This paper deals with the existence of positive solutions of the equation u'+f(t, u)=0 with linear boundary conditions. We show the existence of at least one positive solution if / is neither superlinear nor subli...This paper deals with the existence of positive solutions of the equation u'+f(t, u)=0 with linear boundary conditions. We show the existence of at least one positive solution if / is neither superlinear nor sublinear on u by a simple application of a fixed point Theorem in cones.展开更多
Considering the dependent relationship among wave height,wind speed,and current velocity,we construct novel trivariate joint probability distributions via Archimedean copula functions.Total 30-year data of wave height...Considering the dependent relationship among wave height,wind speed,and current velocity,we construct novel trivariate joint probability distributions via Archimedean copula functions.Total 30-year data of wave height,wind speed,and current velocity in the Bohai Sea are hindcast and sampled for case study.Four kinds of distributions,namely,Gumbel distribution,lognormal distribution,Weibull distribution,and Pearson Type III distribution,are candidate models for marginal distributions of wave height,wind speed,and current velocity.The Pearson Type III distribution is selected as the optimal model.Bivariate and trivariate probability distributions of these environmental conditions are established based on four bivariate and trivariate Archimedean copulas,namely,Clayton,Frank,Gumbel-Hougaard,and Ali-Mikhail-Haq copulas.These joint probability models can maximize marginal information and the dependence among the three variables.The design return values of these three variables can be obtained by three methods:univariate probability,conditional probability,and joint probability.The joint return periods of different load combinations are estimated by the proposed models.Platform responses(including base shear,overturning moment,and deck displacement) are further calculated.For the same return period,the design values of wave height,wind speed,and current velocity obtained by the conditional and joint probability models are much smaller than those by univariate probability.Considering the dependence among variables,the multivariate probability distributions provide close design parameters to actual sea state for ocean platform design.展开更多
We propose a locking-free nonconforming finite element method to solve for the displacement variation in the pure displacement boundary value problem of planar linear elasticity. The method proposed in this paper is r...We propose a locking-free nonconforming finite element method to solve for the displacement variation in the pure displacement boundary value problem of planar linear elasticity. The method proposed in this paper is robust and optimal, in the sense that the convergence estimate in the energy is independent of the Lame parameter λ.展开更多
文摘This paper deals with the existence of positive solutions of the equation u'+f(t, u)=0 with linear boundary conditions. We show the existence of at least one positive solution if / is neither superlinear nor sublinear on u by a simple application of a fixed point Theorem in cones.
基金partially supported by the National Natural Science Foundation of China(No.51479183)the National Key Research and Development Program,China(Nos.2016YFC0302301 and 2016YFC0803401)the Fundamental Research Funds for the Central University(No.201564003)
文摘Considering the dependent relationship among wave height,wind speed,and current velocity,we construct novel trivariate joint probability distributions via Archimedean copula functions.Total 30-year data of wave height,wind speed,and current velocity in the Bohai Sea are hindcast and sampled for case study.Four kinds of distributions,namely,Gumbel distribution,lognormal distribution,Weibull distribution,and Pearson Type III distribution,are candidate models for marginal distributions of wave height,wind speed,and current velocity.The Pearson Type III distribution is selected as the optimal model.Bivariate and trivariate probability distributions of these environmental conditions are established based on four bivariate and trivariate Archimedean copulas,namely,Clayton,Frank,Gumbel-Hougaard,and Ali-Mikhail-Haq copulas.These joint probability models can maximize marginal information and the dependence among the three variables.The design return values of these three variables can be obtained by three methods:univariate probability,conditional probability,and joint probability.The joint return periods of different load combinations are estimated by the proposed models.Platform responses(including base shear,overturning moment,and deck displacement) are further calculated.For the same return period,the design values of wave height,wind speed,and current velocity obtained by the conditional and joint probability models are much smaller than those by univariate probability.Considering the dependence among variables,the multivariate probability distributions provide close design parameters to actual sea state for ocean platform design.
基金Supported by the NSF of the Education Henan(200510078005)
文摘We propose a locking-free nonconforming finite element method to solve for the displacement variation in the pure displacement boundary value problem of planar linear elasticity. The method proposed in this paper is robust and optimal, in the sense that the convergence estimate in the energy is independent of the Lame parameter λ.
