This paper proved the following three facts about the Lipschitz continuous property of Bernstein polynomials and Bezier nets defined on a triangle: suppose f(P) is a real valued function defined on a triangle T, (1) I...This paper proved the following three facts about the Lipschitz continuous property of Bernstein polynomials and Bezier nets defined on a triangle: suppose f(P) is a real valued function defined on a triangle T, (1) If f(P) satisfies Lipschitz continuous condition, i. e. f(P)∈Lip4α, then the corresponding Bernstein Bezier net fn∈LipAsecαψα, here ψ is the half of the largest angle of triangle T; (2) If Bernstein Bezier net fn∈ LipBα, then its elevation Bezier net Efn∈LipBα; and (3) If f(P)∈Lipαa, then the corresponding Bernstein polynomials Bn(f;P)∈LipAsecαψα, and the constant Asecαψ best in some sense.展开更多
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
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
基金Supported by NSF and SF of National Educational Committee
文摘This paper proved the following three facts about the Lipschitz continuous property of Bernstein polynomials and Bezier nets defined on a triangle: suppose f(P) is a real valued function defined on a triangle T, (1) If f(P) satisfies Lipschitz continuous condition, i. e. f(P)∈Lip4α, then the corresponding Bernstein Bezier net fn∈LipAsecαψα, here ψ is the half of the largest angle of triangle T; (2) If Bernstein Bezier net fn∈ LipBα, then its elevation Bezier net Efn∈LipBα; and (3) If f(P)∈Lipαa, then the corresponding Bernstein polynomials Bn(f;P)∈LipAsecαψα, and the constant Asecαψ best in some sense.
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.
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.
