Based on the Sanders thin shell theory and Reddy's higher order shell theory,a general refined shell theory is developed for the analysis of stresses and deformations ofpneumatic radial tires of composite construc...Based on the Sanders thin shell theory and Reddy's higher order shell theory,a general refined shell theory is developed for the analysis of stresses and deformations ofpneumatic radial tires of composite construction. For easy and efficient simulation of the tire apiecewise Rayleigh-Ritz technique is proposed and applied to get a numerical solution to thenonlinear structural problem. Bezier polynomials are used to approximate both the geometry of thesurface of reference and displacement fields of the tires. Stress distributions and deformations ofthe tires subjected to uniform inflation pressure are computed and discussed in details. Fromcomparison of the present results with the numerical predictions by 3D finite element method, it hasbeen shown that the present solution procedure is accurate and applicable to much complicatedtime-consuming nonlinear analysis for the high quality tire.展开更多
A rotor manipulation mechanism for micro unmanned helicopter utilizing the inertia and the elasticity of the rotor is introduced. The lagging motion equation of the rotor blades is established, and then the natural fr...A rotor manipulation mechanism for micro unmanned helicopter utilizing the inertia and the elasticity of the rotor is introduced. The lagging motion equation of the rotor blades is established, and then the natural frequencies and mode shapes of the blade for the helicopter are studied by using beam characteristic orthogonal polynomials by the Rayleigh-Ritz method. The variation of natural frequencies with the speed of rotation and the mode shapes at different rotational speeds are plotted. The using of orthogonal polynomials for the bending shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any difficulties.展开更多
Based on Reddy higher-order shear deformation theory, a general refined shell theory suitable to nonlinear analysis of tire structure is developed in this paper. The piece-wise Rayleigh-Ritz procedure and Bezier polyn...Based on Reddy higher-order shear deformation theory, a general refined shell theory suitable to nonlinear analysis of tire structure is developed in this paper. The piece-wise Rayleigh-Ritz procedure and Bezier polynomials are applied to analyze deformations and stress distributions of the multlayered tire subjected to uniform inflation in detail. Furthermore, 3-dimension FEM analysis of laminated tire by standard software ANSYS is adopted to compare with the present model. It is demonstrated that both two solutions are in fairly good agreement.展开更多
Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonaliza...Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.展开更多
板结构与其他构件的装配关系可用不同的边界条件进行模拟,然而针对不同边界条件的板结构进行动力学特性分析,目前缺乏统一的数学建模方法。以混合弹性边界条件下加筋、开孔的板类结构的横向振动为例,利用Rayleigh-Ritz法和模态叠加法求...板结构与其他构件的装配关系可用不同的边界条件进行模拟,然而针对不同边界条件的板结构进行动力学特性分析,目前缺乏统一的数学建模方法。以混合弹性边界条件下加筋、开孔的板类结构的横向振动为例,利用Rayleigh-Ritz法和模态叠加法求解矩形加筋多孔板在简谐激励下的动力学响应问题。采用将开孔板与加强筋沿交界面进行分离,结合改进的傅里叶级数设定开孔板的横向振动位移函数,利用不同刚度弹簧模拟混合弹性边界,推导加筋矩形开多孔板和边界弹簧系统的动能与势能,求解其在简谐激励下的动力学响应。经对比,理论计算结果与有限元(Finite Element Method,FEM)结果吻合良好。此外,用同样的方法分析不同孔尺寸对结构固有频率和响应的影响。研究发现,可通过改变加筋板的开孔形状、尺寸对结构的振动特性进行调整。研究成果可为混合弹性边界板结构动力分析提供一种新的技术途径,可以简化加筋开孔板结构动力分析的步骤。展开更多
提出一种用于求解任意边界条件下带有任意集中质量的连续多跨梁的自振特性的方法。求解过程为:运用改进的傅里叶级数法(Improved Fourier Series Method,IFSM)确定梁的位移形函数,通过Rayleigh-Ritz法得到梁的拉格朗日方程,然后利用Hami...提出一种用于求解任意边界条件下带有任意集中质量的连续多跨梁的自振特性的方法。求解过程为:运用改进的傅里叶级数法(Improved Fourier Series Method,IFSM)确定梁的位移形函数,通过Rayleigh-Ritz法得到梁的拉格朗日方程,然后利用Hamilton原理得到频率特征矩阵,通过求解广义特征值求得自振频率及位移振型。随后,对所提出的方法的收敛性和精度进行讨论,与现有文献中的方法对比,该方法具有计算精度较高、收敛性好、收敛速度快等特点。讨论不同边界条件下截断数、跨数以及频率阶数之间的关系。最后通过工程中的实际案例说明该方法的实用性,与现有文献对比可知,其精度可达99.9%以上,由此验证了该方法的可靠性以及适用性。该方法易于通过编程实现快速计算,可为工程运用提供便捷有效的理论支撑。展开更多
Most iterative algorithms for eigenpair computation consist of two main steps:a subspace update(SU)step that generates bases for approximate eigenspaces,followed by a Rayleigh-Ritz(RR)projection step that extracts app...Most iterative algorithms for eigenpair computation consist of two main steps:a subspace update(SU)step that generates bases for approximate eigenspaces,followed by a Rayleigh-Ritz(RR)projection step that extracts approximate eigenpairs.So far the predominant methodology for the SU step is based on Krylov subspaces that builds orthonormal bases piece by piece in a sequential manner.In this work,we investigate block methods in the SU step that allow a higher level of concurrency than what is reachable by Krylov subspace methods.To achieve a competitive speed,we propose an augmented Rayleigh-Ritz(ARR)procedure.Combining this ARR procedure with a set of polynomial accelerators,as well as utilizing a few other techniques such as continuation and deflation,we construet a block algorithm designed to reduce the number of RR steps and elevate concurrency in the SU steps.Extensive computational experiments are conducted in C on a representative set of test problems to evaluate the performance of two variants of our algorithm.Numerical results,obtained on a many-core computer without explicit code parallelization,show that when computing a relatively large number of eigenpairs,the performance of our algorithms is competitive with that of several state-of-the-art eigensolvers.展开更多
文摘Based on the Sanders thin shell theory and Reddy's higher order shell theory,a general refined shell theory is developed for the analysis of stresses and deformations ofpneumatic radial tires of composite construction. For easy and efficient simulation of the tire apiecewise Rayleigh-Ritz technique is proposed and applied to get a numerical solution to thenonlinear structural problem. Bezier polynomials are used to approximate both the geometry of thesurface of reference and displacement fields of the tires. Stress distributions and deformations ofthe tires subjected to uniform inflation pressure are computed and discussed in details. Fromcomparison of the present results with the numerical predictions by 3D finite element method, it hasbeen shown that the present solution procedure is accurate and applicable to much complicatedtime-consuming nonlinear analysis for the high quality tire.
