize low-frequency accuracy when high-frequency dissipation is specified. To check the performance of the proposed method, several numerical experiments are conducted and the proposed method is compared with a few up-to-date methods.

关键词： Three-parameter Single-step Optimal scheme Higher accuracy

C^1 conforming quadrilateral finite elements with complete secondorder derivatives on vertices and its application to Kirchhoff plates

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Science China(Technological Sciences) 2020年第6期63卷 1066-1084页

作者： WU Yang xing yufeng LIU Bo Institute of Solid Mechanics Beihang UniversityBeijing 100191China

The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation *** order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape *** is found that the shape functions and the polynomial spaces of the present elements vary with element ***,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular ***,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular *** the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also *** examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.

关键词： finite element method quadrilateral elements C^1 conforming Kirchhoff plates

CHARACTERISTIC EQUATIONS AND CLOSED-FORM SOLUTIONS FOR FREE VIBRATIONS OF RECTANGULAR MINDLIN PLATES

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Acta Mechanica Solida Sinica 2009年第2期22卷 125-136页

作者： yufeng xing Bo Liu The Solid Mechanics Research Center Beijing University of Aeronautics and Astronautic Beijing 100083 China

The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different methods. It is found that the deflection can be expressed by means of the four characteristic roots and the two rotations should be expressed by all the six characteristic roots,which is the particularity of Mindlin plate theory. And the closed-form solutions,which satisfy two of the three governing equations and all boundary conditions and are accurate for rectangular plates with moderate thickness,are derived for any combinations of simply supported and clamped edges. The free edges can also be dealt with if the other pair of opposite edges is simply supported. The present results agree well with results published previously by other methods for different aspect ratios and relative thickness.

关键词： Mindlin plate free vibration closed-form solution separation of variables

EXACT SOLUTIONS FOR FREE IN-PLANE VIBRATIONS OF RECTANGULAR PLATES

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Acta Mechanica Solida Sinica 2011年第6期24卷 556-567页

作者： Bo Liu yufeng xing The Solid Mechanics Research Center Beijing University of Aeronautics and Astronautics Beijing 100191 China

All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates. The plates have simply supported condition at two opposite edges and any combination of classical boundary conditions at the other two edges. The exact solutions are validated through both mathematical proof and comparisons with the solutions of differential quadrature method. Some unusual phenomena are revealed in free in-plane vibrations of rectangular plates due to one of the eigenvalues being zero. This work constitutes an improved version of very recent corresponding work by the same authors lint. J. Mech. Sci., 2009, 51： 246-255]. Both the solution forms and solving procedures in the previous work are substantially simplified. Some new results are also given, which are useful for validation purpose in future.

关键词： rectangular plate in-pane free vibration frequency mode shape exact solution

An Improved Higher-Order Time Integration Algorithm for Structural Dynamics

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Computer Modeling in Engineering & Sciences 2021年第2期126卷 549-575页

作者： Yi Ji yufeng xing Institute of Solid Mechanics Beihang UniversityBeijing100083China Shen Yuan Honors College Beihang UniversityBeijing100083China

Based on the weighted residual method,a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed,which is superior to the second-order accurate algorithms in tracking long-term *** improving such a higher-order accurate algorithm,this paper proposes a two sub-step higher-order algorithm with unconditional stability and controllable *** the proposed algorithm,a time step interval[t_(k),t_(k)+h]where h stands for the size of a time step is divided into two sub-steps[t_(k),t_(k)+γh]and[t_(k)+γh,t_(k)+h].A non-dissipative fourth-order algorithm is used in the rst sub-step to ensure low-frequency accuracy and a dissipative third-order algorithm is employed in the second sub-step to lter out the contribution of high-frequency ***,two approaches are used to design the algorithm parameterγ.The rst approach determinesγby maximizing low-frequency accuracy and the other determinesγfor quickly damping out highfrequency *** present algorithm usesρ_(∞)to exactly control the degree of numerical dissipation,and it is third-order accurate when 0≤ρ_(∞)<1 and fourth-order accurate whenρ_(∞)=***,the proposed algorithm is self-starting and easy to *** illustrative linear and nonlinear examples are solved to check the performances of the proposed two sub-step higher-order algorithm.

