A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack grow...A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate. Results are presented for two load conditions： remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained with the weight function method. It is demonstrated that the Wu- Carlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.展开更多
Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of contin...Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.展开更多
The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the bas...The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.展开更多
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is ort...Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.展开更多
An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolu...An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.展开更多
This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the correspon...This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).展开更多
The equation of stress intensity factors（SIF） of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the intern...The equation of stress intensity factors（SIF） of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method. The weight function formulas were worked out and can be used for all kinds of depth of cracks, rotating speed, material, size of thick-walled cylinder to calculate the stress intensity factors. The results indicated the validity and effectiveness of these formulas. Meanwhile, the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied. The studies are valuable to engineering application.展开更多
A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-ele...A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-electrode electromagnetic flowmeter. The two-dimensional distribution of the weight function of the electromagnetic flowmeter obtained was verified by the analytical solution. Three-dimensional distribution of the weight function was also presented in the paper. It can be employed to analyze the sensitivity and linearity of the electromagnetic flowmeter with non-uniform magnetic field, and even to assist the design of the excitation coil pair.展开更多
In this paper, the solution to the structure consisting of a bead and a board is given as a result of the application of the subregion function method which was suggested in ref. [1]. The same problem is also computed...In this paper, the solution to the structure consisting of a bead and a board is given as a result of the application of the subregion function method which was suggested in ref. [1]. The same problem is also computed with finite element method. The comparison between the two results shows that the application of the subregion function in the method of weighted residuals is practical and effective, especially for solving compound structures.展开更多
当直流母线电压发生扰动或者阻性负载和阻感负载出现突加和突卸时,中频电源易出现不稳定、鲁棒性差等现象,使得输出电压效果不理想。为此,提出数字信号处理技术(Digital Signal Process,DSP)应用下串联式中频电源鲁棒性能改进方法。在...当直流母线电压发生扰动或者阻性负载和阻感负载出现突加和突卸时,中频电源易出现不稳定、鲁棒性差等现象,使得输出电压效果不理想。为此,提出数字信号处理技术(Digital Signal Process,DSP)应用下串联式中频电源鲁棒性能改进方法。在明确基于DSP的串联式中频电源主电路拓扑结构,利用混合灵敏度方法建立中频电源控制器,选取合适的加权函数,提高中频电源的跟踪能力,消除其中不确定因素,实现鲁棒性能的提升。实验结果表明,经由所提方法控制后,串联式中频电源的输出电压波形整体较为稳定,没有发生较为突出的波动,整体电源总谐波失真值小,具有优秀的稳定性和鲁棒性。展开更多
频谱兼容波形利用多段离散寂静带宽合成大带宽,在满足带宽要求的同时有效对抗频域密集干扰。为了抑制频谱兼容波形的峰值旁瓣水平,提出一种低峰值旁瓣频谱兼容波形设计方案。所提方案综合考虑波形的自相关峰值旁瓣性能和抗干扰性能,构...频谱兼容波形利用多段离散寂静带宽合成大带宽,在满足带宽要求的同时有效对抗频域密集干扰。为了抑制频谱兼容波形的峰值旁瓣水平,提出一种低峰值旁瓣频谱兼容波形设计方案。所提方案综合考虑波形的自相关峰值旁瓣性能和抗干扰性能,构建加权目标函数。在波形恒模约束下,该问题为非确定多项式难(non-deterministic polynomial-hard,NP-hard)问题。为此,首先利用指数对数平滑技术逼近目标函数,进而提出基于快速傅里叶变换的共轭梯度(conjugate gradient method based on fast Fourier transformation,CGFFT)法求解该问题。此外,波形设计中需要根据性能指标要求选择合适的加权值,为此提出一种加权值自适应确定方法,最后通过数值仿真验证了所提方法的有效性。展开更多
The multiple patterns of internal solitary wave interactions(ISWI)are a complex oceanic phenomenon.Satellite remote sensing techniques indirectly detect these ISWI,but do not provide information on their detailed stru...The multiple patterns of internal solitary wave interactions(ISWI)are a complex oceanic phenomenon.Satellite remote sensing techniques indirectly detect these ISWI,but do not provide information on their detailed structure and dynamics.Recently,the authors considered a three-layer fluid with shear flow and developed a(2+1)Kadomtsev-Petviashvili(KP)model that is capable of describing five types of oceanic ISWI,including O-type,P-type,TO-type,TP-type,and Y-shaped.Deep learning models,particularly physics-informed neural networks(PINN),are widely used in the field of fluids and internal solitary waves.However,the authors find that the amplitude of internal solitary waves is much smaller than the wavelength and the ISWI occur at relatively large spatial scales,and these characteristics lead to an imbalance in the loss function of the PINN model.To solve this problem,the authors introduce two weighted loss function methods,the fixed weighing and the adaptive weighting methods,to improve the PINN model.This successfully simulated the detailed structure and dynamics of ISWI,with simulation results corresponding to the satellite images.In particular,the adaptive weighting method can automatically update the weights of different terms in the loss function and outperforms the fixed weighting method in terms of generalization ability.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11402249)
文摘A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate. Results are presented for two load conditions： remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained with the weight function method. It is demonstrated that the Wu- Carlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.
