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Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.
Weixuan Wang; Qinyan Xing; Qinghao Yang. An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation. Applied Sciences 2021, 11, 1932 .
AMA StyleWeixuan Wang, Qinyan Xing, Qinghao Yang. An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation. Applied Sciences. 2021; 11 (4):1932.
Chicago/Turabian StyleWeixuan Wang; Qinyan Xing; Qinghao Yang. 2021. "An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation." Applied Sciences 11, no. 4: 1932.
With the development of big data, AI and other modern technologies, the traditional engineering education, which centers on disciplines and pays attention to the systematic imparting of disciplinary knowledge, has been facing severe challenges in recent years. It has been gradually transforming into the new engineering education, which focuses on students and pays attention to the cultivation of students’ learning mode and thinking capability. Firstly, the newest and most advanced research work and contributions in engineering education were studied and introduced, which shows the total background of the present study. Secondly, the mechanical curriculum in universities’ civil engineering education of China is described. And then the roles that mechanics courses playing in cultivation of students’ thinking abilities are discussed and two detailed reform activities in practical teaching process are proposed, which aims at improving the students’ ability of creative thinking.
Q. Y. Xing. The Roles of Mechanics Courses in Student-Centered Civil Engineering Education. Lecture Notes in Civil Engineering 2020, 1011 -1019.
AMA StyleQ. Y. Xing. The Roles of Mechanics Courses in Student-Centered Civil Engineering Education. Lecture Notes in Civil Engineering. 2020; ():1011-1019.
Chicago/Turabian StyleQ. Y. Xing. 2020. "The Roles of Mechanics Courses in Student-Centered Civil Engineering Education." Lecture Notes in Civil Engineering , no. : 1011-1019.
The reliable and efficient self-adaptive analysis is a modern goal of various numerical computations. Most adaptivity methods, however, adopt energy norm to measure errors, which may not be the most natural and convenient means, e.g., for problems with locally singular gradient of displacement. Based on the Element Energy Projection (EEP) super-convergent technique in the Finite Element Method of Lines (FEMOL) which is a general and powerful semi-discrete method, reliable error estimates of displacements in maximum norm can be obtained anywhere on the FEMOL mesh and hence adaptive FEMOL by maximum norm becomes feasible. However, to tackle singularity problems effectively and efficiently, an automatic and flexible local mesh refinement strategy is required to generate meshes of high quality for more efficient adaptive FEMOL analysis. Taking the two-dimensional Poisson equation as the model problem, the paper firstly introduces the FEMOL and EEP methods with interface sides resulting from local mesh refinement. Then a local mesh refinement strategy and corresponding adaptive algorithm are presented. The numerical results given show that the proposed adaptive FEMOL with local mesh refinement can produce displacement solutions satisfying the specified tolerances in maximum norm and the adaptively-generated meshes reasonably reflect the local difficulties inherent in the physical problems without much redundant accuracy.
Si Yuan; Yiyi Dong; Qinyan Xing; Nan Fang. Adaptive Finite Element Method of Lines with Local Mesh Refinement in Maximum Norm Based on Element Energy Projection Method. International Journal of Computational Methods 2019, 17, 1 .
AMA StyleSi Yuan, Yiyi Dong, Qinyan Xing, Nan Fang. Adaptive Finite Element Method of Lines with Local Mesh Refinement in Maximum Norm Based on Element Energy Projection Method. International Journal of Computational Methods. 2019; 17 (4):1.
Chicago/Turabian StyleSi Yuan; Yiyi Dong; Qinyan Xing; Nan Fang. 2019. "Adaptive Finite Element Method of Lines with Local Mesh Refinement in Maximum Norm Based on Element Energy Projection Method." International Journal of Computational Methods 17, no. 4: 1.
This paper presents a step-by-step time integration method for transient solutions of nonlinear structural dynamic problems. Taking the second-order nonlinear dynamic equations as the model problem, this self-starting one-step algorithm is constructed using the Galerkin finite element method (FEM) and Newton–Raphson iteration, in which it is recommended to adopt time elements of degree m = 1,2,3. Based on the mathematical and numerical analysis, it is found that the method can gain a convergence order of 2m for both displacement and velocity results when an ordinary Gauss integral is implemented. Meanwhile, with reduced Gauss integration, the method achieves unconditional stability. Furthermore, a feasible integration scheme with controllable numerical damping has been established by modifying the test function and introducing a special integral rule. Representative numerical examples show that the proposed method performs well in stability with controllable numerical dissipation, and its computational efficiency is superior as well.
Qinyan Xing; Qinghao Yang; Weixuan Wang. A Time Integration Method Based on Galerkin Weak Form for Nonlinear Structural Dynamics. Applied Sciences 2019, 9, 3076 .
AMA StyleQinyan Xing, Qinghao Yang, Weixuan Wang. A Time Integration Method Based on Galerkin Weak Form for Nonlinear Structural Dynamics. Applied Sciences. 2019; 9 (15):3076.
Chicago/Turabian StyleQinyan Xing; Qinghao Yang; Weixuan Wang. 2019. "A Time Integration Method Based on Galerkin Weak Form for Nonlinear Structural Dynamics." Applied Sciences 9, no. 15: 3076.