基金This work was supported by the "985"foundation of China(No.082200102).
文摘A rotor manipulation mechanism for micro unmanned helicopter utilizing the inertia and the elasticity of the rotor is introduced. The lagging motion equation of the rotor blades is established, and then the natural frequencies and mode shapes of the blade for the helicopter are studied by using beam characteristic orthogonal polynomials by the Rayleigh-Ritz method. The variation of natural frequencies with the speed of rotation and the mode shapes at different rotational speeds are plotted. The using of orthogonal polynomials for the bending shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any difficulties.
文摘Based on Reddy higher-order shear deformation theory, a general refined shell theory suitable to nonlinear analysis of tire structure is developed in this paper. The piece-wise Rayleigh-Ritz procedure and Bezier polynomials are applied to analyze deformations and stress distributions of the multlayered tire subjected to uniform inflation in detail. Furthermore, 3-dimension FEM analysis of laminated tire by standard software ANSYS is adopted to compare with the present model. It is demonstrated that both two solutions are in fairly good agreement.
文摘Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.
文摘板结构与其他构件的装配关系可用不同的边界条件进行模拟,然而针对不同边界条件的板结构进行动力学特性分析,目前缺乏统一的数学建模方法。以混合弹性边界条件下加筋、开孔的板类结构的横向振动为例,利用Rayleigh-Ritz法和模态叠加法求解矩形加筋多孔板在简谐激励下的动力学响应问题。采用将开孔板与加强筋沿交界面进行分离,结合改进的傅里叶级数设定开孔板的横向振动位移函数,利用不同刚度弹簧模拟混合弹性边界,推导加筋矩形开多孔板和边界弹簧系统的动能与势能,求解其在简谐激励下的动力学响应。经对比,理论计算结果与有限元(Finite Element Method,FEM)结果吻合良好。此外,用同样的方法分析不同孔尺寸对结构固有频率和响应的影响。研究发现,可通过改变加筋板的开孔形状、尺寸对结构的振动特性进行调整。研究成果可为混合弹性边界板结构动力分析提供一种新的技术途径,可以简化加筋开孔板结构动力分析的步骤。
文摘提出一种用于求解任意边界条件下带有任意集中质量的连续多跨梁的自振特性的方法。求解过程为:运用改进的傅里叶级数法(Improved Fourier Series Method,IFSM)确定梁的位移形函数,通过Rayleigh-Ritz法得到梁的拉格朗日方程,然后利用Hamilton原理得到频率特征矩阵,通过求解广义特征值求得自振频率及位移振型。随后,对所提出的方法的收敛性和精度进行讨论,与现有文献中的方法对比,该方法具有计算精度较高、收敛性好、收敛速度快等特点。讨论不同边界条件下截断数、跨数以及频率阶数之间的关系。最后通过工程中的实际案例说明该方法的实用性,与现有文献对比可知,其精度可达99.9%以上,由此验证了该方法的可靠性以及适用性。该方法易于通过编程实现快速计算,可为工程运用提供便捷有效的理论支撑。
文摘Most iterative algorithms for eigenpair computation consist of two main steps:a subspace update(SU)step that generates bases for approximate eigenspaces,followed by a Rayleigh-Ritz(RR)projection step that extracts approximate eigenpairs.So far the predominant methodology for the SU step is based on Krylov subspaces that builds orthonormal bases piece by piece in a sequential manner.In this work,we investigate block methods in the SU step that allow a higher level of concurrency than what is reachable by Krylov subspace methods.To achieve a competitive speed,we propose an augmented Rayleigh-Ritz(ARR)procedure.Combining this ARR procedure with a set of polynomial accelerators,as well as utilizing a few other techniques such as continuation and deflation,we construet a block algorithm designed to reduce the number of RR steps and elevate concurrency in the SU steps.Extensive computational experiments are conducted in C on a representative set of test problems to evaluate the performance of two variants of our algorithm.Numerical results,obtained on a many-core computer without explicit code parallelization,show that when computing a relatively large number of eigenpairs,the performance of our algorithms is competitive with that of several state-of-the-art eigensolvers.