文摘Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.
文摘The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.
基金theNationalNaturalScienceFoundationofChina (No .50 40 90 0 8)
文摘Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.
文摘An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.
文摘This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).
文摘The equation of stress intensity factors（SIF） of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method. The weight function formulas were worked out and can be used for all kinds of depth of cracks, rotating speed, material, size of thick-walled cylinder to calculate the stress intensity factors. The results indicated the validity and effectiveness of these formulas. Meanwhile, the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied. The studies are valuable to engineering application.
基金Supported by Chinese National Programs for High Technology Research and Development(2008AA042207)
文摘A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-electrode electromagnetic flowmeter. The two-dimensional distribution of the weight function of the electromagnetic flowmeter obtained was verified by the analytical solution. Three-dimensional distribution of the weight function was also presented in the paper. It can be employed to analyze the sensitivity and linearity of the electromagnetic flowmeter with non-uniform magnetic field, and even to assist the design of the excitation coil pair.
文摘In this paper, the solution to the structure consisting of a bead and a board is given as a result of the application of the subregion function method which was suggested in ref. [1]. The same problem is also computed with finite element method. The comparison between the two results shows that the application of the subregion function in the method of weighted residuals is practical and effective, especially for solving compound structures.
文摘当直流母线电压发生扰动或者阻性负载和阻感负载出现突加和突卸时,中频电源易出现不稳定、鲁棒性差等现象,使得输出电压效果不理想。为此,提出数字信号处理技术(Digital Signal Process,DSP)应用下串联式中频电源鲁棒性能改进方法。在明确基于DSP的串联式中频电源主电路拓扑结构,利用混合灵敏度方法建立中频电源控制器,选取合适的加权函数,提高中频电源的跟踪能力,消除其中不确定因素,实现鲁棒性能的提升。实验结果表明,经由所提方法控制后,串联式中频电源的输出电压波形整体较为稳定,没有发生较为突出的波动,整体电源总谐波失真值小,具有优秀的稳定性和鲁棒性。
文摘频谱兼容波形利用多段离散寂静带宽合成大带宽,在满足带宽要求的同时有效对抗频域密集干扰。为了抑制频谱兼容波形的峰值旁瓣水平,提出一种低峰值旁瓣频谱兼容波形设计方案。所提方案综合考虑波形的自相关峰值旁瓣性能和抗干扰性能,构建加权目标函数。在波形恒模约束下,该问题为非确定多项式难(non-deterministic polynomial-hard,NP-hard)问题。为此,首先利用指数对数平滑技术逼近目标函数,进而提出基于快速傅里叶变换的共轭梯度(conjugate gradient method based on fast Fourier transformation,CGFFT)法求解该问题。此外,波形设计中需要根据性能指标要求选择合适的加权值,为此提出一种加权值自适应确定方法,最后通过数值仿真验证了所提方法的有效性。
基金supported by the National Natural Science Foundation of China under Grant Nos.12275085,12235007,and 12175069Science and Technology Commission of Shanghai Municipality under Grant Nos.21JC1402500 and 22DZ2229014.
文摘The multiple patterns of internal solitary wave interactions(ISWI)are a complex oceanic phenomenon.Satellite remote sensing techniques indirectly detect these ISWI,but do not provide information on their detailed structure and dynamics.Recently,the authors considered a three-layer fluid with shear flow and developed a(2+1)Kadomtsev-Petviashvili(KP)model that is capable of describing five types of oceanic ISWI,including O-type,P-type,TO-type,TP-type,and Y-shaped.Deep learning models,particularly physics-informed neural networks(PINN),are widely used in the field of fluids and internal solitary waves.However,the authors find that the amplitude of internal solitary waves is much smaller than the wavelength and the ISWI occur at relatively large spatial scales,and these characteristics lead to an imbalance in the loss function of the PINN model.To solve this problem,the authors introduce two weighted loss function methods,the fixed weighing and the adaptive weighting methods,to improve the PINN model.This successfully simulated the detailed structure and dynamics of ISWI,with simulation results corresponding to the satellite images.In particular,the adaptive weighting method can automatically update the weights of different terms in the loss function and outperforms the fixed weighting method in terms of generalization ability.