关键词： Time integration algorithm two-sub-step higher-order accuracy controllable dissipation unconditional stability

Analytical transient phase change heat transfer model of wearable electronics with a thermal protection substrate

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Applied Mathematics and Mechanics(English Edition) 2020年第11期41卷 1599-1610页

作者： Yingli SHI Junyun JI Yafei YIN Yuhang LI yufeng xing Institute of Solid Mechanics Beihang UniversityBeijing 100191China BOE Technology Group Company Limited Beijing 100176China University Electronic Science and Technology China State Key Laboratory of Electronic Thin Films and Integrated DeviceChengdu 610054China Institute of Structure and Environment Engineering Beijing 100076China State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of TechnologyDalian 116024Liaoning ProvinceChina

As thermal protection substrates for wearable electronics,functional soft composites made of polymer materials embedded with phase change materials and metal layers demonstrate unique capabilities for the thermal protection of human ***,we develop an analytical transient phase change heat transfer model to investigate the thermal performance of a wearable electronic device with a thermal protection *** model is validated by experiments and the finite element analysis(FEA).The effects of the substrate structure size and heat source power input on the temperature management efficiency are investigated systematically and *** results show that the objective of thermal management for wearable electronics is achieved by the following thermal protection *** metal thin film helps to dissipate heat along the in-plane direction by reconfiguring the direction of heat flow,while the phase change material assimilates excessive *** results will not only promote the fundamental understanding of the thermal properties of wearable electronics incorporating thermal protection substrates,but also facilitate the rational design of thermal protection substrates for wearable electronics.

关键词： wearable electronics functional composite theoretical heat transfer analysis thermal management

Accurate closed-form eigensolutions of three-dimensional panel flutter with arbitrary homogeneous boundary conditions

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Chinese Journal of Aeronautics 2023年第1期36卷 266-289页

作者： Qiaozhen SUN yufeng xing Bo LIU Bocheng ZHANG Zekun WANG COMAC Beijing Aircraft Technology Research Institute Beijing 102211China Institute of Solid Mechanics Beihang UniversityBeijing 100191China

Highly accurate closed-form eigensolutions for flutter of three-dimensional(3D)panel with arbitrary combinations of simply supported(S),glide(G),clamped(C)and free(F)boundary conditions(BCs),such as cantilever panels,are achieved according to the linear thin plate theory and the first-order piston theory as well as the complex modal analysis,and all solutions are in a simple and explicit *** iterative Separation-of-Variable(iSOV)method proposed by the pre-sent authors is employed to obtain the highly accurate *** flutter mechanism is studied with the benefit of eigenvalue properties from mathematical *** effects of boundary conditions,chord-thickness ratios,aerodynamic damping,aspect ratios and in-plane loads on flut-ter properties are *** results are compared with those of Kantorovich method and Galerkin method,and also coincide well with analytical solutions in literature,verifying the accu-racy of the present closed-form *** is revealed that,(A)the flutter characteristics are domi-nated by the cross section properties of panels in the direction of stream flow;(B)two types of flutter,called coupled-mode flutter and zero-frequency flutter which includes zero-frequency single-mode flutter and buckling,are observed;(C)boundary conditions and in-plane loads can affect both flutter boundary and flutter type;(D)the flutter behavior of 3D panel is similar to that of the two-dimensional(2D)panel if the aspect ratio is up to a certain value;(E)four to six modes should be used in the Galerkin method for accurate eigensolutions,and the results converge to that of Kantorovich method which uses the same mode functions in the direction perpendicular to the stream *** present analysis method can be used as a reference for other stability issues characterized by complex eigenvalues,and the highly closed-form solutions are useful in parameter designs and can also be taken as benchmarks for the validation of numerical methods.

关键词： Analytical Closed-form Eigenvalues Flutter Three-dimensional