This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method (FEM) by recursive application of the one-dimensional (1D) element energy projection (EEP) technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully dis-cretized standard finite element (FE) model is reached. This conceptual dimension-by-dimension (D-by-D) discretization procedure is entirely equivalent to a full FE discretiza-tion. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional (2D) and three-dimensional (3D) problems can be obtained over the domain. Numerical examples of 3D Poisson’s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.
Si Yuan; Yue Wu; Qinyan Xing. Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy projection technique. Applied Mathematics and Mechanics 2018, 39, 1031 -1044.
AMA StyleSi Yuan, Yue Wu, Qinyan Xing. Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy projection technique. Applied Mathematics and Mechanics. 2018; 39 (7):1031-1044.
Chicago/Turabian StyleSi Yuan; Yue Wu; Qinyan Xing. 2018. "Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy projection technique." Applied Mathematics and Mechanics 39, no. 7: 1031-1044.
Analyses of dynamic responses are significantly important for the design, maintenance and rehabilitation of asphalt pavement. In order to evaluate the dynamic responses of asphalt pavement under moving loads, a specific computational program, SAFEM, was developed based on a semi-analytical finite element method. This method is three-dimensional and only requires a two-dimensional FE discretization by incorporating Fourier series in the third dimension. In this paper, the algorithm to apply the dynamic analysis to SAFEM was introduced in detail. Asphalt pavement models under moving loads were built in the SAFEM and commercial finite element software ABAQUS to verify the accuracy and efficiency of the SAFEM. The verification shows that the computational accuracy of SAFEM is high enough and its computational time is much shorter than ABAQUS. Moreover, experimental verification was carried out and the prediction derived from SAFEM is consistent with the measurement. Therefore, the SAFEM is feasible to reliably predict the dynamic response of asphalt pavement under moving loads, thus proving beneficial to road administration in assessing the pavement’s state.
Pengfei Liu; Qinyan Xing; Dawei Wang; Markus Oeser. Application of Dynamic Analysis in Semi-Analytical Finite Element Method. Materials 2017, 10, 1010 .
AMA StylePengfei Liu, Qinyan Xing, Dawei Wang, Markus Oeser. Application of Dynamic Analysis in Semi-Analytical Finite Element Method. Materials. 2017; 10 (9):1010.
Chicago/Turabian StylePengfei Liu; Qinyan Xing; Dawei Wang; Markus Oeser. 2017. "Application of Dynamic Analysis in Semi-Analytical Finite Element Method." Materials 10, no. 9: 1010.
The finite element (FE) method has been widely used in predicting the structural responses of asphalt pavements. However, the three-dimensional (3D) modeling in general-purpose FE software systems such as ABAQUS requires extensive computations and is relatively time-consuming. To address this issue, a specific computational code EasyFEM was developed based on the finite layer method (FLM) for analyzing structural responses of asphalt pavements under a static load. Basically, it is a 3D FE code that requires only a one-dimensional (1D) mesh by incorporating analytical methods and using Fourier series in the other two dimensions, which can significantly reduce the computational time and required resources due to the easy implementation of parallel computing technology. Moreover, a newly-developed Element Energy Projection (EEP) method for super-convergent calculations was implemented in EasyFEM to improve the accuracy of solutions for strains and stresses over the whole pavement model. The accuracy of the program is verified by comparing it with results from BISAR and ABAQUS for a typical asphalt pavement structure. The results show that the predicted responses from ABAQUS and EasyFEM are in good agreement with each other. The EasyFEM with the EEP post-processing technique converges faster compared with the results derived from ordinary EasyFEM applications, which proves that the EEP technique can improve the accuracy of strains and stresses from EasyFEM. In summary, the EasyFEM has a potential to provide a flexible and robust platform for the numerical simulation of asphalt pavements and can easily be post-processed with the EEP technique to enhance its advantages.
Pengfei Liu; Qinyan Xing; Yiyi Dong; Dawei Wang; Markus Oeser; Si Yuan. Application of Finite Layer Method in Pavement Structural Analysis. Applied Sciences 2017, 7, 611 .
AMA StylePengfei Liu, Qinyan Xing, Yiyi Dong, Dawei Wang, Markus Oeser, Si Yuan. Application of Finite Layer Method in Pavement Structural Analysis. Applied Sciences. 2017; 7 (6):611.
Chicago/Turabian StylePengfei Liu; Qinyan Xing; Yiyi Dong; Dawei Wang; Markus Oeser; Si Yuan. 2017. "Application of Finite Layer Method in Pavement Structural Analysis." Applied Sciences 7, no. 6: 611.
The element energy projection (EEP) method for computation of superconvergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton’s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a result, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation of second-order as the model problem, this paper describes the related fundamental idea, the implementation strategy, and the computational algorithm. Representative numerical examples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.
Si Yuan; Yan Du; Qin-Yan Xing; Kang-Sheng Ye. Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method. Applied Mathematics and Mechanics 2014, 35, 1223 -1232.
AMA StyleSi Yuan, Yan Du, Qin-Yan Xing, Kang-Sheng Ye. Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method. Applied Mathematics and Mechanics. 2014; 35 (10):1223-1232.
Chicago/Turabian StyleSi Yuan; Yan Du; Qin-Yan Xing; Kang-Sheng Ye. 2014. "Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method." Applied Mathematics and Mechanics 35, no. 10: 1223-1232.